Reddit mentions: The best science & math books

>Not familiar as I probably ought to be. I know that there were other homo species -possibly at the same time as humans. I think I heard something about interbreeding at some point, but maybe that was just speculation?

To be honest, I'm not exactly an expert on the specifics. However, Wikipedia provides as always - If the article and the numerous citations are to be believed, they're considered separate species as mitochondria genetic data (that I could explain further if you like) shows little significant breeding. However, there is indeed some evidence of limited interbreeding.

>This is fascinating stuff!

I'm glad you like it!

>To clarify: do all the primates share the same mutation which is different from the mutation in other creatures, ex. guinea pigs?'

Precisely! Mind you, I believe there are a few changes which have accumulated since divergence (since if they don't need the gene once it's "off", further mutations won't be selected against), but the crucial changes are indeed the same within primates - and those within guinea pigs are the same within guinea pigs and their nearby relatives (I believe), but different from those from simians. Amusingly, because mutations occur at a generally steady rate, the number of further divergences between the pseudogenes (no-longer-functional genes which resemble working copies in other organisms) in different species will give hints at how long ago those species had a common ancestor (this, and related calculations, are termed the "genetic clock").

Nifty, isn't it?

>I guess I don't see why it would be demeaning to be patterned after other homo species which were adapted to the environment we would inhabit. Maybe I'm way off here, but it seems like the case for common ancestry could also point to a common creator. (obviously it is outside the bounds of science to consider that possibility, but philosophically, it might have merit?)

I have indeed heard that before; the suggestion of a common creator as opposed to common descent is a fairly common suggestion, pardon the pun. The typical arguments against fall first to traits which can be considered "poor design" in pure engineering terms, even if they're traits that are now needed. I can point to the genetic baggage of the human eye compared to that of the cephelopod (nerve fibers over vs. under the retina), or the human back (not great for walking upright), or further traits along those lines which suggest that we're still closer to our origins. Indeed, we can also look at things like the pseudogene involved with vitamin C above as unnecessary addons; genetic artifacts which hint at our descent.

While this additional argument, I will grant, is better at addressing general creation then special human creation, we can also look at repeated motifs. For example, the same bones that form our hand also form a bird's wing, a whale's flipper, a dog's paw, a horse's hoof, and all the other mammalian, reptile, and avian forelimbs - though sometimes you need to go to the embryo before you see the similarity. When taken alone, that may suggest either evolution or design; it would make sense for a creator to reuse traits. It becomes more stark when you consider examples that should be similar - for example, the wings of the bat, bird, and pterodactyl, despite using the same bones, have vastly different structures, despite all being used for the same purpose (that is, flight).

The way that my evolutionary biology professor phrased this is that "design can explain this, but cannot predict it; evolution both explains and predicts." This idea - that natural observations may be explained or excused (begging your pardon) in a creation model, but are what are expected from an evolutionary model - is the major point I wish to make in this regard. And, I shall admit, perhaps as close as I can get to "disproving" special creation; it tends to approach unfalsifiability, if I understand it correctly.

>If I recall correctly, this is the position of Francis Collins / BioLogos. It's possible, but I have a few concerns. The first being that I think animals do have souls. If that's correct, ensoulment doesn't help make sense of the theology.

Yup; ensoulment as special is less compatible in that case.

>It would also mean that (at least at some point) there were other creatures who were genetically equal to human beings, but didn't have souls. Cue slave trade and nazi propaganda -they're human, but they aren't people. It would have been possible (probable?) that ensouled humans would breed with the soulless humans -and that just seems . . . squicky.

Point taken; even if you were to claim ensoulment for all humans existing at a specific point and thereafter, there can be...negative connotations.

>So, for now, it's a possibility, but it seems to be more problematic than special creation.

To be perfectly frank, I'm not really equipped to argue otherwise. As an atheist, my tendency is to end up arguing against ensoulment, as it's not something we can really draw a line at either. Still, I figured I'd put it out there; I'm a little delighted at your dissection of it honestly, as you brought up things I'd not yet considered.

>Like I said, the genetics is fascinating, and I am naive to much of it. Short of becoming a geneticist, could you recommend a good book on the subject of human genetics and common descent? I took basic genetics in college, so I was able to follow the discussion about chromosomes, telomeres, etc. But I would like to know more about the discoveries that have been made.

Oooh, that's a rough question. Don't get me wrong, it's a wonderful question, but I rarely read books aimed at laymen dealing with my specialty; most of my information comes from text books, papers, and profs, if you take my meaning. Which in the end is a way for me to provide my disclaimer: I can provide recommendations, but I've generally not read them myself; sorry.

Having said that, I'm not about to discourage your curiosity - indeed, I cannot laud it highly enough! - and so I shall do what I can:

• Why Evolution is True is the one I generally hear the best things about; due to the possible audience, it is partially written as a refutation of intelligent design, but it also gives a lovely primer on evolutionary science - and compared to some of Dawkins's texts, it's more focused on the evidence.
  
• I have a copy of Genome: The Autobiography of a Species in 23 Chapters on my bedside table right now - largely unread, I'm afraid. Basically, it takes a peek at one gene from each of our chromosomes and explores its relevance and its evolutionary history. It's by no means comprehensive; we have hundreds of thousands of genes, and it looks at twenty-three. None the less, It's been an interesting read thus far.
  
• Similarly, Your Inner Fish explores the human form, and where it comes from; it looks at various structures in the human body and draws evolutionary parallels; this one is more heavily focused on common descent in relation to humans.
  
  I think I'll hold off there for the moment. The latter two are focused more on humans, while the former is about evolution in general. I'm sure there are more books I could recommend - Dawkin's The Greatest Show on Earth has been lauded, for example. I tried to stick with texts which were at a slightly higher level, not merely addressing the basics but delving a little deeper, as you noted you have a measure of familiarity already, and those which were related to humans. I hope they help!
  
  It's not an alternative to books, but Wikipedia does have a fair article on the topic (which I linked near the very top as well). And believe it or not, I do enjoy this sort of thing; you are more then welcome to ask more questions if and when they occur to you.

This is a compilation of what I gathered from reading on the internet about self-learning higher maths, I haven't come close to reading all this books or watching all this lectures, still I hope it helps you.

General Stuff:
The books here deal with large parts of mathematics and are good to guide you through it all, but I recommend supplementing them with other books.

1. Mathematics: A very Short Introduction : A very good book, but also very short book about mathematics by Timothy Gowers, a Field medalist and overall awesome guy, gives you a feelling for what math is all about.
   
   
2. Concepts of Modern Mathematics: A really interesting book by Ian Stewart, it has more topics than the last book, it is also bigger though less formal than Gower's book. A gem.
   
   
3. What is Mathematics?: A classic that has aged well, it's more textbook like compared to the others, which is good because the best way to learn mathematics is by doing it. Read it.
   
   
4. An Infinitely Large Napkin: This is the most modern book in this list, it delves into a huge number of areas in mathematics and I don't think it should be read as a standalone, rather it should guide you through your studies.
   
   
5. The Princeton Companion to Mathematics: A humongous book detailing many areas of mathematics, its history and some interesting essays. Another book that should be read through your life.
   
   
6. Mathematical Discussions: Gowers taking a look at many interesting points along some mathematical fields.
   
   
7. Technion Linear Algebra Course - The first 14 lectures: Gets you wet in a few branches of maths.
   
   Linear Algebra: An extremelly versatile branch of Mathematics that can be applied to almost anything, also the first "real math" class in most universities.
   
   
8. Linear Algebra Done Right: A pretty nice book to learn from, not as computational heavy as other Linear Algebra texts.
   
   
9. Linear Algebra: A book with a rather different approach compared to LADR, if you have time it would be interesting to use both. Also it delves into more topics than LADR.
   
   
10. Calculus Vol II : Apostols' beautiful book, deals with a lot of lin algebra and complements the other 2 books by having many exercises. Also it doubles as a advanced calculus book.
    
    
11. Khan Academy: Has a nice beginning LinAlg course.
    
    
12. Technion Linear Algebra Course: A really good linear algebra course, teaches it in a marvelous mathy way, instead of the engineering-driven things you find online.
    
    
13. 3Blue1Brown's Essence of Linear Algebra: Extra material, useful to get more intuition, beautifully done.
    
    Calculus: The first mathematics course in most Colleges, deals with how functions change and has many applications, besides it's a doorway to Analysis.
    
    
14. Calculus: Tom Apostol's Calculus is a rigor-heavy book with an unorthodox order of topics and many exercises, so it is a baptism by fire. Really worth it if you have the time and energy to finish. It covers single variable and some multi-variable.
    
    
15. Calculus: Spivak's Calculus is also rigor-heavy by Calculus books standards, also worth it.
    
    
16. Calculus Vol II : Apostols' beautiful book, deals with many topics, finishing up the multivariable part, teaching a bunch of linalg and adding probability to the mix in the end.
    
    
17. MIT OCW: Many good lectures, including one course on single variable and another in multivariable calculus.
    
    Real Analysis: More formalized calculus and math in general, one of the building blocks of modern mathematics.
    
    
18. Principle of Mathematical Analysis: Rudin's classic, still used by many. Has pretty much everything you will need to dive in.
    
    
19. Analysis I and Analysis II: Two marvelous books by Terence Tao, more problem-solving oriented.
    
    
20. Harvey Mudd's Analysis lectures: Some of the few lectures on Real Analysis you can find online.
    
    Abstract Algebra: One of the most important, and in my opinion fun, subjects in mathematics. Deals with algebraic structures, which are roughly sets with operations and properties of this operations.
    
    
21. Abstract Algebra: Dummit and Foote's book, recommended by many and used in lots of courses, is pretty much an encyclopedia, containing many facts and theorems about structures.
    
    
22. Harvard's Abstract Algebra Course: A great course on Abstract Algebra that uses D&F as its textbook, really worth your time.
    
    
23. Algebra: Chapter 0: I haven't used this book yet, though from what I gathered it is both a category theory book and an Algebra book, or rather it is a very different way of teaching Algebra. Many say it's worth it, others (half-jokingly I guess?) accuse it of being abstract nonsense. Probably better used after learning from the D&F and Harvard's course.
    
    There are many other beautiful fields in math full of online resources, like Number Theory and Combinatorics, that I would like to put recommendations here, but it is quite late where I live and I learned those in weirder ways (through olympiad classes and problems), so I don't think I can help you with them, still you should do some research on this sub to get good recommendations on this topics and use the General books as guides.

> I assume I ought to check it out after my discrete math class? Or does CLRS teach the proofs as if the reader has no background knowledge about proofs?

Sadly it does not teach proofs. You will need to substitute this on your own. You don't need deep proof knowledge, but just the ability to follow a proof, even if it means you have to sit there for 2-3 minutes on one sentence just to understand it (which becomes much easier as you do more of this).

> We didn't do proof by induction, though I have learned a small (very small) amount of it through reading a book called Essentials of Computer Programs by Haynes, Wand, and Friedman. But I don't really count that as "learning it," more so being exposed to the idea of it.

This is better than nothing, however I recommend you get very comfortable with it because it's a cornerstone of proofs. For example, can you prove that there are less than 2 ^ (h+1) nodes in any perfect binary tree of height h? Things like that.

> We did go over Delta Epsilon, but nothing in great detail (unless you count things like finding the delta or epsilon in a certain equation). If it helps give you a better understanding, the curriculum consisted of things like derivatives, integrals, optimization, related rates, rotating a graph around the x/y-axis or a line, linearization, Newton's Method, and a few others I'm forgetting right now. Though we never proved why any of it could work, we were just taught the material. Which I don't disagree with since, given the fact that it's a general Calc 1 course, so some if not most students aren't going to be using the proofs for such topics later in life.

That's okay, you will need to be able to do calculations too. There are people who spend all their time doing proofs and then for some odd reason can't even do basic integration. Being able to do both is important. Plus this knowledge will make dealing with other math concepts easier. It's good.

> I can completely understand that. I myself want to be as prepared as possible, even if it means going out and learning about proofs of Calc 1 topics if it helps me become a better computer scientist. I just hope that's a last resort, and my uni can at least provide foundation for such areas.

In my honest opinion, a lot of people put too much weight on calculus. Computer science is very much in line with discrete math. The areas where it gets more 'real numbery' is when you get into numerical methods, machine learning, graphics, etc. Anything related to theory of computation will probably be discrete math. If your goal is to get good at data structures and algorithms, most of your time will be spent on discrete topics. You don't need to be a discrete math genius to do this stuff, all you need is some discrete math, some calc (which you already have), induction, and the rest you can pick up as you go.

If you want to be the best you can be, I recommend trying that book I linked first to get your feet wet. After that, try CLRS. Then try TAOCP.

Do not however throw away the practical side of CS if you want to get into industry. Reading TAOCP would make you really good but it doesn't mean shit if you can't program. Even the author of TAOCP, Knuth, says being polarized completely one way (all theory, or all programming, and none of the other) is not good.

> From reading ahead in your post, is Skiena's Manual something worth investing to hone my skills in topics like proof skills? I'll probably pick it up eventually since I've heard nothing but good things about it, but still. Does Skiena's Manual teach proofing skills to those without them/are not good at them? Or is there a separate book for that?

You could, at worst you will get a deeper understanding of the data structure and how to implement them if the proof goes over your head... which is okay, no one on this planet starts off good at this stuff. After you do this for a year you will be able to probably sit down and casually read the proofs in these books (or that is how long it took me).

Overall his book is the best because it's the most fun to read (CLRS is sadly dry), and TAOCP may be overkill right now. There are probably other good books too.

> I guess going off of that, does one need a certain background to be able to do proofs correctly/successfully, such as having completed a certain level of math or having a certain mindset?

This is developed over time. You will struggle... trust me. There will be days where you feel like you're useless but it continues growing over a month. Try to do a proof a day and give yourself 20-30 minutes to think about things. Don't try insane stuff cause you'll only demoralize yourself. If you want a good start, this is a book a lot of myself and my classmates started on. If you've never done formal proofs before, you will experience exactly what I said about choking on these problems. Don't give up. I don't know anyone who had never done proofs before and didn't struggle like mad for the first and second chapter.

> I mean, I like the material I'm learning and doing programming, and I think I'd like to do at least be above average (as evident by the fact that I'm going out of my way to study ahead and read in my free time). But I have no clue if I'll like discrete math/proving things, or if TAOCP will be right for me.

Most people end up having to do proofs and are forced to because of their curriculum. They would struggle and quit otherwise, but because they have to know it they go ahead with it anyways. After their hard work they realize how important it is, but this is not something you can experience until you get there.

I would say if you have classes coming up that deal with proofs, let them teach you it and enjoy the vacation. If you really want to get a head start, learning proofs will put you on par with top university courses. For example at mine, you were doing proofs from the very beginning, and pretty much all the core courses are proofs. I realized you can tell the quality of a a university by how much proofs are in their curriculum. Any that is about programming or just doing number crunching is literally missing the whole point of Computer Science.

Because of all the proofs I have done, eventually you learn forever how a data structure works and why, and can use it to solve other problems. This is something that my non-CS programmers do not understand and I will always absolutely crush them on (novel thinking) because its what a proper CS degree teaches you how to do.

There is a lot I could talk about here, but maybe such discussions are better left for PM.

> Can you recommend some eyepieces which I should get?

Well, for starters you'll want to replace that 9mm with something better, and you'll want a planetary eyepiece. For planetary a 5-6mm eyepiece will work nicely. As for which one in particular -- whichever you can afford from what I linked :)

5-6mm planetaries:

• TS 5mm HR Planetary
  
• Omegon 5mm ED Flatfield
  
• Celestron X-Cel LX 5mm
  
• Omegon Ultrawide 6mm
  
  9mm replacements:
  
  
• William Optics SWAN 9mm
  
• Omegon Ultrawide 9mm
  
  Later on you might want to get something in the mid range, like 15-20 mm, but honestly, pretty much anything will work here. Higher AFoV (degrees) is preferred over longer focal length in most cases.
  
  And finally at some point you'll want to replace the 30mm 2" one. I would highly recommend the Explore Scientific 30mm 82° one, but it's definitely nowhere near being important purchase, your kit 30mm will serve you well. Alternatively, a William Optics SWAN 33mm eyepiece is another good choice, but it's barely different from your current one, though the FoV is still larger. But for your scope 30-35mm eyepiece is the limit, don't go with larger ones, you'll be losing light from too large exit pupil.
  
  As it is with most astronomy stuff, higher quality stuff will cost you more.
  
  > Where should I spend more money? and what sort of filters should I get? I need one for the Moon atleast dont I?
  
  Priority list:
  
  

1. Telescope -- you cannot upgrade aperture, everything else can be changed later. But the 10" you chose will be a superb starting instrument, congratulations :)
   
2. "Turn Left at Orion" or "Nightwatch" -- your essential night sky guides! Stellarium for the cloudy nights and lazy days :)
   
3. Missing eyepiece ranges -- as I have mentioned above. Planetary is a must-have if you want to view planets (you do want, trust me). Then look into either mid-range plug, or the 9mm replacement, depending on how well the kit 9mm performs for you. If you're happy with it, stick with it. I'd order the planetary of choice along with scope, and wait for the rest until you've got chance to field test the setup a couple of times.
   
4. Filters -- Yes, Moon filter is a must with this telescope, however I would highly recommend a much more versatile Variable Polarizing Filter instead. The 2" is more expensive, however, the low-magnification is where you need it the most. And 2" filters should be able to be mounted on the 2"-to-1.25" adapters to work with 1.25" eyepieces. Alternative is to wear your sunglasses at night. Another great choice is a narrowband UHC filter, like this one from Baader. It will also help out against the light pollution. On the other hand, I would recommend against spending money on a wideband "light pollution" filter, as in my experience I haven't found them to be of any use whatsoever.
   
5. Telrad/Rigel QuickFinder -- I've already covered those in my previous post.
   
6. Dew heaters -- self-explanatory. If dewing up of eyepieces and/or mirrors becomes a problem, and you have no hairdryer at hand, there's your more portable (but more expensive) solution.
   
7. Binoculars -- surprisingly good accessory to telescope, and on their own! Wide field of view and super high portability makes them excellent tool for quick stargazing, observing of objects otherwise too large to fit into telescope's view, and useful for finding a good star-hopping route to the next faint fuzzy of your choice! Also useful for travelling, birdwatching, and other daytime activities. A simple but good set of 7x50/10x50/8x42 binoculars will set you back like 80-150€ tops, unless you want something of highest quality. But once again, entirely optional!

Friend asked for a similar list a while ago and I put this together. Would love to see people thoughts/feedback.

Very High Level Introductions:

• Mr. Tompkins in Paperback
  
  • A super fast read that spends less time looking at the "how" but focused instead on the ramifications and impacts. Covers both GR as well as QM but is very high level with both of them. Avoids getting into the details and explaining the why.
    
    
• Einstein's Relativity and the Quantum Revolution (Great Courses lecture)
  
  • This is a great intro to the field of non-classical physics. This walks through GR and QM in a very approachable fashion. More "nuts and bolts" than Mr. Tompkins but longer/more detailed at the same time.
    
    
    Deeper Pop-sci Dives (probably in this order):
    
    
• Quantum Theory: A Very Brief Introduction
  
  • Great introduction to QM. Doesn't really touch on QFT (which is a good thing at this point) and spends a great deal of time (compared to other texts) discussing the nature of QM interpretation and the challenges around that topic.
    
• The Lightness of Being: Mass, Ether, and the Unification of Forces
  
  • Now we're starting to get into the good stuff. QFT begins to come to the forefront. This book starts to dive into explaining some of the macro elements we see as explained by QM forces. A large part of the book is spent on symmetries and where a proton/nucleon's gluon binding mass comes from (a.k.a. ~95% of the mass we personally experience).
    
• The Higgs Boson and Beyond (Great Courses lecture)
  
  • Great lecture done by Sean Carroll around the time the Higgs boson's discovery was announced. It's a good combination of what role the Higgs plays in particle physics, why it's important and what's next. Also spends a little bit of time discussing how colliders like the LHC work.
    
• Mysteries of Modern Physics: Time (Great Courses lecture)
  
  • Not really heavy on QM at all, however I think it does best to do this lecture after having a bit of the physics under your belt first. The odd nature of time symmetry in the fundamental forces and what that means with regards to our understanding of time as we experience it is more impactful with the additional knowledge (but, like I said, not absolutely required).
    
• Deep Down Things: The Breathtaking Beauty of Particle Physics
  
  • This is not a mathematical approach like "A Most Incomprehensible Thing" are but it's subject matter is more advanced and the resulting math (at least) an order of magnitude harder (so it's a good thing it's skipped). This is a "high level deep dive" (whatever that means) into QFT though and so discussion of pure abstract math is a huge focus. Lie groups, spontaneous symmetry breaking, internal symmetry spaces etc. are covered.
    
• The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory
  
  • This is your desert after working through everything above. Had to include something about string theory here. Not a technical book at all but best to be familiar with QM concepts before diving in.
    
    Blending the line between pop-sci and mathematical (these books are not meant to be read and put away but instead read, re-read and pondered):
    
    
• A Most Incomprehensible Thing: Intro to GR
  
  • Sorry, this is GR specific and nothing to do with QM directly. However I think it's a great book acting as an introduction. Definitely don't go audible/kindle. Get the hard copy. Lots of equations. Tensor calculus, Lorentz transforms, Einstein field equations, etc. While it isn't a rigorous textbook it is, at it's core, a mathematics based description not analogies. Falls apart at the end, after all, it can't be rigorous and accessible at the same time, but still well worth the read.
    
• The Theoretical Minimum: What You Need to Know to Start Doing Physics
  
  • Not QM at all. However it is a great introduction to using math as a tool for describing our reality and since it's using it to describe classical mechanics you get to employ all of your classical intuition that you've worked on your entire life. This means you can focus on the idea of using math as a descriptive tool and not as a tool to inform your intuition. Which then would lead us to...
    
• Quantum Mechanics: The Theoretical Minimum
  
  • Great introduction that uses math in a descriptive way AND to inform our intuition.
    
• The Road to Reality: A Complete Guide to the Laws of the Universe
  
  • Incredible book. I think the best way to describe this book is a massive guidebook. You probably won't be able to get through each of the topics based solely on the information presented in the book but the book gives you the tools and knowledge to ask the right questions (which, frankly, as anybody familiar with the topic knows, is actually the hardest part). You're going to be knocking your head against a brick wall plenty with this book. But that's ok, the feeling when the brick wall finally succumbs to your repeated headbutts makes it all worth while.

You are in a very special position right now where many interesing fields of mathematics are suddenly accessible to you. There are many directions you could head. If your experience is limited to calculus, some of these may look very strange indeed, and perhaps that is enticing. That was certainly the case for me.

Here are a few subject areas in which you may be interested. I'll link you to Dover books on the topics, which are always cheap and generally good.

• The Nature and Power of Mathematics, Donald M. Davis. This book seems to be a survey of some history of mathematics and various modern topics. Check out the table of contents to get an idea. You'll notice a few of the subjects in the list below. It seems like this would be a good buy if you want to taste a few different subjects to see what pleases your palate.
  
  
• Introduction to Graph Theory, Richard J. Trudeau. Check out the Wikipedia entry on graph theory and the one defining graphs to get an idea what the field is about and some history. The reviews on Amazon for this book lead me to believe it would be a perfect match for an interested high school student.
  
  
• Game Theory: A Nontechnical Introduction, Morton D. Davis. Game theory is a very interesting field with broad applications--check out the wiki. This book seems to be written at a level where you would find it very accessible. The actual field uses some heavy math but this seems to give a good introduction.
  
  
• An Introduction to Information Theory, John R. Pierce. This is a light-on-the-maths introduction to a relatively young field of mathematics/computer science which concerns itself with the problems of storing and communicating data. Check out the wiki for some background.
  
  
• Lady Luck: The Theory of Probability, Warren Weaver. This book seems to be a good introduction to probability and covers a lot of important ideas, especially in the later chapters. Seems to be a good match to a high school level.
  
  
• Elementary Number Theory, Underwood Dudley. Number theory is a rich field concerned with properties of numbers. Check out its Wikipedia entry. I own this book and am reading through it like a novel--I love it! The exposition is so clear and thorough you'd think you were sitting in a lecture with a great professor, and the exercises are incredible. The author asks questions in such a way that, after answering them, you can't help but generalize your answers to larger problems. This book really teaches you to think mathematically.
  
  
• A Book of Abstract Algebra, Charles C. Pinter. Abstract algebra formalizes and generalizes the basic rules you know about algebra: commutativity, associativity, inverses of numbers, the distributive law, etc. It turns out that considering these concepts from an abstract standpoint leads to complex structures with very interesting properties. The field is HUGE and seems to bleed into every other field of mathematics in one way or another, revealing its power. I also own this book and it is similarly awesome. The exposition sets you up to expect the definitions before they are given, so the material really does proceed naturally.
  
  
• Introduction to Analysis, Maxwell Rosenlicht. Analysis is essentially the foundations and expansion of calculus. It is an amazing subject which no math student should ignore. Its study generally requires a great deal of time and effort; some students would benefit more from a guided class than from self-study.
  
  
• Principles of Statistics, M. G. Bulmer. In a few words, statistics is the marriage between probability and analysis (calculus). The wiki article explains the context and interpretation of the subject but doesn't seem to give much information on what the math involved is like. This book seems like it would be best read after you are familiar with probability, say from Weaver's book linked above.
  
  
• I have to second sellphone's recommendation of Naive Set Theory by Paul Halmos. It's one of my favorite math books and gives an amazing introduction to the field. It's short and to the point--almost a haiku on the subject.
  
  
• Continued Fractions, A. Ya. Khinchin. Take a look at the wiki for continued fractions. The book is definitely terse at times but it is rewarding; Khinchin is a master of the subject. One review states that, "although the book is rich with insight and information, Khinchin stays one nautical mile ahead of the reader at all times." Another review recommends Carl D. Olds' book on the subject as a better introduction.
  
  Basically, don't limit yourself to the track you see before you. Explore and enjoy.

My main hobby is reading textbooks, so I decided to go beyond the scope of the question posed. I took a look at what I have on my shelves in order to recommend particularly good or standard books that I think could characterize large portions of an undergraduate degree and perhaps the beginnings of a graduate degree in the main fields that interest me, plus some personal favorites.

Neuroscience: Theoretical Neuroscience is a good book for the field of that name, though it does require background knowledge in neuroscience (for which, as others mentioned, Kandel's text is excellent, not to mention that it alone can cover the majority of an undergraduate degree in neuroscience if corequisite classes such as biology and chemistry are momentarily ignored) and in differential equations. Neurobiology of Learning and Memory and Cognitive Neuroscience and Neuropsychology were used in my classes on cognition and learning/memory and I enjoyed both; though they tend to choose breadth over depth, all references are research papers and thus one can easily choose to go more in depth in any relevant topics by consulting these books' bibliographies.

General chemistry, organic chemistry/synthesis: I liked Linus Pauling's General Chemistry more than whatever my school gave us for general chemistry. I liked this undergraduate organic chemistry book, though I should say that I have little exposure to other organic chemistry books, and I found Protective Groups in Organic Synthesis to be very informative and useful. Unfortunately, I didn't have time to take instrumental/analytical/inorganic/physical chemistry and so have no idea what to recommend there.

Biochemistry: Lehninger is the standard text, though it's rather expensive. I have limited exposure here.

Mathematics: When I was younger (i.e. before having learned calculus), I found the four-volume The World of Mathematics great for introducing me to a lot of new concepts and branches of mathematics and for inspiring interest; I would strongly recommend this collection to anyone interested in mathematics and especially to people considering choosing to major in math as an undergrad. I found the trio of Spivak's Calculus (which Amazon says is now unfortunately out of print), Stewart's Calculus (standard text), and Kline's Calculus: An Intuitive and Physical Approach to be a good combination of rigor, practical application, and physical intuition, respectively, for calculus. My school used Marsden and Hoffman's Elementary Classical Analysis for introductory analysis (which is the field that develops and proves the calculus taught in high school), but I liked Rudin's Principles of Mathematical Analysis (nicknamed "Baby Rudin") better. I haven't worked my way though Munkres' Topology yet, but it's great so far and is often recommended as a standard beginning toplogy text. I haven't found books on differential equations or on linear algebra that I've really liked. I randomly came across Quine's Set Theory and its Logic, which I thought was an excellent introduction to set theory. Russell and Whitehead's Principia Mathematica is a very famous text, but I haven't gotten hold of a copy yet. Lang's Algebra is an excellent abstract algebra textbook, though it's rather sophisticated and I've gotten through only a small portion of it as I don't plan on getting a PhD in that subject.

Computer Science: For artificial intelligence and related areas, Russell and Norvig's Artificial Intelligence: A Modern Approach's text is a standard and good text, and I also liked Introduction to Information Retrieval (which is available online by chapter and entirely). For processor design, I found Computer Organization and Design to be a good introduction. I don't have any recommendations for specific programming languages as I find self-teaching to be most important there, nor do I know of any data structures books that I found to be memorable (not that I've really looked, given the wealth of information online). Knuth's The Art of Computer Programming is considered to be a gold standard text for algorithms, but I haven't secured a copy yet.

Physics: For basic undergraduate physics (mechanics, e&m, and a smattering of other subjects), I liked Fundamentals of Physics. I liked Rindler's Essential Relativity and Messiah's Quantum Mechanics much better than whatever books my school used. I appreciated the exposition and style of Rindler's text. I understand that some of the later chapters of Messiah's text are now obsolete, but the rest of the book is good enough for you to not need to reference many other books. I have little exposure to books on other areas of physics and am sure that there are many others in this subreddit that can give excellent recommendations.

Other: I liked Early Theories of the Universe to be good light historical reading. I also think that everyone should read Kuhn's The Structure of Scientific Revolutions.

Hi there, and thank you for your trust!

It sounds like your boyfriend is going about this a bit insensitively. Logical arguments are OK for debates, when both sides do it for the intellectual challenge. It's not humane to tear a person's world view out from under them when they're unprepared for it and a captive audience. I'm sure he means well and wants you to be closer to him, but he's being a bit of a caveman about it. Don't be mad at him, but tell him you think you'll be better off if you do your own information seeking, at your own pace. Ask him to have the patience and the trust to let you educate yourself. If he really cares for you, he should be fine with this: It may even be taking a burden off his shoulders.

I think there are some things you can consider and think about that will put things into focus and make this mess seem less of a problem.

Do you remember that song by Elton John Sting? "I hope the Russians love their children too."

Consider, first, some family in Tibet. Mom and dad live in a simple hut, doing some farming or whatever Tibetans do, and they have a bunch of children. They work hard to feed the family, and in the evening when they get together for supper they talk and smile and laugh a lot. They hug their children, they care for them when they're sick. They observe some kind of religious rituals, though they've probably never heard of Jesus. When a neighbor has a problem, they help them out. When someone dies, they mourn their passing and wish them a happy afterlife. Apart from the fact that they look Asian, they're people just like you, and they're good people. They have similar hopes and fears, they have stories to share and comfort them, and so forth. Two thirds of the world's people don't believe in Jesus, yet they're humans just like you and mostly decent people, just like your neighbors. Do you think they're all going to hell? Do you think they're paralyzed by their distance from your god, from their fear of death? No. Forget what religion these folks are, they're human.

Atheists are just a special case of those "other" humans. They believe in even less "other-worldly" stuff than the folks in Tibet do. Yet you probably meet atheists on the street every day. Some of them greet you and smile, most of them would help you if you had a problem and they were around. Atheists are not like vampires: They're not evil, they don't have to stay out of God's sunlight, and they don't burn up in churches and from contact with holy water ;)

Atheists have stories too, about the creation of the universe, which is really awesomely huge and inspiring. About the struggle of life to evolve to the fine humans we are today. About the many important achievements humans have made in their short time of being intelligent and basically masters of the world.

Rather than wrenching at your faith, I suggest you take a look at other cultures and religions for a bit. Consider that there humans out there who think other things than you, yet manage to be good people and lead happy lives. I'm almost embarrassed enough to delete my sappy paragraph about the Tibetan family, but I'll leave it in there to let you know what I'm getting at.

Then, inhale a bit of science. Go to church if you feel you need to, but also listen to videos by Carl Sagan. Get an appreciation for the wonders of the universe and of nature here on our planet. It's a rich and wonderful world out there. There is so much to see, to learn! Some people are in awe of God for producing all this; but you can just as easily be in awe of nature, of the intricate mechanisms that brought all this about without anyone taking a hand in it.

More stuff on nature and evolution can be learned, more or less gently, from Richard Dawkins' The Greatest Show on Earth. Get your boyfriend to buy it for you! But stay away from The God Delusion. While Dawkins is thoughtful and sensible, you don't want him telling you about how bad your god is - at least not right away.

A thought from me about a metaphor for God. Training wheels! You know how you have those wheels on your bike to keep it from tipping over as you're starting out? And how, once you've learned to keep your cycle straight, those training wheels are no longer really doing anything any more? That's God. It's comforting to feel that God is behind you in everything you do, it gives you strength and confidence. But everything you've achieved... that was you! You're standing up straight and doing fine, God is the training wheels you don't really need. On the other hand, I'm not going to say he really, truly absolutely isn't there. If you want him to be there, let him be there. Your BF will just have to put up with him for a while longer as you outgrow your training wheels.

Finally, about death: The good news is, it's not nearly the problem you think it is. There's a statistic that says, devout Christians are more than three times as likely, in their final week, to demand aggressive life-extending treatment than atheists. In English: Christians are more scared of dying than atheists are. You'd think that with heaven waiting, they'd be anxious to go! Actually, their religion -your religion- is telling them a comforting lie, letting them stick their heads in the sand all their lives. At the end, they panic because they're not sure what they believe is true. And they struggle for every minute of life.

I was religious once, and I had the "fear of death" phase, as many other atheists here report. You know what? I got over it. I confronted the idea, wrapped my head around it, got over it... and I've been completely unworried about death ever since. You'll get other people quoting Mark Twain for you here: About death being the same as the state you were in before you were born, and that didn't inconvenience you either, did it? Seriously, while I worry that my death may be painful or unpleasant, being dead is something I almost look forward to. It's like the long vacation I've always been meaning to take.

Well, I don't know if that will convince you, but... other people have been there too, and it turns out not to be the horrible problem you think it is. Things will be fine! Just allow yourself some time, and remind your BF to not be pushy about things. You can keep a spare room for when God comes to visit, but don't be surprised if that room turns out to fill up with other junk you're throwing out ;)

Astrophotography is a hobby in its own right.
For the budget you have listed, you would most likely end up buying a mount that is not up to the task.

I would suggest a nice pair of 10x50 binoculars and this book first.

If you are committed to getting a scope, then this is my suggestion assuming the $1000 budget is all inclusive meaning scope, accessories, and books.

1. Get a dobsonian. 8inches F4.5-5 10" or 12" would be nice but would blow your budget for the necessary accessories. Something like this would be a great place to start. Also nice would be the 10" Meade Lightbridge.
   
   2)The skywatcher comes with 2 eyepieces (25mm and 10mm IRC) THe light bridge comes with one. In either case I would invest in a NICE barlow like this one Barlows are an inexpensive way to improve your options. A 24 mm EP in a 2x barlow becomes a 12mm a 10mm becomes a 5mm. Its not as great as discrete eps in those sizes, but it is an economical way to get more versatility out of your existing eyepieces. I also can't talk enough about the Televue Panoptic EPs. They are affordable and incredibly nice. Eyepieces are something that will last through many scopes. I have 10 or so but only ever use about 3 of them.
   Get a Telrad or a Rigel finder. The Skywatcher has a finderscope, the meade has a red dot finder. Personally I hate red dot finders. I think they are complete junk. Telrad is the defacto standard for zero magnification finders, I prefer the rigel for its smaller size and built in pulse circuit. They are both about the same price. You will need to collimate your scope, a cheshire works great, or a laser collimator will do as well. Many folks use a combination of both. I have gone both ways, cheshire is fine, laser is fine, a combination of both is also fine. Accessories can go on forever, the only other must have that I can think of is a redlight flashlight. This is a good one or you can add red film to an existing flashlight you have or you can do what myself and many others have done and get an LED headlamp and replace the white LEDs with red ones.
   
   
2. books
   
   

• Nightwatch
  
• Turn Left at Orion
  
• The Backyard Astronomers Guide
  
• The Pocket Sky Atlas
  
• The Collins Guide to stars and planets as a pocket field guide I prefer this to the petersen field guide.
  
• The Ultimate Messier Object Log Its free! Has Telrad charts for all the Messier objects and you can download a PDF and print it out. A few years ago I printed a portion of the PDF out, laminated it and took it to kinkos and had it spiral bound. FANTASTIC resource and is my goto for finding messier objects.
  
  I would start with the backyard astronomers guide. Buy that first before you buy anything. It has some very good sections on scopes and observing that can help you answer some questions.
  
  

4. find a local club. Join it. ask questions and goto meetings. Check out Cloudynights.com. Remember that this is something you are doing for FUN.
   
   Lastly I always say go with a dobsonian scope. They are easy to setup and use and they force you to learn the sky. Once you are comfortable operating a scope and moving around the night sky, then I would think about investing in an equatorial mount and scope for astrophotography use.
   
   Good luck and Clear Skies!

Your mileage with certifications may vary depending on your geographical area and type of IT work you want to get into. No idea about Phoenix specifically.

For programming work, generally certifications aren't looked at highly, and so you should think about how much actual programming you want to do vs. something else, before investing in training that employers may not give a shit about at all.

The more your goals align with programming, the more you'll want to acquire practical skills and be able to demonstrate them.

I'd suggest reading the FAQ first, and then doing some digging to figure out what's out there that interests you. Then, consider trying to get in touch with professionals in the specific domain you're interested in, and/or ask more specific questions on here or elsewhere that pertain to what you're interested in. Then figure out a plan of attack and get to it.

A lot of programming work boils down to:

• Using appropriate data structures, and algorithms (often hidden behind standard libraries/frameworks as black boxes), that help you solve whatever problems you run into, or tasks you need to complete. Knowing when to use a Map vs. a List/Array, for example, is fundamental.
  
• Integrating 3rd party APIs. (e.g. a company might Stripe APIs for abstracting away payment processing... or Salesforce for interacting with business CRM... countless 3rd party APIs out there).
  
• Working with some development framework. (e.g. a web app might use React for an easier time producing rich HTML/JS-driven sites... or a cross-platform mobile app developer might use React-Native, or Xamarin to leverage C# skills, etc.).
  
• Working with some sort of platform SDKs/APIs. (e.g. native iOS apps must use 1st party frameworks like UIKit, and Foundation, etc.)
  
• Turning high-level descriptions of business goals ("requirements") into code. Basic logic, as well as systems design and OOD (and a sprinkle of FP for perspective on how to write code with reliable data flows and cohesion), is essential.
  
• Testing and debugging. It's a good idea to write code with testing in mind, even if you don't go whole hog on something like TDD - the idea being that you want it to be easy to ask your code questions in a nimble, precise way. Professional devs often set up test suites that examine inputs and expected outputs for particular pieces of code. As you gain confidence learning a language, take a look at simple assertion statements, and eventually try dabbling with a tdd/bdd testing library (e.g. Jest for JS, or JUnit for Java, ...). With debugging, you want to know how to do it, but you also want to minimize having to do it whenever possible. As you get further into projects and get into situations where you have acquired "technical debt" and have had to sacrifice clarity and simplicity for complexity and possibly bugs, then debugging skills can be useful.
  
  As a basic primer, you might want to look at Code for a big picture view of what's going with computers.
  
  For basic logic skills, the first two chapters of How to Prove It are great. Being able to think about conditional expressions symbolically (and not get confused by your own code) is a useful skill. Sometimes business requirements change and require you to modify conditional statements. With an understanding of Boolean Algebra, you will make fewer mistakes and get past this common hurdle sooner. Lots of beginners struggle with logic early on while also learning a language, framework, and whatever else. Luckily, Boolean Algebra is a tiny topic. Those first two chapters pretty much cover the core concepts of logic that I saw over and over again in various courses in college (programming courses, algorithms, digital circuits, etc.)
  
  Once you figure out a domain/industry you're interested in, I highly recommend focusing on one general purpose programming language that is popular in that domain. Learn about data structures and learn how to use the language to solve problems using data structures. Try not to spread yourself too thin with learning languages. It's more important to focus on learning how to get the computer to do your bidding via one set of tools - later on, once you have that context, you can experiment with other things. It's not a bad idea to learn multiple languages, since in some cases they push drastically different philosophies and practices, but give it time and stay focused early on.
  
  As you gain confidence there, identify a simple project you can take on that uses that general purpose language, and perhaps a development framework that is popular in your target industry. Read up on best practices, and stick to a small set of features that helps you complete your mini project.
  
  When learning, try to avoid haplessly jumping from tutorial to tutorial if it means that it's an opportunity to better understand something you really should understand from the ground up. Don't try to understand everything under the sun from the ground up, but don't shy away from 1st party sources of information when you need them. E.g. for iOS development, Apple has a lot of development guides that aren't too terrible. Sometimes these guides will clue you into patterns, best practices, pitfalls.
  
  Imperfect solutions are fine while learning via small projects. Focus on completing tiny projects that are just barely outside your skill level. It can be hard to gauge this yourself, but if you ever went to college then you probably have an idea of what this means.
  
  The feedback cycle in software development is long, so you want to be unafraid to make mistakes, and prioritize finishing stuff so that you can reflect on what to improve.

On science and evolution:

Genetics is where it's at. There is a ton of good fossil evidence, but genetics actually proves it on paper. Most books you can get through your local library (even by interlibrary loan) so you don't have to shell out for them just to read them.

Books:

The Making of the Fittest outlines many new forensic proofs of evolution. Fossil genes are an important aspect... they prove common ancestry. Did you know that humans have the gene for Vitamin C synthesis? (which would allow us to synthesize Vitamin C from our food instead of having to ingest it directly from fruit?) Many mammals have the same gene, but through a mutation, we lost the functionality, but it still hangs around.

Deep Ancestry proves the "out of Africa" hypothesis of human origins. It's no longer even a debate. MtDNA and Y-Chromosome DNA can be traced back directly to where our species began.

To give more rounded arguments, Hitchens can't be beat: God Is Not Great and The Portable Atheist (which is an overview of the best atheist writings in history, and one which I cannot recommend highly enough). Also, Dawkin's book The Greatest Show on Earth is a good overview of evolution.

General science: Stephen Hawking's books The Grand Design and A Briefer History of Time are excellent for laying the groundwork from Newtonian physics to Einstein's relativity through to the modern discovery of Quantum Mechanics.

Bertrand Russell and Thomas Paine are also excellent sources for philosophical, humanist, atheist thought; but they are included in the aforementioned Portable Atheist... but I have read much of their writings otherwise, and they are very good.

Also a subscription to a good peer-reviewed journal such as Nature is awesome, but can be expensive and very in depth.

Steven Pinker's The Blank Slate is also an excellent look at the human mind and genetics. To understand how the mind works, is almost your most important tool. If you know why people say the horrible things they do, you can see their words for what they are... you can see past what they say and see the mechanisms behind the words.

I've also been studying Zen for about a year. It's non-theistic and classed as "eastern philosophy". The Way of Zen kept me from losing my mind after deconverting and then struggling with the thought of a purposeless life and no future. I found it absolutely necessary to root out the remainder of the harmful indoctrination that still existed in my mind; and finally allowed me to see reality as it is instead of overlaying an ideology or worldview on everything.

Also, learn about the universe. Astronomy has been a useful tool for me. I can point my telescope at a galaxy that is more than 20 million light years away and say to someone, "See that galaxy? It took over 20 million years for the light from that galaxy to reach your eye." Creationists scoff at millions of years and say that it's a fantasy; but the universe provides real proof of "deep time" you can see with your own eyes.

Videos:

I recommend books first, because they are the best way to learn, but there are also very good video series out there.

BestofScience has an amazing series on evolution.

AronRa's Foundational Falsehoods of Creationism is awesome.

Thunderfoot's Why do people laugh at creationists is good.

Atheistcoffee's Why I am no longer a creationist is also good.

Also check out TheraminTrees for more on the psychology of religion; Potholer54 on The Big Bang to Us Made Easy; and Evid3nc3's series on deconversion.

Also check out the Evolution Documentary Youtube Channel for some of the world's best documentary series on evolution and science.

I'm sure I've overlooked something here... but that's some stuff off the top of my head. If you have any questions about anything, or just need to talk, send me a message!

Hello! I'm interested in trying to cultivate a better understanding/interest/mastery of mathematics for myself. For some context:

 




To be frank, Math has always been my least favorite subject. I do love learning, and my primary interests are Animation, Literature, History, Philosophy, Politics, Ecology & Biology. (I'm a Digital Media Major with an Evolutionary Biology minor) Throughout highschool I started off in the "honors" section with Algebra I, Geometry, and Algebra II. (Although, it was a small school, most of the really "excelling" students either doubled up with Geometry early on or qualified to skip Algebra I, meaning that most of the students I was around - as per Honors English, Bio, etc - were taking Math courses a grade ahead of me, taking Algebra II while I took Geometry, Pre-Calc while I took Algebra II, and AP/BC Calc/Calc I while I took Pre-Calc)

By my senior year though, I took a level down, and took Pre-Calculus in the "advanced" level. Not the lowest, that would be "College Prep," (man, Honors, Advanced, and College Prep - those are some really condescending names lol - of course in Junior & Senior year the APs open up, so all the kids who were in Honors went on to APs, and Honors became a bit lower in standard from that point on) but since I had never been doing great in Math I decided to take it a bit easier as I focused on other things.

So my point is, throughout High School I never really grappled with Math outside of necessity for completing courses, I never did all that well (I mean, grade-wise I was fine, Cs, Bs and occasional As) and pretty much forgot much of it after I needed to.

Currently I'm a sophmore in University. For my first year I kinda skirted around taking Math, since I had never done that well & hadn't enjoyed it much, so I wound up taking Statistics second semester of freshman year. I did okay, I got a C+ which is one of my worse grades, but considering my skills in the subject was acceptable. My professor was well-meaning and helpful outside of classes, but she had a very thick accent & I was very distracted for much of that semester.

Now this semester I'm taking Applied Finite Mathematics, and am doing alright. Much of the content so far has been a retread, but that's fine for me since I forgot most of the stuff & the presentation is far better this time, it's sinking in quite a bit easier. So far we've been going over the basics of Set Theory, Probability, Permutations, and some other stuff - kinda slowly tbh.

 




Well that was quite a bit of a preamble, tl;dr I was never all that good at or interested in math. However, I want to foster a healthier engagement with mathematics and so far have found entrance points of interest in discussions on the history and philosophy of mathematics. I think I could come to a better understanding and maybe even appreciation for math if I studied it on my own in some fashion.

So I've been looking into it, and I see that Dover publishes quite a range of affordable, slightly old math textbooks. Now, considering my background, (I am probably quite rusty but somewhat secure in Elementary Algebra, and to be honest I would not trust anything I could vaguely remember from 2 years ago in "Advanced" Pre-Calculus) what would be a good book to try and read/practice with/work through to make math 1) more approachable to me, 2) get a better and more rewarding understanding by attacking the stuff on my own, and/or 3) broaden my knowledge and ability in various math subjects?

Here are some interesting ones I've found via cursory search, I've so far just been looking at Dover's selections but feel free to recommend other stuff, just keep in mind I'd have to keep a rather small budget, especially since this is really on the side (considering my course of study, I really won't have to take any more math courses):
Prelude to Mathematics
A Book of Set Theory - More relevant to my current course & have heard good things about it
Linear Algebra
Number Theory
A Book of Abstract Algebra
Basic Algebra I
Calculus: An Intuitive and Physical Approach
Probability Theory: A Concise Course
A Course on Group Theory
Elementary Functional Analysis

Sure thing! The great, and not so great, thing about learning about evolution is that there is so much information out there it can be a bit overwhelm at times, and it is not always easy to know where to start. The best place to start it probably a university class, but that is not always an accessible resource. In lieu of that, I will strong recommend learning from biologist Richard Dawkins. While he is currently well-known for his stance on religion, he has devoted his life to teaching about evolution to the public. I'll give you a few of my favorite references of his. They are arranged in terms of the length of time they will probably take you. Also, so that you won't be intimidated, they are not references in which he explicitly denounces religion or anything; although, as you will see, he does explain evolution in contrast to some of the claims of creationism. I hope that is not a problem, as it is kind of necessary to learn why biologists take one view as opposed to the other.

Anyway, here are the references! =)

This video (5 parts, 10 min each) is a great introduction to some of the basic concepts of evolution, and was really eye-opening for me.

This lecture series (5 episodes, 1 hour each) goes into much more detail than the above video, gives much more evidence, illustrates some of the arguments, and has many fun and beautiful examples.

The Selfish Gene is a book that answered a huge number of questions about evolution for me (e.g., how can a "survival of the fittest" scheme give rise to people being nice to each other? The answer, it turns out, is fascinating.)

The The Greatest Show on Earth: The Evidence for Evolution May be the book you are looking for. This book clearly lays down the evidence for evolution, complete with wonderful illustrations. It is very detailed, and very readable.


There are many other great authors besides Richard Dawkins, but this is a great place to start. You are about to go on a very beautiful and moving journey, if you decide to take it. I envy you! I would love to do it all over again. Enjoy!

Pretty much everything that passes by. I love learning new things and expand my knowledge, but here are my biggest passions:

-Music: I'm studying to become a composer and music has been a major part of my life since birth, as I was born into a musical family. It's such a joy when I find a new band or composer and start going through their works and discover many new, exciting works. It's even better when you analyse scores and play then on piano, and everything starts to make sense, the melodies, harmonic structure,... sometimes it gives you the same feeling as when you open your christmas present, except you have been given an insight into a mind of a musical genius from the past.

-Lore: A lot of times I pick up a new game/book/TV series/movie, if I really like it, I go and read as much background lore as possible. The extra information and insight behind the main plot is really interesting to read and I tend to memorize unhealthy amounts of useless information :) So far it spans through Star Wars, Jurassic Park, Harry Potter, Warhammer 40k, Elder Scrolls, and probably a few more I forgot.

-History: It's real life lore :) Big emphasis on Roman empire/Viking culture/WW2.

-Philosophy: Basically discussing everything ranging from old philosophical problems to problems and dilemmas of the today's world.

-Physics: I love reading about space, black holes, wave-particle duality, electricity,... The more experimental it is, the better. I highly recommend this book.

-Motorsports: Rally and F1 mostly, but I love to drive and I am always blown away by the skills these drivers have. Also, the tech behind the cars is amazing and very interesting.

But the best part is if I can explain the above things to somebody else. It's really one of my favorite things to do. I really like to share my enthusiasm with other people and I can go on for hours at the time :)

Sounds like you are about 4 years behind me (Future physics PhD candidate). Glad to know you have discovered Dover books, they really are great and so cheap. It also sounds like you know what you're doing so good job, keep at it and you might make a good case for graduate school (if that's your destination). But I will warn you that upper division mathematics courses are different. I have seen so many people who think they are really great at mathematics up to vector calculus and then get completely shit on by more abstract courses like real analysis, abstract algebra and topology. The reason for this is that it requires more formalism and is very rigorous as far as proofs go. You'll eventually learn that math is all about making sure you have checked every possible condition in order to move on. I think something you will need is mathematical logic before you tackle abstract courses. If you do collect textbooks (like I do) then I would also recommend this textbook. It teaches you how to think like a mathematician and the logic behind proofs. I think a mathematics logic course is essential to students and it's a shame many mathematics students don't go through a formal logic course before they tackle advanced courses. Of course, some don't need it but unless you are brilliant, I would recommend it (Even if you are brilliant it would be a easy read). Just dig deep and focus and good luck with your future work. Mathematics and Physics are two beautiful subjects and it's always great to talk to future mathematicians or physicists(or any aspiring scientist in that case!) and help them get inspired or motivated!

P.S. Funny story, I had a friend who thought it would be funny to make people believe that Euler is pronounce "you-ler" with the argument that Euclid is pronounced "you-clid". It was pretty funny seeing people believe him.

Learning proofs can mean different things in different contexts. First, a few questions:

1. What's your current academic level? (Assuming, of course, you're still a student, rather than trying to learn mathematical proofs as an autodidact.)
   
   The sort of recommendations for a pre-university student are likely to be very different from those for a university student. For example, high school students have a number of mathematics competitions that you could consider (at least in The United States; the structure of opportunities is likely different in other countries). At the university level, you might want to look for something like a weekly problem solving seminar. These often have as their nominal goal preparing for the Putnam, which can often feel like a VERY ambitious way to learn proofs, akin to learning to swim by being thrown into a lake.
   
   As a general rule, I'd say that working on proof-based contest questions that are just beyond the scope of what you think you can solve is probably a good initial source of problems. You don't want something so difficult that it's simply discouraging. Further, contest questions typically have solutions available, either in printed books or available somewhere online.
   
   
2. What's your current mathematical background?
   
   This may be especially true for things like logic and very elementary set theory.
   
   
3. What sort of access do you have to "formal" mathematical resources like textbooks, online materials, etc.?
   
   Some recommendations will make a lot more sense if, for example, you have access to a quality university-level library, since you won't have to spend lots of money out-of-pocket to get copies of certain textbooks. (I'm limiting my recommendations to legally-obtained copies of textbooks and such.)
   
   
4. What resources are available to you for vetting your work?
   
   Imagine trying to learn a foreign language without being able to practice it with a fluent speaker, and without being able to get any feedback on how to improve things. You may well be able to learn how to do proofs on your own, but it's orders of magnitude more effective when you have someone who can guide you.
   
   
5. Are you trying to learn the basics of mathematical proofs, or genuinely rigorous mathematical proofs?
   
   Put differently, is your current goal to be able to produce a proof that will satisfy yourself, or to produce a proof that will satisfy someone else?
   
   
6. What experience have you already had with proofs in particular?
   
   Have you had at least, for example, a geometry class that's proof-based?
   
   
7. How would you characterize your general writing ability?
   
   Proofs are all about communicating ideas. If you struggle with writing in complete, grammatically-correct sentences, then that will definitely be a bottleneck to your ability to make progress.
   
   ---
   
   With those caveats out of the way, let me make a few suggestions given what I think I can infer about where you in particular are right now.
   
   

• The book How to Prove It: A Structured Approach by Daniel Velleman is a well-respected general introduction to ideas behind mathematical proof, as is How to Solve It: A New Aspect of Mathematical Method by George Pólya.
  
  
• Since you've already taken calculus, it would be worth reviewing the topic using a more abstract, proof-centric text like Calculus by Michael Spivak. This is a challenging textbook, but there's a reason people have been recommending its different editions over many decades.
  
  
• In order to learn how to write mathematically sound proofs, it helps to read as many as you can find (at a level appropriate for your background and such). You can find plenty of examples in certain textbooks and other resources, and being able to work from templates of "good" proofs will help you immeasurably.
  
  
• It's like the old joke about how to get to Carnegie Hall: practice, practice, practice.
  
  Learning proofs is in many ways a skill that requires cultivation. Accordingly, you'll need to be patient and persistent, because proof-writing isn't a skill one typically can acquire passively.
  
  ---
  
  How to improve at proofs is a big question beyond the scope of what I can answer in a single reddit comment. Nonetheless, I hope this helps point you in some useful directions. Good luck!

There would have been a time that I would have suggested getting a curriculum
text book and going through that, but if you're doing this for independent work
I wouldn't really suggest that as the odds are you're not going to be using a
very good source.

Going on the typical

Arithmetic > Algebra > Calculus

****

Arithmetic

Arithmetic refresher. Lots of stuff in here - not easy.


I think you'd be set after this really. It's a pretty terse text in general.

*****

Algebra

Algebra by Chrystal Part I

Algebra by Chrystal Part II

You can get both of these algebra texts online easily and freely from the search

chrystal algebra part I filetype:pdf

chrystal algebra part II filetype:pdf

I think that you could get the first (arithmetic) text as well, personally I
prefer having actual books for working. They're also valuable for future
reference. This filetype:pdf search should be remembered and used liberally
for finding things such as worksheets etc (eg trigonometry worksheet<br /> filetype:pdf for a search...).

Algebra by Gelfland

No where near as comprehensive as chrystals algebra, but interesting and well
written questions (search for 'correspondence series' by Gelfand).

Calculus

Calculus made easy - Thompson

This text is really good imo, there's little rigor in it but for getting a
handle on things and bashing through a few practical problems it's pretty
decent. It's all single variable. If you've done the algebra and stuff before
this then this book would be easy.

Pauls Online Notes (Calculus)

These are just a solid set of Calculus notes, there're lots of examples to work
through which is good. These go through calc I, II, III... So a bit further than
you've asked (I'm not sure why you state up to calc II but ok).

Spivak - Calculus

If you've gone through Chrystals algebra then you'll be used to a formal
approach. This text is only single variable calculus (so that might be calc I
and II in most places I think, ? ) but it's extremely well written and often
touted as one of the best Calculus books written. It's very pure, where as
something like Stewart has a more applied emphasis.

**

Geometry

I've got given any geometry sources, I'm not too sure of the best source for
this or (to be honest) if you really need it for the above. If someone has
good geometry then they're certainly better off, many proofs are given
gemetrically as well and having an intuition for these things is only going to
be good. But I think you can get through without a formal course on it.... I'm
not confident suggesting things on it though, so I'll leave it to others. Just
thought I'd mention it.

****

If you, perchance, liked the Harry Potter series, you might enjoy Harry Potter and the Methods of Rationality, as a fairly pain free and enjoyable introduction to cognitive biases, logical fallacies, and other useful tools to better thinking. Elizer Yudkowsky, the author of HPatMoR maintains several resources that can also be useful in training your mind to be more rational, and a better critical thinker.

​

The Demon-haunted world: science as a candle in the dark by Carl Sagan is a fantastic book in praise of science, a primer for the scientific method, and a decent guide to why and how science works. Further, it covers the nature of conspiracy thinking and pseudoscience, how to identify these things, and why they are harmful to society. Available in audiobook, ebook, and paper formats.

​

Algorithms to Live by is a bit off to the side of your requested topic, but it's an interesting treatise on how computer science can teach you some of the optimal ways one can make certain types of decisions. It's a bit counterintuitive, in the advice given, for example: messiness is often more efficient than spending a lot of time organizing everything, humans can't really multitask, and hunches are sometimes your best tool for deciding a course of action. I've read the book and posses the audiobook, both are great.

​

Almost anything written by Richard Feynman is accessible, humorous, and wise, in an askew sort of way. He's good at approaching topics from odd angles.

​

The Great Courses offers many resources on Audible: I've read and enjoyed Your Deceptive Mind, Skepticism 101, and Your Best Brain, which cover cognitive biases, and logical fallacies in detail, how to think more clearly without false, misleading thought, and how to take care of you mind through better lifestyle choices.

This sub can be pretty good, but you're sure to find much more activity over on /r/physics. We usually like to direct questions to /r/AskPhysics but it's definitely not as well trafficked.

The main introductory textbook for physics undergrads is Griffiths, and for good reason. It's widely agreed to be the best book to begin a proper undertaking of QM if you have the key prerequisites down. You definitely need to be comfortable with linear algebra (the most important) as well as multivariable calculus and basic concepts of partial differential equations.

Im sure you can find some good free resources as well. One promising free book I've found is A Course in Quantum Computing (pdf). It actually teaches you the basics of linear algebra and complex numbers that you need, so if you feel weak on those this might be a good choice. I haven't really used it myself but it certainly looks like a good resource.

Finally, another well-regarded resource are Susskind's lectures at his website The Theoretical Minimum. He also has a book by the same name. They tend to be rather laid back and very gentle, while introducing you to the basic substance of the field. If you wanted, I'm sure you could find some more proper university-style lectures on Youtube as well.

I love science books. These are all on my bookshelf/around my apt. They aren't all chemistry, but they appeal to my science senses:

I got a coffee table book once as a gift. It's Theodore Gray's The Elements. It's beautiful, but like I said, more of a coffee table book. It's got a ton of very cool info about each atom though.

I tried The Immortal Life of Henrieta Lacks, which is all about the people and family behind HeLa cells. That was a big hit, but I didn't care for it.

I liked The Emperor of all Maladies which took a long time to read, but was super cool. It's essentially a biography of cancer. (Actually I think that's it's subtitle)

The Wizard of Quarks and Alice in Quantumland are both super cute allegories relating to partical physics and quantum physics respectively. I liked them both, though they felt low-level, tying them to high-level physics resulted in a fun read.

Unscientific America I bought on a whim and didn't really enjoy since it wasn't science enough.

The Ghost Map was a suuuper fun read about Cholera. I love reading about mass-epidemics and plague.

The Bell that Rings Light, In Search of Schrödinger's Cat, Schrödinger's Kittens, The Fabric of the Cosmos and Beyond the God Particle are all pleasure reading books that are really primers on Quantum.

I also tend to like anything by Mary Roach, which isn't necessarily chemistry or science, but is amusing and feels informative. I started with Stiff but she has a few others that I also enjoyed.

Have fun!

Good question OP! I drafted a blog article on this topic a while back but haven't published it yet. An excerpt is below.
--------

With equations, I sometimes just visualize what I'd usually do on paper. For arithmetic, there are actually a lot of computational methods that are better suited to mental computation than the standard pencil-and-paper algorithms.

In fact, mathematician Arthur Benjamin has written a book about this called Secrets of Mental Math.

There are tons of different options, often for the same problem. The main thing is to understand some general principles, such as breaking a problem down into easier sub-problems, and exploiting special features of a particular problem.

Below are some basic methods to give you an idea. (These may not all be entirely different from the pencil-and-paper methods, but at the very least, the format is modified to make them easier to do mentally.)

ADDITION
(1) Separate into place values: 27+39= (20+30)+(7+9)=50+16=66

We've reduced the problem into two easier sub-problems, and combining the sub-problems in the last step is easy, because there is no need to carry as in the standard written algorithm.

(2) Exploit special features: 298+327 = 300 + 327 -2 = 625

We could have used the place value method, but since 298 is close to 300, which is easy to work with, we can take advantage of that by thinking of 298 as 300 - 2.

SUBTRACTION

(1) Number-line method: To find 71-24, you move forward 6 units on the number line to get to 30, then 41 more units to get to 71, for a total of 47 units along the number line.

(2) There are other methods, but I'll omit these, since the number-line method is a good starting point.

MULTIPLICATION

(1) Separate into place values: 18*22 = 18*(20+2)=360+36=396.

(2) Special features: 18*22=(20-2)*(20+2)=400-4=396

Here, instead of using place values, we use the feature that 18*22 can be written in the form (a-b)*(a+b) to obtain a difference of squares.

(3) Factoring method: 14*28=14*7*4=98*4=(100-2)*4=400-8=392

Here, we've turned a product of two 2-digit numbers into simpler sub-problems, each involving multiplication by a single-digit number (first we multiply by 7, then by 4).

(4) Multiplying by 11: 11*52= 572 (add the two digits of 52 to get 5+2=7, then stick 7 in between 5 and 2 to get 572).

This can be done almost instantaneously; try using the place-value method to see why this method works. Also, it can be modified slightly to work when the sum of the digits is a two digit number.

DIVISION
(1) Educated guess plus error correction: 129/7 = ? Note that 7*20=140, and we're over by 11. We need to take away two sevens to get back under, which takes us to 126, so the answer is 18 with a remainder of 3.

(2) Reduce first, using divisibility rules. Some neat rules include the rules for 3, 9, and 11.

The rules for 3 and 9 are probably more well known: a number is divisible by 3 if and only if the sum of its digits is divisible by 3 (replace 3 with 9 and the same rule holds).

For example, 5654 is not divisible by 9, since 5+6+5+4=20, which is not divisible by 9.

The rule for 11 is the same, but it's the alternating sum of the digits that we care about.

Using the same number as before, we get that 5654 is divisible by 11, since 5-6+5-4=0, and 0 is divisible by 11.

PRACTICE
I think it's kind of fun to get good at finding novel methods that are more efficient than the usual methods, and even if it's not that fun, it's at least useful to learn the basics.

If you want to practice these skills outside of the computations that you normally do, there's a nice online arithmetic game I found that's simple and flexible enough for you to practice any of the four operations above, and you can set the parameters to work on numbers of varying sizes.

Happy calculating!
Greg at Higher Math Help

Edit: formatting

Machine learning is largely based on the following chain of mathematical topics

Calculus (through Vector, could perhaps leave out a subsequent integration techniques course)

Linear Algebra (You are going to be using this all, a lot)

Abstract Algebra (This isn't always directly applicable but it is good to know for computer science and the terms of groups, rings, algebras etc will show up quite a bit)

General Topology (Any time we are going to deal with construction of a probability space on some non trivial manifold, we will need this. While most situations are based on just Borel sets in R^n or C^n things like computer vision, genomics, etc are going to care about Random Elements rather than Random Variables and those are constructed in topological spaces rather than metric ones. This is also helpful for understanding definitions in well known algorithms like Manifold Training)

Real Analysis (This is where you learn proper constructive formulations and a bit of measure theory as well as bounding theorems etc)

Complex Analysis (This is where you will get a proper treatment of Hilbert Spaces, Holomorphic functions etc, honestly unless you care about QM / QFT, P-chem stuff in general like molecular dynamics, you are likely not going to need a full course in this for most ML work, but I typically just tell people to read the full Rudin: Real and Complex Analysis. You'll get the full treatment fairly briefly that way)

Probability Theory (Now that you have your Measure theory out of the way from Real Analysis, you can take up a proper course on Measure Theoretic Probability Theory. Random Variables should be defined here as measurable functions etc, if they aren't then your book isn't rigorous enough imho.)

Ah, Statistics. Statistics sits atop all of that foundational mathematics, it is divided into two main philosophical camps. The Frequentists, and the Bayesians. Any self respecting statistician learns both.

After that, there are lots, and lots, and lots, of subfields and disciplines when it comes to statistical learning.

A sample of what is on my reference shelf includes:

Real and Complex Analysis by Rudin

Functional Analysis by Rudin

A Book of Abstract Algebra by Pinter

General Topology by Willard

Machine Learning: A Probabilistic Perspective by Murphy

Bayesian Data Analysis Gelman

Probabilistic Graphical Models by Koller

Convex Optimization by Boyd

Combinatorial Optimization by Papadimitriou

An Introduction to Statistical Learning by James, Hastie, et al.

The Elements of Statistical Learning by Hastie, et al.

Statistical Decision Theory by Liese, et al.

Statistical Decision Theory and Bayesian Analysis by Berger

I will avoid listing off the entirety of my shelf, much of it is applications and algorithms for fast computation rather than theory anyway. Most of those books, though, are fairly well known and should provide a good background and reference for a good deal of the mathematics you should come across. Having a solid understanding of the measure theoretic underpinnings of probability and statistics will do you a great deal--as will a solid facility with linear algebra and matrix / tensor calculus. Oh, right, a book on that isn't a bad idea either... This one is short and extends from your vector classes

Tensor Calculus by Synge

Anyway, hope that helps.

Yet another lonely data scientist,

Tim.

I study topology and I can give you some tips based on what I've done. If you want extra info please PM me. I'd love to help someone discover the beautiful field of topology. TLDR at bottom.

If you want to study topology or knot theory in the long term (actually knot theory is a pretty complicated application of topology), it would be a great idea to start reading higher math ASAP. Higher math generally refers to anything proof-based, which is pretty much everything you study in college. It's not that much harder than high school math and it's indescribably beneficial to try and get into it as soon as you possibly can. Essentially, your math education really begins when you start getting into higher math.

If you don't know how to do proofs yet, read How to Prove It. This is the best intro to higher math, and is not hard. Absolutely essential going forward. Ask for it for the holidays.

Once you know how to prove things, read 1 or 2 "intro to topology" books (there are hundreds). I read this one and it was pretty good, but most are pretty much the same. They'll go over definitions and basic theorems that give you a rough idea of how topological spaces (what topologists study) work.

After reading an intro book, move on to this book by Sutherland. It is relatively simple and doesn't require a whole lot of knowledge, but it is definitely rigorous and is definitely necessary before moving on.

After that, there are kind of two camps you could subscribe to. Currently there are two "main" topology books, referred to by their author's names: Hatcher and Munkres. Both are available online for free, but the Munkres pdf isn't legally authorized to be. Reading either of these will make you a topology god. Hatcher is all what's called algebraic topology (relating topology and abstract algebra), which is super necessary for further studies. However, Hatcher is hella hard and you can't read it unless you've really paid attention up to this point. Munkres isn't necessarily "easier" but it moves a lot slower. The first half of it is essentially a recap of Sutherland but much more in-depth. The second half is like Hatcher but less in-depth. Both books are outstanding and it all depends on your skill in specific areas of topology.

Once you've read Hatcher or Munkres, you shouldn't have much trouble going forward into any more specified subfield of topology (be it knot theory or whatever).

If you actually do end up studying topology, please save my username as a resource for when you feel stuck. It really helps to have someone advanced in the subject to talk about tough topics. Good luck going forward. My biggest advice whatsoever, regardless of what you study, is read How to Prove It ASAP!!!

TLDR: How to Prove It (!!!) -> Mendelson -> Sutherland -> Hatcher or Munkres

No problem!

Philosophy of time is an enormous area!

Not only are there many distinct positions that attempt to address the scientific and philosophical questions in different ways, there are different positions regarding the very method by which we should attempt to answer these questions! Some of these certainly overlap.

What do I mean by this?

Putting it roughly:

There are those who tend to think that we should use science to answer these questions about time. All we should care about is what observations are made; we should only care about the empirical data. These people might point to the great success of our best scientific theories that refer to 'time', such as those in physics, including; Einstein's Theory of Relativity, Entropy (The Arrow of Time), and even Quantum Theory, but also those in neuroscience and psychology, where our perception of time becomes relevant (such as the Inference Model of Time and the Strength Model of Time). So we have notions of physical/objective time, and subjective/mental time. We may talk about time slowing down around a massive body such as a black hole, or time slowing down when a work-shift is boring or when we're experiencing a traumatic event.

But there are also those who tend to think that we should use not just science, but also uniquely philosophical methods as well. Conceptual analysis is one such method; one that involves thinking very carefully about our concepts. This method is a distinctically a priori method (A priori is just philosophical jargon meaning; "Can be known without experience," for example, the statement "All triangles have three sides"). These people think we can learn a great deal about time by reflecting on our concepts about time, our intuitions about time, and the laws of thought (or logic) and how they relate to time. This philosophical approach to answering questions about time is distinctively metaphysical opposed to the former physical and cognitive theories about time.

Of course there are many who may see the use in all of these different approaches!

Recommendations:

Physics:

Hawking, S 1988, A Brief History of Time: From The Big Bang to Black Holes, Bantam Books, Toronto; New York. [Chapters 2, 9 & 10. Absolute Classic, little dated but still great read]

Gardner, M 1988, Time Travel and Other Mathematical Bewilderments, W.H. Freeman, UK. [Chapter 1]

Greene, B 2010, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, W. W. Norton, New York. [Chapter 2 is a great introduction for Special Relativity]

Physics and Metaphysics:

Dainton, B 2010, Time and Space, 2nd edn, McGill-Queen's University Press, Montreal; Ithaca N.Y. [Chapters 1-8, 18, 19 & 21. This book is incredible in scope, it even has a chapter on String Theory, and it really acknowledges the intimate connection between space and time given to us by physics]

Metaphyics:

Hawley, K 2015, Temporal Parts, The Stanford Encyclopedia of Philosophy <http://plato.stanford.edu/entries/temporal-parts/>. [Discussion of Perdurantism, the view that objects last over time without being wholly present at every time at which they exist.]

Markosian, N 2014, Time, The Standford Encyclopedia of Philosophy <http://plato.stanford.edu/archives/fall2016/entries/time/>.

Hunter, J 2016, Time Travel, The Internet Encyclopedia of Philosophy
<http://www.iep.utm.edu/timetrav/>.

Callender, C & Edney, R 2014, Introducing Time: A Graphic Guide, Icon Books Limited, UK. [Great book if you want something a bit less wordy and fun, but still very informative, having comprehensive coverage. It also has many nice illustrations and is cheap!]

Curtis, B & Robson, J 2016, A Critical Introduction to the Metaphysics of Time, Bloomsbury Publishing, UK. [Very good recent publication that comes from a great series of books in metaphysics]

Ney, A 2014, Metaphysics: An Introduction, Routledge Taylor & Francis Group, London; New York. [Chapters 5 & 6 (Chapter 4 looks at critiques of Metaphysics in general as a way of answer questions and Chapter 9 looks at Free-will/Determinism/Compatiblism)]

More advanced temporal Metaphysics:

Sider, T 2001, Four-Dimensionalism: An Ontology of Persistence and Time, Clarendon Press; Oxford University Press, Oxford New York. [Great book defending what Sider calls "Four-Dimensionalism" (this is confusing given how others have used the same term differently) but by it he means Perdurantism, the view that objects last over time without being wholly present at every time at which they exist.]

Hawley, K 2004, How Things Persist, Clarendon Press, UK. [Another great book: It's extremely similar to the one above in terms of the both content and conclusions reached]

Some good Time travel movies:

Interstellar (2014)

Timecrimes (2007)

Looper (2012)

Primer (2004) [Time Travel on drugs]

12 Monkeys (1995)

Donnie Darko (2001)

The Terminator (1984)

Groundhog Day (1993)

Predestination (2014)

Back To the Future (1-3) (1985-1990)

Source Code (2011)

Edge of Tomorrow (2014)

> Thank you for the attempt at clarification. I am afraid that I still do not understand - it makes more scientific sense to claim that something came from nothing?

This is a common misunderstanding of what the Big Bang is referring to.

The Big Bang is not an event 13.7 billion years ago that created the universe. The Big Bang is the currently happening expansion and evolution of the universe. It is an event that happened after time=0. The Big Bang is not an explosion into spacetime. It is an explosion OF spacetime.

When atheists say things like 'Time didn't exist before the Big Bang, so it's nonsense to ask what happened before the Big Bang' they are not being facetious or evasive.

It really is like asking 'What's north of the North Pole?' If you are standing on the North pole, there is no direction you can face that can be described as being 'north' of your position. Even looking straight up or straight down are not 'north' of your position.

There is no 'before' the Big Bang, because time starts with the Big Bang.

What happened at time=0? "We don't know, and it is possible we CAN NEVER know." In fact, it is possible that the question is meaningless.

What I do know though, is that saying 'God did it' doesn't answer the question, and prevents exploration that may answer the question.

> Matter has always existed a priori, which therefore allowed the chemical reaction of the Big Bang.

The Big Bang was not a chemical reaction. I hope by my brief explanation above you get that now.

> Matter came as a result of the "Big Bang," but we do not know what caused the "Big Bang" in terms of quantifiable, physical evidence. All that is offered is conjecture.

Essentially correct. However, the conjecture has a grounding and does not violate ANY of the known laws of the universe. I HIGHLY recommend watching the lecture by Laurence Krauss, "A Universe From Nothing".

Now, as for how matter came to be, we actually have very good explanations, based on particle accelerator experiments. Very early, the universe was so hot and dense that there was no matter, just a lot of heat and energy. As the universe expanded, it cooled. Once it cooled enough, the energy was able to bundle into discrete particles, when then combined into mostly hydrogen atoms, with a little helium thrown in for variety. The rest of everything in the universe came about by nuclear fusion within the heart of stars. We are literally made from the dust of the stars.

I highly recommend The Fabric of the Cosmos, by Brian Greene and Big Bang: The Origin of the Universe by Simon Singh as a good introduction to the science of cosmology.

> The problem is that if we do not apply the attribute of eternity to God, then we will find ourselves citing an infinite regression of "God X created God Y, who was created by God Z." But, again, I simply point back to the acceptance of either the Big Bang or matter always existing - scientists do not know with absolute certainty, but still make the claim.

Exactly the same issue here on the other side: you believe, but do not KNOW (remember what I said about semantics mattering sometimes?) that God is in fact eternal. You MUST assert the eternal nature of God for precisely the reason you presented; to end the infinite regress. However, you haven't answered the question, you have made an assertion, based on belief, not knowledge.

> Both atheist materialists and Christians have to accept something a priori to defend a premise and a conclusion. First and foremost, of course, is the premise that we really exist. Second is that we can come to know something. Third would be that reality as we see it is real.

Totally agree. And philosophy is useful for thinking about these premises. However, no matter what you think about the situation, if we do not accept these three premises, we can't accomplish much.

First, you have to assume you exist. Trying to operate while assuming anything contrary to that is meaningless. You literally cannot do it. Part of the nature of consciousness is the implied fact that you exist, for without that implication, you would not be conscious. Sure, it's a tautology, but there you go.

Second, obviously we can come to know things, because otherwise we would be a brain in a vat, cut off from all sensory perception. Since we have sensory perception, we have information flowing into our consciousness. If nothing else, we come to know that sensory input. The question becomes how trust worthy is it? Since it is fairly obvious to anyone who has seen an optical illusion that our senses can be tricked, we have developed the scientific method to test our sensory perception.

And that's where we hit the third premise. Science allows us the best way yet found to determine if what we know does in fact reflect the nature of reality. How do we know science is the best way we have found? Because SCIENCE WORKS BITCHES!!! Yes, I am invoking utilitarianism.

> And yet we hold to abstract ideas of non-provable ideals. The human race (in general) holds to concepts of "morality" and "truth" and "goodness" and "badness", but we cannot test or defend those ideas with physical, repeatable, empirical evidence.

Correct. I agree 100%. Science cannot tell us what is good, right, wrong, moral, immoral, bad, evil, etc. Science can only tell us what is. The value judgments are left up to us.

Now, science CAN (and in fact is beginning to) tell us where and how these 'moral ideals' we have came from/developed.

As an atheist, if you follow the the concept to it's logical end, you come to the realization that there is no such thing as objective morality. All morality is subjective. The best I have ever heard it stated:

The difference between good and evil is EXACTLY the difference between the lion and the gazelle.

I don't see a collision between science and philosophy. Generally what I see is a failure to understand how best to integrate the two disciplines.

The claim that "time is exactly like space" is not true. Time is treated as a dimension in Special Relativity (SR) and General Relativity (GR), but it is very different from the "usual" spatial dimensions. (It boils down to "distance" along the time direction being negative, but that statement doesn't really mean anything out of context.) The central idea of relativity is that while the entire four dimensional "thing" (spacetime) just is (is invariant), different observers will have different ideas about which way the time direction points; it turns out to be convenient for our description of nature to respect the natural "democratic" equivalence of all hypothetical observers.

I can point you to a couple of good resources:

This
is a very good, book about SR, and some "other stuff". It's pretty mathematical, and I wouldn't recommend it to someone who isn't totally comfortable with college level intro physics and calculus.

This
is the "standard" text for undergraduate SR; it's less demanding than the above, but uses mathematical language that won't translate immediately if you go on to study GR. (I have not read this myself.)

This is the book that I learned from; I thought it was pretty good.

This is Brian Greene's famous popularization of String Theory. It has chapters in the beginning on SR and Quantum Mechanics that I think are quite good.

This is Einstein's own popularization, only algebra required. All the examples that others use to explain SR pretty much come from here, and sometimes it's good to go right to the source.

This is a collection of the most important works leading up to and including relativity, from Galileo to Einstein, in case you'd like to take a look at the original paper (translated). The SR paper requires more of a conceptual physical background than a mathematical one; the same can't be said of the included GR paper.

I don't know what your background is--the first three options above are textbooks, and that's probably much more than you were hoping to get into. The last three are not; the book by Brian Greene and the collection (edited by Stephen Hawking) are interesting for other reasons besides relativity as well. For SR, though, another book by Greene might be a bit better: this.

Lots of people are going to say 8" dob, Z8 specifically, and I have nothing but good to say about that. For a lot of people that's the only answer necessary.

However, let me offer an alternative case in favor of OneSky telescope by Astronomers Without Borders.

Three reasons for this recommendation:

SIZE The OneSky is a collapsible tabletop reflector. It is quite modestly sized when collapsed. It will fit in the front seat or trunk of a car and can easily be carried by even a child. Size ultimately is the thing that keeps a telescope indoors. There have been several nights this year where I've had 20 minutes to sneak a peek out at a beautiful crescent moon or something, but haven't, because I knew it would take me 20 minutes to set up my telescope and I would have no observing time. Plus all the work of lugging the heavy parts from my shed to my front yard. With a tabletop scope there's none of that. It takes 2 minutes to set up and requires no heavy lifting.

You will never miss an observing session due to the work of setting up the telescope, and you will never have to leave the telescope at home on a trip. An 8" Dob is going to show more simply because it's a larger scope, but the OneSky is going to show more than an 8" scope in the shed.

COST With a budget of $400, you will be able to afford some killer accessories after getting the $200 OneSky. Turn Left At Orion is the ideal book for a new telescope owner. A wide-field eyepiece like this one will give really good views of clusters like the pleiades and large nebulae like the Great Orion Nebula. A 6mm, 66 degree eyepiece will allow excellent, comfortable viewing of planets and smaller objects like binary stars. In addition you will be able to afford a comfortable stool to place the scope on, and a nice chair to sit on.

If you buy an 8" scope you will not be able to get all that stuff and stay in your $400 budget.

COMMUNITY The OneSky is well reviewed (review 1, review 2 under the Heritage 130 name) and has an active community of fans who have a lot of ideas about how to improve the performance of the scope for very little money/effort.

Troubleshooting this telescope is a breeze and the community is favorable. Even among seasoned enthusiasts the OneSky is popular.

OK, one of my favorite topics.
First of all, do you live in a city? Light pollution will play a big role in what you can see.

Now, my advice in chronological order:

• Buy a Planisphere
  
• Buy a copy of Nightwatch
  
• Get some decent binoculars. If you don't have any, aim for something with a magnification of 8-10x (don't go bigger!), and make sure that the objective is at least 5 times the magnification. In other words, you're looking at 8x42 or 10x50, something in that sort of range.
  
• Spend a year looking up at the sky with your books and planisphere. You'll fall totally in love.
  
  When you get a telescope, here are some crucial factors:
  
  
• Magnification is (mostly) irrelevant.
  
• Diameter = brightness, and thus better deep-sky viewing.
  
• Diameter = weight, and a huge telescope that you never use is a big waste of money.
  
• Decent optics are surprisingly affordable. A good mount is essesntial
  
• Electronics are nice, but not necessary.
  
  Refractors are long, expensive (for the diameter) and have great sharpness and contrast when done well. Fantastic for planets, the moon, etc.
  Reflectors are cheap, and when mounted on a Dobsonian mount, are the cheapest scopes per inch out there. That makes them great for deep sky viewing. They tend to be big and need more maintenance (i.e. alignment) though.
  Cats, of various forms are moderately expensive and that is exacerbated by the fact that they're usually on nice motorized mounts. Great scopes though, and fantastically compact. Ideal for photography, if you're so inclined.
  
  The general advice for a first scope is to spend a year getting to know the sky, and then get a 6" dobsonian. It's small enough that you'll actually use it, large enough to get a good amount of light, and simple enough that you don't have to spend any time setting it up. Just plunk and go. 8" may be OK, but don't go larger than that for a first scope - you won't use it.
  
  Be aware that you won't see the rich colours you're used to seeing in pictures, though - you're more likely to see a barely-visible veil for a nebula. However, you can see gorgeous things already with your little scope. Look for the open clusters - the double cluster, the Pleiades, the Beehive, and so forth. Look for Andromeda, and the Orion nebula. They're all naked-eye objects from a sufficiently dark area, and that much better with a low-power scope (or binoculars).
  

These rules arise from the solutions of the Schroedinger equation for a central potential.

The nucleus of the atom provides an attractive potential in which electrons can be bound. As the mass of even a single proton is roughly 1800 times that of an electron the nuclei can be treated as stationary charged points that the electrons orbit around. The resulting coulomb potential is a central potential, that is it only depends on the distance from the nucleus, not the direction from the nucleus.

See http://en.wikipedia.org/wiki/Hydrogen-like_atom for some of the derivation, but if you don't know differential equations and quantum mechanics at least at an introductory level it will not make much sense. Griffiths does a good introductory quantum text if you are interested in reading more. Link on amazon.com.

As it is a bound system in quantum mechanics only certain values of energy and momentum can be taken. The allowed energy levels are denoted by the quantum number n. The energy of a level is given is proportional to -1/n^2 in the simple hydrogenic atom model where the energy is negative that gives a bound state, and energies above zero are unbound, so as the energy increase the electrons in the higher n orbitals require less energy to become unbound.

For a given n there are certain values of angular momentum that can occur, and these are designated l and range from 0 to n. For a given l there are then the m_l magnetic quantum numbers ranging from +l to -l in integer steps. In the simple atom models the m_l do not effect the energy level.

Higher angular momentum of the electron implies a higher energy So 2s (n=1,l=0, m_l=0) has lower energy than 2p (n=2, l=1, m_l= 1,0,-1)

Each letter corresponds to an l value and arose from the way the lines looked in spectrographs and the meaning of the letter abbreviation is pretty much ignored these days with the current understanding of the the underlying quantum numbers.

s-> l=0 (sharp lines)

p->l=1 (principle lines)

d->l=2 (diffuse lines)

f->l=3 (fundamental lines)

http://www.tutorvista.com/content/chemistry/chemistry-iii/atomic-structure/electronic-configuration.php

Shows some of the simpler rules for determining the order of filling of the orbitals based on the energy level of the combined n and l values.

Two show how oxygen needs an octet to be stable we can do:

Oxygen has 8 protons and will be neutral with 8 electrons.

2 go into the 1s orbital, and it it is designated 1s^2, the superscript giving the number of electrons present in the n=1 l=0 m_l=0 and m_s =+1/2,-1/2. m_s is the magnetic quantum number for the electrons own internal angular momentum which has s=1/2 so can take m_s=+1/2 or m_s=-1/2.

The next higher energy orbital (look at the squiggly line diagram giving the filling order for electrons into orbitals, this is essentially filling in order of lowest energy orbitals first) is the 2s and it can have two electrons like the 1s, so we write 2s^2 for the full orbital.

There are now 4 more electrons to take care of, and they can go into the 2p orbital and that can hold up to 6 electrons, but we only fill in 4 for 2p^4 .

We can fully write the electron configuration as 1s^2 2s^2 2p^4 . If the oxygen borrows two more electrons (say one each from two hydrogens) they can move into the remaining 2p orbitals that are not full.

In the n=2 orbitals that then gives a total of 8 electrons.

Going into the higher orbitals requires more energy than the lower orbitals so it would not be a stable ground state. To put it differently if two hydrogen atoms are going bond to an oxygen it needs to go into a lower energy state than the separate atoms. If a bound state does occur with the lower energy atoms this is then an excited state that will decay into the grounds state by emission of a photon (light).

1. The Bible: Eh. I can sort of get behind this, but not for the reason he gives. The Bible's just really culturally important. I also wouldn't bother reading all of it. When I reread the Bible it's normally just Genesis, Exodus, the Gospels, and Eccelesiastes. A lot of it (especially Leviticus) is just tedious. The prophets are fun but I wouldn't call them essential.
   
   
2. The System of the World: Newton intentionally wrote the Principia to make it inaccessible to layman and dabblers. I really don't think you should be recommending a book like this to people who aren't specialists. Sagan's A Demon Haunted World will probably fulfill the stated purpose Tyson sets out better.
   
   
3. On the Origin of Species: A good book that's held up remarkably well, but a more recent book of evolution might be better. The Extended Phenotype or The Selfish Gene would both probably do a better job.
   
   
4. Gulliver's Travels: This is a great book. I support this recommendation.
   
   
5. Age of Reason: Haven't read it. I like Paine otherwise though. No comment.
   
   
6. The Wealth of Nations: Similar to On the Origin of Species. It's still a great read that's held up really well and offers an interesting historical perspective. That said, economic theory has made some pretty important advancements in two centuries (the Marginal Revolution, Keynes, etc). Still, if you want to stick to the time you'll probably get more out of reading Ricardo's Principles of Political Economy.
   
   
7. The Art of War: Very good book. I have nothing to add.
   
   
8. The Prince: Same as the above. Fantastic book.

Awesome, it's great you're so proud of her!

Haha knowledge that leads to everlasting boredom! Book studies were the worst, I always felt super obligated to study extra hard because there were so few people that often nobody would answer!

Don't be so sure that your family will keep abandoning you, it's possible sure, but there's always hope! Often they're surprised that you can leave the witnesses and live a normal, or even better than normal life (of course there's always the "blessed by satan" get out clause) but they do expect people who leave to get aids and die from a heroin overdose.

It's easy to prove them wrong! Either way though, you have your own family to look out for and you can learn what not to do!

On to the suggested reading. I've mentioned many on here before but I don't expect everyone to be aware of it all so here goes:

Reading (I have a kindle and love reading, but they're all available for ebook and in paperback)

• Michael Shermer's Why People Believe Weird Things: Pseudoscience, Superstition, and Other Confusions of Our Time and The Believing Brain: From Ghosts and Gods to Politics and Conspiracies---How We Construct Beliefs and Reinforce Them as Truths these books really really helped me comprehend how I allowed myself to be fooled and that I can learn from my mistakes
  
• Richard Dawkins - The greatest show on earth and Coyne's Why evolution is true concreted the fact that the earth wasn't made and that animals didn't magically appear
  
• Carl Sagan's Demon Haunted World - it is a bit similar to shermers books, but a great read nonetheless, Sagan has an amazing awe at the universe and it's beautiful to read!
  
• Christopher Hitchens - God Is Not Great: How Religion Poisons Everything This book is by far among my favorites but it has a more aggressive tone, which is why I wouldn't start with it. Hitchens was awesome, even though I didn't agree with everything he said.
  
  Web
  
  
• JWFacts, of course...an invaluable site but it WILL make you mad
  
• Bad astronomy - add it to your RSS reader, often breathtaking, and generally about space
  
• Jerry Coyne's Why Evolution is True blog - science and politics
  
  
  Pocasts
  
  (all on iTunes etc, i like them because I can listen at work or download to my phone)
  
  
• The skeptic's guide to the universe it's intelligent, they discuss science and science news and skepticism and I always learn something
  
• Dogma debate just great, lots of debates with christians of various kinds and you can hear how both sides present their arguments
  
• Rationally speaking you said philosophy is of interest, if so this is a must!!!
  
• Cognitive dissonance - they are angry they talk news and politics and religion, it's very funny, informative and irreverent
  
• Caustic soda just a generally awesome science / history / factual podcast
  
  
  That's about it for now, if you soak all that in / want more / have suggestions let me know, and I'd love to hear what you think! :)
  
  

If you're not already familiar, I suggest you start with the Wikipedia article on a priori and a posteriori knowledge.

> I understand what he means by the love example in that, while love is a series of chemical reactions, you can't really scientifically measure how "in love someone is" or the nuances of those feelings. Does this apply to the concept of God also?

Not exactly. The closest analogy to the claim that a god exists would be the claim that love exists. How would you prove that love exists? First, you would have to clearly define what you mean by love.

If you define it such that it's an unfalsifiable proposition, then the search is over before it begins; unfalsifiable claims are effectively indistinguishable from false claims and are only treated as true (or possible) by the exercise of wishful thinking.

On the other hand, if you define love in a way that is testable then run your tests etc. Note that in this scenario, how "in love someone is" may well be measurable.

This is why it's important to address someone's god claim first by insisting that they provide a testable definition. Obviously theists reject this approach, as it lays bare the weakness of their reasoning. You typically get deflective responses like "Well how would you test for happiness, or love, or whatever (immaterial concept they grasp at)." Of course anything that exists, even if it only has a subjective existence in the mind of one individual, can (theoretically) be tested if it is defined properly. Another common response is "Everything is evidence for (their) god." This is basically presuppositionalism, or circular reasoning. Circular reasoning proves nothing. And then there's "My god can't be defined, because that would set limits on him and he's too awesome for limitations." This makes the claim incoherent, because the god's attributes are incoherent. Incoherence is nonsense, by definition.

If you haven't read it, Carl Sagan's "The Demon Haunted World" is highly rated. I'm giving a copy to my youngest daughter.

I double majored in math and CS as an undergrad and I enjoyed math more than CS. I'm a graduate student right now planning on doing research in a mathy area of CS. Everything I write below comes from that perspective.

• In my experience Wikipedia has some pretty good math articles. Many articles do a decent job of explaining the intuition behind of various concepts, not just the formalism.
  
  
• Math.StackExchange.com is similar to stackoverflow and I've found it to be quite helpful on occasion. Example of a question with some great answers
  
  
• /r/math is pretty active and has a very knowledgeable user base.
  
  
• One of the best known living mathematicians is Terrence Tao. He has a math blog but you might not have the background necessary to understand much of the material; I would guess that you need knowledge covering at least the standard undergraduate math major coursework to understand many of the posts.
  
  But if you're interested in really digging in and understanding some math at an advanced undergraduate level (analysis, abstract algebra, topology, etc.) then I don't think there is any substitute for books.
  
  
• A personal favorite is The Princeton Companion to Math. It has expository articles that provide high level overviews of different branches of math, important theorems, biographies of mathematicians, articles about the historical development of math, and more. It has some top notch contributors and was designed to be approachable by anyone with a good knowledge of calculus. This would be a great place to get a sense of the areas of study in math. I bought this book right after it came out after graduating high school and have loved it ever since. Everyone with a love of math should own this book.
  
  
• How to Prove It does a great job of introducing proofs and set theory which are both fundamental to higher math.
  
  
• Dover is a well loved publisher among math folks because they offer extremely cheap books on math that are of fairly high quality if a little old. You can find textbooks on any topic in the undergraduate math curriculum for less than $20 from Dover.
  

I guess it really depends on how familiar you are with the night sky - but there's one book that's literally invaluable for astronomers of all levels - Turn Left At Orion - there's no finer book, quite frankly, and the authors are an inspiration to me. If my books were anywhere near as good as theirs, I'd be very pleased and proud.

(Get the larger, spiral bound edition - http://www.amazon.com/Turn-Left-Orion-Hundreds-Telescope/dp/0521153972/ref=sr_1_1?ie=UTF8&qid=1414368749&sr=8-1&keywords=turn+left+at+orion)

I would also buy Astronomy Hacks - there are a TON of tips and tricks in there and, again, it's aimed at astronomers of all levels.

(http://www.amazon.com/Astronomy-Hacks-Tools-Observing-Night/dp/0596100604/ref=sr_1_1?ie=UTF8&qid=1414368782&sr=8-1&keywords=astronomy+hacks)

I had an Orion XT 4.5" Dobsonian and loved it. Celestrons are also excellent and both companies have equipment that are reasonably priced and well suited to amateurs of all levels. I'd start with something relatively small, like a 4" or 6" reflector and then go from there.

Beyond that, I would highly recommend joining a local club or, at the very least, ask a question here on Reddit or join a group in Facebook.

The two I like the most are the Telescope Addicts (https://www.facebook.com/groups/telescopeaddicts/) and Astronomy 4 Beginners. (https://www.facebook.com/groups/astro4beginners/)

I hope this helps. Feel free to email me at astronomywriter@gmail.com at any time. At some point in the nearish future I'd like to write an astronomy book for suburban astronomers (especially beginners) but I'm not sure when that might happen!

(In the meantime, have a look at my other book, 2015 An Astronomical Year - the Kindle version has a lot of graphics and text highlighting the best naked eye sights throughout the year - http://www.amazon.com/dp/B00LVEUJI2/)

Clear skies!

> Mathematical Logic

It's not exactly Math Logic, just a bunch of techniques mathematicians use. Math Logic is an actual area of study. Similarly, actual Set Theory and Proof Theory are different from the small set of techniques that most mathematicians use.

Also, looks like you have chosen mostly old, but very popular books. While studying out of these books, keep looking for other books. Just because the book was once popular at a school, doesn't mean it is appropriate for your situation. Every year there are new (and quite frankly) pedagogically better books published. Look through them.

Here's how you find newer books. Go to Amazon. In the search field, choose "Books" and enter whatever term that interests you. Say, "mathematical proofs". Amazon will come up with a bunch of books. First, sort by relevance. That will give you an idea of what's currently popular. Check every single one of them. You'll find hidden jewels no one talks about. Then sort by publication date. That way you'll find newer books - some that haven't even been published yet. If you change the search term even slightly Amazon will come up with completely different batch of books. Also, search for books on Springer, Cambridge Press, MIT Press, MAA and the like. They usually house really cool new titles. Here are a couple of upcoming titles that might be of interest to you: An Illustrative Introduction to Modern Analysis by Katzourakis/Varvarouka, Understanding Topology by Shaun Ault. I bet these books will be far more pedagogically sound as compared to the dry-ass, boring compendium of facts like the books by Rudin.

If you want to learn how to do routine proofs, there are about one million titles out there. Also, note books titled Discrete Math are the best for learning how to do proofs. You get to learn techniques that are not covered in, say, How to Prove It by Velleman. My favorites are the books by Susanna Epp, Edward Scheinerman and Ralph Grimaldi. Also, note a lot of intro to proofs books cover much more than the bare minimum of How to Prove It by Velleman. For example, Math Proofs by Chartrand et al has sections about doing Analysis, Group Theory, Topology, Number Theory proofs. A lot of proof books do not cover proofs from Analysis, so lately a glut of new books that cover that area hit the market. For example, Intro to Proof Through Real Analysis by Madden/Aubrey, Analysis Lifesaver by Grinberg(Some of the reviewers are complaining that this book doesn't have enough material which is ridiculous because this book tackles some ugly topological stuff like compactness in the most general way head-on as opposed to most into Real Analysis books that simply shy away from it), Writing Proofs in Analysis by Kane, How to Think About Analysis by Alcock etc.

Here is a list of extremely gentle titles: Discovering Group Theory by Barnard/Neil, A Friendly Introduction to Group Theory by Nash, Abstract Algebra: A Student-Friendly Approach by the Dos Reis, Elementary Number Theory by Koshy, Undergraduate Topology: A Working Textbook by McClusckey/McMaster, Linear Algebra: Step by Step by Singh (This one is every bit as good as Axler, just a bit less pretentious, contains more examples and much more accessible), Analysis: With an Introduction to Proof by Lay, Vector Calculus, Linear Algebra, and Differential Forms by Hubbard & Hubbard, etc

This only scratches the surface of what's out there. For example, there are books dedicated to doing proofs in Computer Science(for example, Fundamental Proof Methods in Computer Science by Arkoudas/Musser, Practical Analysis of Algorithms by Vrajitorou/Knight, Probability and Computing by Mizenmacher/Upfal), Category Theory etc. The point is to keep looking. There's always something better just around the corner. You don't have to confine yourself to books someone(some people) declared the "it" book at some point in time.

Last, but not least, if you are poor, peruse Libgen.

> as I have no proof that we evolved from other animals/etc.

Such proof abounds. If you're going to debate these people, you need to know some of it.

I don't mean enough to ask a couple of questions, I mean enough to carry both sides of the conversation, because he'll make you do all the heavy lifting.

Start with talkorigins.org.

First, the FAQ
Maybe the 29+ Evidences for Macroevolution next,
then the pieces on observed instances of speciation

See the extensive FAQs index

Here are their questions for creationsists - see both links there

and then read the index to creationist claims

That's just to start. Take a look at the Outline (which starts with an outline of the outline!)

If you're going to talk with a creationist, you either need to get some idea of the topography or you'll end up chasing in circles around the same tree again and again.

Yes, it looks like a major time investment, but once you start to become familiar with it, it gets easier quickly. Don't aim to learn it all by heart - but you should know when there is an answer to a question, and where to find it.

read books like Your Inner Fish and Why Evolution Is True and The Greatest Show on Earth

I list Your Inner Fish first because it tells a great story about how Shubin and his colleagues used evolutionary theory and geology to predict where they should look for an intermediate fossil linking ancient fish and amphibians (a "transitional form") - and they went to that location, and found just such a fossil. This makes a great question for your creationist - given fossils are kind of rare, how the heck did he manage that? If evolution by natural selection is false, why does that kind of scientific prediction WORK? Is God a deceiver, trying to make it look exactly like evolution happens?? Or maybe, just maybe, the simpler explanation is true - that evolution actually occurs. (Then point out that many major Christian churches officially endorse evolution. They understand that the evidence is clear)

It's a good idea to read blogs like Panda's Thumb, Why Evolution Is True, Pharyngula, erv (old posts here) and so on, which regularly blog on new research that relates to evolution.

Make sure you know about the experiments by Lenski et al on evolution of new genes

Don't take "no proof" as an argument. The evidence is overwhelming.

It's not a terrible scope but it's not really a good one either as you might expect given the low retail price. The good news is that you might have an okay time with it being as you're under dark skies. Dark skies and a cheap scope trumps light pollution and an expensive scope any day and twice on Tuesdays.

The best thing through it will, of course, be the moon.

You should be able to see Jupiter as a bright white disc with the 4 main moons visible as tiny stars beside it. If you're really really lucky, you might see the two highest contrast belts through this scope, but I wouldn't bank on it with this scope.

Saturn will be visible as a small disc with a blurry line representing the rings... something a bit like this

You'll be able to make out the brightest deep sky objects such as the great nebula in Orion, and the Andromeda galaxy as fuzzy gray "clouds". Clusters such as the Pleiades will look great, because they look great through just about anything :-)

I'd recommend you grab a copy of Turn Left at Orion, it's your indispensable guide to viewing and to your next telescope upgrade.

Just to note the 4mm eyepiece that comes with the scope is way too powerful for its aperture, not worth using really, but stick to the 20mm and you'll see some stuff.

Happy viewing!

When I was a sophomore in high school, I was just starting to get interested in philosophy. I took an unusual route, but I can sure recommend some good books that will change how you think!

• This might be above your level, but Evolutionaries by Carter Phipps will certainly change the way you look at the world! Many concepts are explored. It's a great jumping off point to any of the books he references.
  
  
• While this is more pop-philosophy, Richard Brodie's Virus of the Mind is great for your age level. Highly recommended!
  
  
• I'm a huge fan of Nietzsche, and his Beyond Good and Evil is profound and influential. It can make you question some of your most basic assumptions.
  
  
• More science-y but The Elegant Universe by Brian Greene is truly an amazing book that demonstrates just how strange and non-intuitive the universe really is. Natural philosophy at its finest.

Don't trust everything you read online, either. Books are still generally your best bet, because people who might not know what they're talking about can't edit them while you're reading them.

Obviously I'm not saying all books are better than all internets, but find some credible ones and you're much better off.

I'm not a scientist by training, but I can suggest a few books that will provide a pretty good counterbalance to what your mom will be teaching you. (A few of them have quasi-religious-sounding titles, too, so if she happened to find them lying around she might not get too angry.)

The Chosen Species: The Long March of Human Evolution

The Dragons of Eden: Speculations on the Evolution of Human Intelligence

The Demon-Haunted World: Science as a Candle in the Dark

A Brief History of Time

I can recommend more if you'd like. These ones are pretty broad surveys of the topics of (in order) evolution, more evolution, the role of science in society, and the physical nature of the universe. If you're homeschooled, I'm assuming high school-level? None of these books is technical - they're all 'popular science', intended to explain broad concepts to non-scientists. They're very, highly interesting, though, and it's easy to find recommended reading lists once you discover some specific topics that interest you. The Chosen Species itself has a lengthy and detailed bibliography and recommended reading section at the end.

I hope I've been able to help! Good luck!

It's less math intensive in the sense that you won't be solving calculus problems very often (or at all), but there are classes where a (basic) understanding of calculus will be helpful. For instance, I just completed algorithms and was pretty glad that I had taken Calculus. Knowing a lot about limits and knowing L'Hopital's rule made parts of asymptotic analysis a lot more intuitive than it otherwise would have been.

With that said, discrete math (which you'll cover in CS 225) is a pretty big part of the program and computer science as a whole. You'll serve yourself well by getting a solid understanding of discrete math--even in classes where it's not an explicit requirement.

To give an example, in CS 344 (operating systems), there was an assignment where we had to build a pretty simple dungeon-crawler game where a player moved through a series of rooms. Each time the player played the game, there needed to be a new random dungeon, and the connections between rooms needed to be two-way. Calculus isn't really going to help you solve this problem, but if you're good with discrete math, you'll quickly realize that this sort of problem can easily be solved with a graph. Further, you can represent the graph as a 2D array, and at that point the implementation becomes pretty easy.

So, there is math in the program, but not the type that you've probably been doing throughout your academic career. Discrete math comes naturally to some, and it's really difficult for others. I'd recommend picking up this book (which is used in the program) whenever you get a chance:

https://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328

I'm almost done with the program, but I've been returning to that a lot to review concepts we covered in class and to learn new stuff that we didn't have time for in the term. It's a great book.

Good luck!

Quinault and Hoh rainforests are definitely worth your time. I've haven't been to the Queets or Bogacheil yet, so I'm not sure about them but I've been told the Queets is amazing even though there was a fire a ways into it a couple summers ago.

The Quinault valley has many largest of type trees in it. You can hike to the end of the valley to a place called "The Enchanted Valley" that has an old abandoned lodge in it and during the snow melt season has hundreds of waterfalls cascading down the cliffs behind it. It's truly beautiful. I went late spring last year and missed the most impressive melt time, but there were still tons of waterfalls and it was amazingly beautiful. The Olympic coast is also an exquisitely beautiful place to camp. I find the coastal spruce forests to be very magical, if somewhat ominous. My favorite plant book states that "the sharp needles of spruce were believed to give it special powers for protection against evil thoughts." There is definitely something very protective about them. Both the Quinault (some parts, check with the ranger to see if your specific campsite requires) and the coast (all areas) require bear cannisters which you can get for a couple dollar deposit at the Quinault ranger station or in Port Angeles.

The Snoqualmie Middle Fork area is also really awesome and much closer, however it's been mostly logged so the trees aren't massive like they are in ONP.

I also strongly recommend doing some mushroom hunting. In the spring, east of the mountains you can find Morels. I haven't been out morel hunting yet because I don't have a car, but I know they grow on burned areas. In the fall you can find tons of delicious edibles. Chanterelles abound. Make sure you have a good guide.

Closer in is Cougar, Squak and Tiger Mountains in Issaquah. We call them the Issaquah Alps. There're over 100 miles of trails and all three mountains have access within ~1 mile of a bus stop.

Not having a car I don't get far out as often as I'd like so I'm always looking for opportunities to go on nature adventures! Hit me up if you're ever interested.

You should read Richard Dawkin's "The Greatest Show On Earth". Most of chapter 1 is used to explain the scientific use of "theory" and how the pundits manipulate the word to remove authority from it. Here is a large excerpt from the book:

"WHAT IS A THEORY? WHAT IS A FACT?

Only a theory? Let’s look at what ‘theory’ means. The Oxford English Dictionary gives two meanings (actually more, but these are the two that matter here).

Theory, Sense 1: A scheme or system of ideas or statements held as an explanation or account of a group of facts or phenomena; a hypothesis that has been confirmed or established by observation or experiment, and is propounded or accepted as accounting for the known facts; a statement of what are held to be the general laws, principles, or causes of something known or observed.

Theory, Sense 2: A hypothesis proposed as an explanation; hence, a mere hypothesis, speculation, conjecture; an idea or set of ideas about something; an individual view or notion.

Obviously the two meanings are quite different from one another. And the short answer to my question about the theory of evolution is that the scientists are using Sense 1, while the creationists are – perhaps mischievously, perhaps sincerely – opting for Sense 2. A good example of Sense 1 is the Heliocentric Theory of the Solar System, the theory that Earth and the other planets orbit the sun. Evolution fits Sense 1 perfectly. Darwin’s theory of evolution is indeed a ‘scheme or system of ideas or statements’. It does account for a massive ‘group of facts or phenomena’. It is ‘a hypothesis that has been confirmed or established by observation or experiment’ and, by generally informed consent, it is ‘a statement of what are held to be the general laws, principles, or causes of something known or observed’. It is certainly very far from ‘a mere hypothesis, speculation, conjecture’. Scientists and creationists are understanding the word ‘theory’ in two very different senses. Evolution is a theory in the same sense as the heliocentric theory. In neither case should the word ‘only’ be used, as in ‘only a theory’.

As for the claim that evolution has never been ‘proved’, proof is a notion that scientists have been intimidated into mistrusting. Influential philosophers tell us we can’t prove anything in science. Mathematicians can prove things – according to one strict view, they are the only people who can – but the best that scientists can do is fail to disprove things while pointing to how hard they tried. Even the undisputed theory that the moon is smaller than the sun cannot, to the satisfaction of a certain kind of philosopher, be proved in the way that, for example, the Pythagorean Theorem can be proved. But massive accretions of evidence support it so strongly that to deny it the status of ‘fact’ seems ridiculous to all but pedants. The same is true of evolution. Evolution is a fact in the same sense as it is a fact that Paris is in the Northern Hemisphere. Though logic-choppers rule the town, some theories are beyond sensible doubt, and we call them facts. The more energetically and thoroughly you try to disprove a theory, if it survives the assault, the more closely it approaches what common sense happily calls a fact.

I could carry on using ‘Theory Sense 1’ and ‘Theory Sense 2’ but numbers are unmemorable. I need substitute words. We already have a good word for ‘Theory Sense 2’. It is ‘hypothesis’. Everybody understands that a hypothesis is a tentative idea awaiting confirmation (or falsification), and it is precisely this tentativeness that evolution has now shed, although it was still burdened with it in Darwin’s time. ‘Theory Sense 1’ is harder. It would be nice simply to go on using ‘theory’, as though ‘Sense 2’ didn’t exist. Indeed, a good case could be made that Sense 2 shouldn’t exist, because it is confusing and unnecessary, given that we have ‘hypothesis’. Unfortunately Sense 2 of ‘theory’ is in common use and we can’t by fiat ban it. I am therefore going to take the considerable, but just forgivable, liberty of borrowing from mathematics the word ‘theorem’ for Sense 1. It is actually a mis-borrowing, as we shall see, but I think the risk of confusion is outweighed by the benefits. As a gesture of appeasement towards affronted mathematicians, I am going to change my spelling to ‘theorum’. First, let me explain the strict mathematical usage of theorem, while at the same time clarifying my earlier statement that, strictly speaking, only mathematicians are licensed to prove anything (lawyers aren’t, despite well-remunerated pretensions).

To a mathematician, a proof is a logical demonstration that a conclusion necessarily follows from axioms that are assumed. Pythagoras’ Theorem is necessarily true, provided only that we assume Euclidean axioms, such as the axiom that parallel straight lines never meet. You are wasting your time measuring thousands of right-angled triangles, trying to find one that falsifies Pythagoras’ Theorem. The Pythagoreans proved it, anybody can work through the proof, it’s just true and that’s that. Mathematicians use the idea of proof to make a distinction between a ‘conjecture’ and a ‘theorem’, which bears a superficial resemblance to the OED’s distinction between the two senses of ‘theory’. A conjecture is a proposition that looks true but has never been proved. It will become a theorem when it has been proved. A famous example is the Goldbach Conjecture, which states that any even integer can be expressed as the sum of two primes. Mathematicians have failed to disprove it for all even numbers up to 300 thousand million million million, and common sense would happily call it Goldbach’s Fact. Nevertheless it has never been proved, despite lucrative prizes being offered for the achievement, and mathematicians rightly refuse to place it on the pedestal reserved for theorems. If anybody ever finds a proof, it will be promoted from Goldbach’s Conjecture to Goldbach’s Theorem, or maybe X’s Theorem where X is the clever mathematician who finds the proof."

Now, if you managed to read all that. I definitely recommend buying it: http://www.amazon.com/Greatest-Show-Earth-Evidence-Evolution/dp/1416594787/ref=sr_1_1?ie=UTF8&s=books&qid=1269444004&sr=8-1

It really is an education.

http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?ie=UTF8&qid=1342068971&sr=8-1&keywords=spivak%27s+calculus

This book starts with basic properties of numbers (associativity, commutativity, etc), then moves onto some proof concepts followed by a very good foundation (functions, vectors, polar coordinate). Be forewarned that the content is VERY challenging in this book, and will definitely require a determined effort, but it will certainly be good if you can get through it.

A more gentle introduction to Calculus is http://www.amazon.com/Thomas-Calculus-12th-George-B/dp/0321587995/ref=sr_1_1?s=books&ie=UTF8&qid=1342069166&sr=1-1&keywords=thomas%27+calculus and it is a much easier book, but you don't prove much in this one. Both of these can likely be found online for free. Also, if you want to get a decent understanding I recommend, http://www.amazon.com/How-Prove-Structured-Daniel-Velleman/dp/0521675995/ref=sr_1_1?s=books&ie=UTF8&qid=1342069253&sr=1-1&keywords=how+to+prove+it or http://www.people.vcu.edu/~rhammack/BookOfProof/index.html the latter is definitely free.

You may also need a more introductory text for trig and functions. I can't find the book my school used for precalc, hopefully someone else can offer a good recommendation.

Also, getting a dummies book to read alongside was pretty helpful for me, and Paul's online notes(website) is very nice.

Depends on what you are looking for. You might not be aware that the concepts in that book are literally the foundations of math. All math is (or can be) essentially expressed in set theory, which is based on logic.

You want to improve math reasoning, you should study reasoning, which is logic. It's really not that hard. I mean, ok its hard sometimes but its not rocket science, its doable if you dedicate real time to it and go slowly.

Two other books you may be interested in instead, that teach the same kinds of things:

Introduction to Mathematical Thinking which he wrote to use in his Coursera course.

How to Prove It which is often given as the gold standard for exactly your question. I have it, it is fantastic, though I only got partway through it before starting my current class. Quite easy to follow.

Both books are very conversational -- I know the second one is and I'm pretty sure the first is as well.

What books like this do is teach you the fundamental logical reasoning and math structures used to do things like construct the real number system, define operations on the numbers, and then build up to algebra step by step. You literally start at the 1+1=2 type level and build up from there by following a few rules.

Also, I just googled "basic logic" and stumbled across this, it looks like a fantastic resource that teaches the basics without any freaky looking symbols, it uses nothing but plain-English sentences. But scanning over it, it teaches everything you get in the first chapter or two of books like those above. http://courses.umass.edu/phil110-gmh/text/c01_3-99.pdf

Honestly if I were starting out I would love that last link, it looks fantastic actually.

Two general types of experience you can get: hands-on, and book learning.

The former is very important, but not too difficult to do. A fair number of people in the Portland area go mushroom hunting occasionally, even if they only know a species of two. Sucking up to the right people is surprisingly effective. Also, getting in touch with or joining organizations like Oregon Mycological Society or the Cascade Mycological Society can be immensely helpful in making contacts and finding hunting partners/mentors.

The latter is also very important, as there is some much you can learn without actually holding a mushroom in your hands. For books, accessible guides like Mushrooms of the Pacific Northwest and All That the Rain promises and More are great for getting started, and heftier books like Mushrooms Demystified are good for those looking to take the next step in learning. Online, the hunting and identification board on The Shroomery, Mushroom Observer, and /r/mycology are great places to lurk and just soak in info, while sites like Mushroom Expert are good places to explore and follow what interests you.

> I wonder if humanities curious nature towards mysticism is inevitable and that all paths, no matter how diverse, will always use the same formats and formulas to tell their tales.

This is one of the central tenants of Jung's research (well you know "research") and Joseph Cambell basically wrote the book about it... https://www.amazon.com/Thousand-Faces-Collected-Joseph-Campbell/dp/1577315936 sorry if Im being didactic/eg if you already knew that... its a really facinating question/idea. As far as "Embedded in our DNA" eg for a more scientific approach this book is AMAZING https://www.amazon.com/Origin-Consciousness-Breakdown-Bicameral-Mind/dp/0618057072, even though it does veer from the purely scientific, the idea is that our brains have certain regions which act on our spiritual relationship to our "gods" which manifested themselves as voices in our earlier evolutionary states and that as we became more rational our brains still retained these functional but at the same time "disfunctional" anatomy leading to experiances that result for some in uncontrollable states, like schizophrenics for example ... the way he "proves" all of this stuff is a comparison of his experiments in neuroscience with historical texts, legends, sagas, and other implements of earlier humanity like archeological finds. if you are interested in this topic this is an absolutely Mindblowing book right here just saying!


Finally:
"Is this part of our evolutionary growth or yearning for divinity?
Our ego's thirst for magical power or trying to step out of our physical limitations?" I think you are right in that we yearn because, I beleive at least, our evolutionary state has one foot in the past and one in the future, we have evolved beyond our normal need for mere survival and we now use our brains for complex creation and navigation of human institutions but we dont really know "why", we dont really know what meaning is becuase "meaning" is a brand new thing! and without it the universe seems devoid of purpose and therefore I beleive we fill in those gaps with these notions and art, music etc, art and literature helps us define ourselves and music helps us 'engage' with the harmonics/vibrations of the universe on deeper levels (as it is really the only category here that actually relies on the schientific make up of the universe i.e. the ways that ratios of harmonic waves sound pleasing or displeasing based on their relationships in time...). I just love this stuff, am also agnostic but love to celebrate all ideas no matter how objectively "wrong" they may be, thats of c why Im on this sub! Love your questions/keep on searching!!!

First, let me compliment you on a fascinating list. There are some truly great books in there. I'm both impressed and delighted. Based on your choices, I would recommend the following.


Catch-22 by Joseph Hellar. Even more so than Slaughterhouse-Five, this is the quintessential anti-war novel. A hugely influential 20th century masterpiece. And laugh-out-loud funny in parts too!

The Making of the Atomic Bomb by Richard Rhodes is a deserved winner of the Pulitzer Prize. Engrossing, erudite, insightful and educational narrative history of this hugely important event in 20th century history - reads like a novel. Covers not only the Allies, but also the German and (very often overlooked) Japanese side to the story.


Sacred Games by Vikram Chandra, just because of its sweeping scope. Very entertaining modern novel set in India. Touches upon topics and themes as diverse as modern Indian organized crime, international terrorism, Bollywood, the 1948 Partition, Maoist rebels, the caste system, corruption in Indian film, police and government... the list goes on and on. Great fun, and eye-opening.


A Hundred Years of Solitude by Gabriel Marcia Marquez. Whilst not the original "magic realism" novel (despite what Marquez himself my imply), this is the first one to gain international acclaim and is a very influential work. Entertaining in so many ways. Follow the history of the fictional town of Maconda for a hundred years and the lives (the crazy, multifaceted lives) of its inhabitants.


Waiting for Godot by Samuel Beckett. This is a play, not a novel, and one translated from the French at that. Don't let that put you off. Existentialism has never been so interesting...


The Greatest Show on Earth by Richard Dawkins. His latest tour-de-force.


Manufacturing Consent by Noam Chomsky. Dare I say that this expose on how Government and Big Business control public debate and the media is so important, was more influential than Chomsky's review of Skinner's verbal behaviour? Perhaps not. But a very important work none-the-less.

Overviews of the evidence:

The greatest show on earth

Why evolution is true

Books on advanced evolution:

The selfish gene

The extended phenotype

Climbing mount improbable

The ancestors tale

It is hard to find a better author than Dawkins to explain evolutionary biology. Many other popular science books either don't cover the details or don't focus entirely on evolution.

I will hit one point though.

>I have a hard time simply jumping from natural adaption or mutation or addition of information to the genome, etc. to an entirely different species.

For this you should understand two very important concepts in evolution. The first is a reproductive barrier. Basically as two populations of a species remain apart from each other (in technical terms we say there is no gene flow between them) then repoductive barriers becomes established. These range in type. There are behavioral barriers, such as certain species of insects mating at different times of the day from other closely related species. If they both still mated at the same time then they could still produce viable offspring. Other examples of behavior would be songs in birds (females will only mate with males who sing a certain way). There can also be physical barriers to reproduction, such as producing infertile offspring (like a donkey and a horse do) or simply being unable to mate (many bees or flies have different arrangements of their genitalia which makes it difficult or impossible to mate with other closely related species. Once these barriers exist then the two populations are considered two different species. These two species can now further diverge from each other.

The second thing to understand is the locking in of important genes. Evolution does not really take place on the level of the individual as most first year biology courses will tell you. It makes far more sense to say that it takes place on the level of the gene (read the selfish gene and the extended phenotype for a better overview of this). Any given gene can have a mutation that is either positive, negative, of neutral. Most mutations are neutral or negative. Let's say that a certain gene has a 85% chance of having a negative mutation, a 10% chance of a neutral mutation, and a 5% chance of a positive mutation. This gene is doing pretty good, from it's viewpoint it has an 85% chance of 'surviving' a mutation. What is meant by this is that even though one of it's offspring may have mutated there is an 85% chance that the mutated gene will perform worse than it and so the mutation will not replace it in the gene pool. If a neutral mutation happens then this is trouble for the original gene, because now there is a gene that does just as good a job as it in the gene pool. At this point random fluctuations of gene frequency called genetic drift take over the fate of the mutated gene (I won't go into genetic drift here but you should understand it if you want to understand evolution).

The last type of mutation, a positive mutation is what natural selection acts on. This type of mutation would also change the negative/neutral/positive mutation possibilities. so the newly positively mutated gene might have frequencies of 90/7/3 Already it has much better odds than the original gene. OK, one more point before I explain how this all ties together. Once a gene has reached the 100/0/0 point it does not mean that gene wins forever, there can still be mutations in other genes that affect it. A gene making an ant really good at flying doesn't matter much when the ant lives in tunnels and bites off its own wings, so that gene now has altered percentages in ants. It is this very complex web that makes up the very basics of mutations and how they impact evolution (if you are wondering how common mutations are I believe they happen about once every billion base pairs, so every human at conception has on average 4 mutations that were not present in either parent)

This all ties back together by understanding that body plan genes (called hox genes) lock species into their current body plans, by reducing the number of possible positive or neutral mutations they become crucial to the organisms survival. As evolutionary time progresses these genes become more and more locked in, meaning that the body plans of individuals become more and more locked in. So it is no wonder that coming in so late to the game as we are we see such diversity in life and we never see large scale form mutations. Those type of mutations became less likely as the hox genes became locked in their comfy spots on the unimpeachable end of the mutation probability pool. That is why it is hard to imagine one species evolving into another, and why a creationist saying that they will believe evolution when a monkey gives birth to a human is so wrong.

Hopefully I explained that well, it is kind of a dense subject and I had to skip some things I would rather have covered.

Regardless of the OPs eventual interests there's a reason we start with Newtonian stuff in most 101 type courses. I think its reasonable for OP to start there if they are serious, my recommendations are:

IF OP WANTS TO LEARN PHYSICS

• go through this Classical Mechanics course. While I haven't used this one in particular I can vouch for the quality and clarity of Walter Lewin's teaching.
  
  
• Make sure you use the associated problem sets with any course you choose. The importance of solving actual problems can not be over emphasized.
  
  
• When you find yourself struggling with the math (I promise that you will eventually) make sure you take the time to go learn some of the mathematics, if you like the MIT courses I think their math department also has lots of resources online.
  
  
• Stick to a study schedule. Physics is fun but treat it like a sport, you can do it for fun but you won't get anywhere if you never practice
  
  IF OP IS WANTS TO LEARN ABOUT PHYSICS
  
  
• Feynman Lectures are a great middle ground between a rigor and accessibility. I highly recommend these for a fun way to learn the basics
  
  
• Hawking's books are great reads
  
  
• Cosmos was a wonderful series
  
  
• If you want flashy and motivating, check out Brian Greene's stuff.
  
  
  
  From there, op can look at different fields, biophysics seems like it would be the most likely candidate in which case OP might also want to brush up on organic chemistry and learn how to use MATLAB.

> Are the deep mathematical answers to things usually very complex or insanely elegant and simple when you get down to it?

I would say that the deep mathematical answers to questions tend to be very complex and insanely elegant at the same time. The best questions that mathematicians ask tend to be the ones that are very hard but still within reach (in terms of solving them). The solutions to these types of questions often have beautiful answers, but they will generally require lots of theory, technical detail, and/or very clever solutions all of which can be very complex. If they didn't require something tricky, technical, or the development of new theory, they wouldn't be difficult to solve and would be uninteresting.

For any experts that happen to stumble by, my favorite example of this is the classification of semi-stable vector bundles on the complex projective plane by LePotier and Drezet. At the top of page 7 of this paper you'll see a picture representing the fractal structure that arises in this classification. Of course, this required a lot of hard math and complex technical detail to come up with this, but the answer is beautiful and elegant.

> How hard would it be for a non mathematician to go to a pro? Is there just some brain bending that cannot be handled by some? How hard are the concepts to grasp?

I would say that it's difficult to become a professional mathematician. I don't think it has anything to do with an individual's ability to think about it. The concepts are difficult, certainly, but given time and resources (someone to talk to, good books, etc) you can certainly overcome that issue. The majority of the difficulty is that there is so much math! If you're an average person, you've probably taken at most Calculus. The average mathematics PhD (i.e., someone who is just getting their mathematical career going) has probably taken two years of undergraduate mathematics courses, another two years of graduate mathematics courses, and two to three years of research level study beyond calculus to begin to be able tackle the current theory and solve the problems we are interested in today. That's a lot of knowledge to acquire, and it takes a very long time. That doesn't mean you can't start solving problems earlier, however. If you're interested in this type of thing, you might want to consider picking up this book and see if you like it.

Copying my answer from another post:


I was literally in the bottom 14th percentile in math ability when i was 12.

One day, by pure chance, i stumbled across this (free and open) book written by Carl Stitz and Jeff Zeager, of Lakeland Community College

Precalculus

It covers everything from elementary algebra (think grade 5), all the way up to concepts used in Calculus and Linear Algebra (Partial fractions and matrix algebra, respectively.) The book is extremely well organized. Every sections starts with a dozen or so pages of proofs and derivations that show you the logic of why and how the formulas you'll be using work. This book, more than any other resource (and i've tried a lot of them), helped me build my math intuition from basically nothing.


Math is really, really intimidating when you've spent your whole life sucking at it. This book addresses that very well. The proofs are all really well explained, and are very long. You'll basically never go from one step to the next and be completely confused as to how they got there.


Also, there is a metric shitload of exercises, ranging from trivial, to pretty difficult, to "it will literally take your entire class working together to solve this". Many of the questions follow sort of an "arc" through the chapters, where you revisit a previous problem in a new context, and solve it with different means (Also, Sasquatches. You'll understand when you read it.)


I spent 8 months reading this book an hour a day when i got home from work, and by the end of it i was ready for college. I'm now in my second year of computer science and holding my own (although it's hard as fuck) against Calculus II. I credit Stitz and Zeager entirely. Without this book, i would never have made it to college.


Edit: other resources

Khan Academy is good, and it definitely complements Stitz/Zeager, but Khan also lacks depth. Like, a lot of depth. Khan Academy is best used for the practice problems and the videos do a good job of walking you through application of math, but it doesn't teach you enough to really build off of it. I know this from experience, as i completed all of Khan's precalculus content. Trust me, Rely on the Stitz book, and use Khan to fill in the gaps.


Paul's Online Math Notes

This website is so good it's ridiculous. It has a ton of depth, and amazing reference sheets. Use this for when you need that little extra detail to understand a concept. It's still saving my ass even today (Damned integral trig substitutions...)

Stuff that's more important than you think (if you're interested in higher math after your GED)

Trigonometric functions: very basic in Algebra, but you gotta know the common values of all 6 trig functions, their domains and ranges, and all of their identities for calculus. This one bit me in the ass.

Matrix algebra: Linear algebra is p. cool. It's used extensively in computer science, particularly in graphics programming. It's relatively "easy", but there's more conceptual stuff to understand.


Edit 2: Electric Boogaloo

Other good, cheap math textbooks

/u/ismann has pointed out to me that Dover Publications has a metric shitload of good, cheap texts (~$25CAD on Amazon, as low as a few bucks USD from what i hear).

Search up Dover Mathematics on Amazon for a deluge of good, cheap math textbooks. Many are quite old, but i'm sure most will agree that math is a fairly mature discipline, so it's not like it makes a huge difference at the intro level. Here is a Math Overflow Exchange list of the creme de la creme of Dover math texts, all of which can be had for under $30, often much less. I just bought ~1,000 pages of Linear Algebra, Graph Theory, and Discrete Math text for $50. If you prefer paper to .pdf, this is probably a good route to go.

Also, How to Prove it is a very highly rated (and easy to read!) introduction to mathematical proofs. It introduces the basic logical constructs that mathematicians use to write rigorous proofs. It's very approachable, fairly short, and ~$30 new.

I've always enjoyed all types of math but all throughout (engineering) undergrad and grad school all I ever got to do was computational-based math, i.e. solving problems. This was enjoyable but it wasn't until I learned how to read and write proofs (by self-studying How to Prove It) that I really fell in love with it. Proofs are much more interesting because each one is like a logic puzzle, which I have always greatly enjoyed. I also love the duality of intuition and rigorous reasoning, both of which are often necessary to create a solid proof. Right now I'm going back and self-studying Control Theory (need it for my EE PhD candidacy but never took it because I was a CEG undergrad) and working those problems is just so mechanical and uninteresting relative to the real analysis I study for fun.

EDIT: I also love how math is like a giant logical structure resting on a small number of axioms and you can study various parts of it at various levels. I liken it to how a computer works, which levels with each higher level resting on those below it. There's the transistor level (loosely analogous to the axioms), the logic gate level, (loosely analogous set theory), and finally the high level programming language level (loosely analogous to pretty much everything else in math like analysis or algebra).

First off, one does not have to understand evolution to be an atheist. Common misconception.

If you'd like to truly understand evolution, you must be knowledgeable in what evolution is, what evolution is not and the driving mechanics that make it work.

Now what is evolution?

Evolution refers to the change in the frequencies of certain alleles within an interbreeding population of organisms. What the word allele refers to are the acting components of a gene such as, in simple terms, whether someone is short or tall.

Each person carries two copies of each allele and they may be the same or they may be different but each copy is one of two things: dominant or recessive. When two organisms reproduce, one of the two copies from each parent goes to the offspring. If the parents have two dominant alleles for a trait, such as height, their offspring will have the dominant trait. In this instance they would be tall. If they have the recessive versions, they would be short and if they have one of each they would be medium size, which is called heterozygous expression. That's your simple crash course in heredity.

Now how do alleles come about?

This variation can happen in several different ways, such as:

• Mutation: A mutation occurs when the genetic code is changed. This can happen via an external source, like solar radiation, or an internal source, like the DNA being copied wrong when a cell divides. Each time a mutation happens, it can have one of three results: nothing happens, the effect of the gene can be changed or the gene can stop working.
  
  
• Sex and Recombination: This applies to sexual organisms (duh) and refers to the refers to the reorganizing of which alleles match to which. This is in opposition to the linked genome (things don't get reorganized) of asexual organisms.
  
  
• Genetic Drift: This refers to the the exchange of genes between populations and between species. Think for instance about our tall and short alleles from earlier. Say that one population that really only breeds with itself has only the short allele. One day they meet up with another group of similar organisms that they can breed with and they only have the tall allele. As a result, the missing allele becomes present in the other population.
  
  Well, that's fine and dandy, Mr. Montuckian, but these organisms aren't evolving from frogs into birds now are they? No kids, they're not. Not yet at least. You need to apply the mechanisms of evolution to them to make that happen. These are made up of the following:
  
  
• Selection: A lot of people separate this concept into Artificial and Natural Selection. They are the same thing. Basically, when you have a varied population, some organisms will have traits that provide them with a selective advantage when it comes to their environments. Tall organisms may be better able to access food, while shorter organisms may better conserve heat. Depending on the environment, a tall or a short organism may be better able to survive and reproduce, which creates more creatures with the adaptive genotype and fewer with the maladaptive genotype.
  
  
• Sexual Selection: Sometimes genes are chosen because they are preferred by a species but don't have an adaptive purpose necessarily. We've all got our fetishes after all.
  
  Eventually, and sometimes this can take a very long time, new 'species' are created. But like using the word 'code' to refer to DNA, 'species' is a word that we apply to biology and it's not entirely appropriate. The idea of separate 'species' is borne out of the idea of The Great Chain of Being. This idea says that all animals are organized into a hierarchy of greater or lesser organisms with little stuff like bacteria and bugs at the bottom, mammals toward the middle, people higher than that and celestial gods and angels above that. Not a real scientific sort of idea, if you ask me. In reality, and this is the cool thing, we're all really part of the same tree and if we were to go back and look at you, your parents, your grandparents and so on as a sort of flip book, you would see little tiny variations that lead back to the beginning! It's hard to see these in a single generation though, which I think leads people to dispute the fact that it is, in fact happening.
  
  And this brings me to my final point:
  
  *What isn't* evolution?
  
  Evolution is not:
  
  
• Abiogenesis: This is the idea that life emerges from non-life. While many evolutionary biologists think that this is probably how life began, with errant proteins reassembling themselves and reproducing, it's not a tenet of evolution.
  
  
• The Big Bang Theory: That's a cosmological model and a crappy sitcom. Neither of which have a whole lot of life associated with them.
  
  
• Atheism: Atheism is simply the refusal to believe the assertions of theists that there are supernatural beings. While many atheists point to evolution as the most probable method that we know of for the creation of Man, they are wholly unrelated.
  
  Hopefully this gives you a clearer picture of what it means to understand evolution. There are plenty of great books out there, such as Dawkins' The Greatest Show on Earth that can give you a more in depth explanation of the caveats and nuances of evolutionary theory.
  
  Edit: A few text and clarity things.

Griffiths is the go-to for advanced undergraduate level texts, so you might consider his Introduction to Quantum Mechanics and Introduction to Particle Physics. I used Townsend's A Modern Approach to Quantum Mechanics to teach myself and I thought that was a pretty good book.

I'm not sure if you mean special or general relativity. For special, /u/Ragall's suggestion of Taylor is good but is aimed an more of an intermediate undergraduate; still worth checking out I think. I've heard Taylor (different Taylor) and Wheeler's Spacetime Physics is good but I don't know much more about it. For general relativity, I think Hartle's Gravity: An Introduction to Einstein's General Relativity and Carroll's Spacetime and Geometry: An Introduction to General Relativity are what you want to look for. Hartle is slightly lower level but both are close. Carroll is probably better if you want one book and want a bit more of the math.

Online resources are improving, and you might find luck in opencourseware type websites. I'm not too knowledgeable in these, and I think books, while expensive, are a great investment if you are planning to spend a long time in the field.

One note: teaching yourself is great, but a grad program will be concerned if it doesn't show up on a transcript. This being said, the big four in US institutions are Classical Mechanics, E&M, Thermodynamics/Stat Mech, and QM. You should have all four but you can sometimes get away with three. Expectations of other courses vary by school, which is why programs don't always expect things like GR, fluid mechanics, etc.

I hope that helps!

​

>Because you sound like a middle schooler who tried weed for the first time, and gets the million dollar idea that all mind-altering drugs are good because you dissociated for an hour.

I'm actually sharing second-hand the scholarship of Timothy Leary, as well as Carl Sagan's writing in Demon-Haunted World: Science as a Candle in the Dark, which is a phenomenal book. The ideas are certainly not mine, though I do agree with them. I came across them because I was formerly a professor of rhetoric and composition and used counterculture as a topic of study for some of my classes and thus became interested in the psychedelic movement.

I've also never dissociated. Some people depersonalize while taking psychedelics, but I've never experienced that, either. Dissociation is more something you might expect from Ketamine or large doses of DXM. If anything, used responsibly by psychologically healthy people with fully formed brains, psychedelics connect you further with yourself and the world around you, not the other way around.

>Slowing down your synapses and making yourself see things in slow motion or fancy colors isn't going to make you or the population as a whole more enlightened.

This is just not how psychedelics work. Visuals are a very small aspect of the experience. They're also, by far, the most underwhelming aspect. Ideally, if you're doing psychedelics right, you never see anything that isn't there or doesn't really exist, you just notice details and patterns in things that are there everyday, but you usually don't notice.

But that's beside the point. The true value of the psychedelic experience is in the cognitive and emotional component.

Take the work or neuroscientist Andrew Newberg, for example, which demonstrates that brain activity in people tripping on psilocybin is roughly the same as that of mystics and religious clerics engaged in deep meditation or prayer. Or you could look at the various peer reviewed, scholarly studies that demonstrate the dramatic effects of psychedelics on prosocial behavior and psychological function.

If you think psychedelics are still fodder for basement dwelling hippie hangers-on who can't let go of the good old Haight-Ashbury days, you're just kind of behind the times. A lot has happened since then. You should catch up. It's interesting stuff.

>There have already been places where drugs were decriminalized entirely, like Portugal, where people actually started weaning themselves off of them and overall using psychedelics less because, believe it or not, constantly altering your mind with substances is unhealthy. As far as I understand the "euphoria" that was liberated there didn't cause a cultural renaissance either.

Portugal decriminalized drugs as a radical solution to their rampant issues with opioid addiction, but mostly to curb the country's HIV epidemic due to rampant IV drug use. It had basically nothing to do with psychedelics.

Simply put, psychedelics have never been particularly available or popular in Portugal, so to use them as your measuring stick is an odd choice. Portugal is better suited for an argument about relaxing drug laws to reduce overdoses and IV drug related diseases, as well as create better access to treatment options.

The example you're looking for would likely be the Haight-Ashbury in the 1960's, which was an absolute mess. But honestly, psychedelics weren't as much to blame for that as stimulants, opioids, PTSD, other forms mental illness, and the fact that most of the people in the Haight at the time were teenagers. Speaking contemporarily, San Francisco is the highest-ranking American city in terms of overall quality of life according to the Mercer Quality of Living Survey, so do with that what you will.

>All you're doing is highlighting how different attitudes towards substances here are, and how people could get hurt.

Look, I've studied this shit, both experientially and academically. You may not agree with me, and that's fine, but I really don't think I'm the one of the two of us who has weird, misguided ideas about psychedelics and how they work.

Psychedelics are not addictive, have incredibly high overdose thresholds that are nearly impossible to meet, and when used responsibly, have seriously positive applications in the psychological and social sciences, namely when used in conjunction with cognitive behavioral therapy in the care of trained professionals. The fact that you think this is middle-school philosophizing really says more about you than it does about me or psychedelics, namely that you don't know very much about psychedelics.

Lastly, here's a pro-tip for your cake day: when you go ad-hominem against someone with no substantive argument to follow, and they say, "Go on...", probably don't actually go on.

Luna and Jupiter will look fantastic.

With Jupiter you should more than be able to see all four moons pretty well and the bands should be faint but visible. Give your eyes time to adjust and make sure you're in a nice dark place. I'm sure that goes without saying but it can't hurt to reinforce the concept.

That is a great starter scope. Get yourself a good star atlas, I really recommend NightWatch: A Practical Guide to Viewing the Universe as a starter (http://www.amazon.com/NightWatch-Practical-Guide-Viewing-Universe/dp/155407147X/ref=sr_1_2?ie=UTF8&qid=1324071016&sr=8-2). It has good seasonal star charts and lots of practical info about viewing the sky.

I really hope you enjoy the scope and please do post a follow up on the performance and your experiences.

I notice you said you are in CST Time Zone. Where are you located. If you are in the Houston Area we should get a little star party set up with fellow redditors.

I'm assuming you're looking for things geared toward a layman audience, and not textbooks. Here's a few of my personal favorites:

Sagan

Cosmos: You probably know what this is. If not, it is at once a history of science, an overview of the major paradigms of scientific investigation (with some considerable detail), and a discussion of the role of science in the development of human society and the role of humanity in the larger cosmos.

Pale Blue Dot: Similar themes, but with a more specifically astronomical focus.


Dawkins

The Greatest Show on Earth: Dawkins steers (mostly) clear of religious talk here, and sticks to what he really does best: lays out the ideas behind evolution in a manner that is easily digestible, but also highly detailed with a plethora of real-world evidence, and convincing to anyone with even a modicum of willingness to listen.


Hofstadter

Godel, Escher, Bach: An Eternal Golden Braid: It seems like I find myself recommending this book at least once a month, but it really does deserve it. It not only lays out an excruciatingly complex argument (Godel's Incompleteness Theorem) in as accessible a way as can be imagined, and explores its consequences in mathematics, computer science, and neuroscience, but is also probably the most entertainingly and clearly written work of non-fiction I've ever encountered.


Feynman

The Feynman Lectures on Physics: It's everything. Probably the most detailed discussion of physics concepts that you'll find on this list.

Burke

Connections: Not exactly what you were asking for, but I love it, so you might too. James Burke traces the history of a dozen or so modern inventions, from ancient times all the way up to the present. Focuses on the unpredictability of technological advancement, and how new developments in one area often unlock advancements in a seemingly separate discipline. There is also a documentary series that goes along with it, which I'd probably recommend over the book. James Burke is a tremendously charismatic narrator and it's one of the best few documentary series I've ever watched. It's available semi-officially on Youtube.

Thanks for the answer!

Glad to hear about Spivak! I've heard good things about that textbook and am looking forward to going through it soon :). Are the course notes for advanced algebra available online? If so, could you link them?

Is SICP used only in the advanced CS course or the general stream one, too? (last year I actually worked my way through the first two chapters before getting distracted by something else - loved it though!) Also, am I correct in thinking that the two first year CS courses cover functional programming/abstraction/recursion in the first term and then data structures/algorithms in the second?

That's awesome to know about 3rd year math courses! I was under the impression that prerequisites were enforced very strongly at Waterloo, guess I was wrong :).

As for graduate studies in pure math, that's the plan, but I in no way have my heart set on anything. I've had a little exposure to graph theory and I loved it, I'm sure that with even more exposure I'd find it even more interesting. Right now I think the reason I'm leaning towards pure math is 'cause the book I'm going through deals with mathematical logic / set theory and I think it's really fascinating, but I realize that I've got 4/5 years before I will even start grad school so I'm not worrying about it too much!

Anyways, thanks a lot for your answer! I feel like I'm leaning a lot towards Waterloo now :)

You sound like a great audience for the series I recommend to everyone in your position: Lenny Susskind's Theoretical Minimum. He's got free lectures and accompanying books which are designed with the sole purpose of getting you from zero to sixty as fast as possible. I'm sure others will have valuable suggestions, but that's mine.

The series is designed for people who took some math classes in college, and maybe an intro physics class, but never had the chance to go further. However, it does assume that you are comfortable with calculus, and more doesn't hurt. What's your math background like?

As to the LHC and other bleeding-edge physics: unfortunately, this stuff takes a lot of investment to really get at, if you want to be at the level where you can do the actual derivations—well beyond where an undergrad quantum course would land you. If you're okay with a more heuristic picture, you could read popular-science books on particle physics and combine that with a more quantitative experience from other sources.

But if you are thinking of doing this over a very long period of time, I would suggest that you could pretty easily attain an advanced-undergraduate understanding of particle physics through self-study—enough to do some calculations, though the actual how and why may not be apparent. If you're willing to put in a little cash and more than a little time for this project, here's what I suggest:

• Pick up a book on introductory physics (with calculus). It doesn't really matter which. Make sure you're good with the basic concepts—force, momentum, energy, work, etc.
  
  
• Learn special relativity. It does not take too long, and is not math-intensive, but it can be very confusing. There are lots of ways to do it—lots of online sources too. My favorite book for introductory SR is this one.
  
  
• Use a book or online resources to become familiar with the basics (just the basics) of differential equations and linear algebra. It sounds more scary than it is.
  
  
• Get a copy of Griffiths' books on quantum mechanics and particle physics. These are undergrad-level textbooks, but pretty accessible! Read the quantum book first—and do at least a few exercises—and then you should be able to get a whole lot out of reading the particle physics book.
  
  Note that this is sort of the fastest way to get into particle physics. If you want to take this route, you should still be prepared to spread it out over a couple years—and it will leave a whole smattering of gaps in your knowledge. But hey, if you enjoy it, you could legitimately come to understand a lot about the universe through self-study!

Random selection of some of my favorites to help you expand your horizons:

The Demon-Haunted World by Carl Sagan is a great introduction to scientific skepticism.

Letter to a Christian Nation by Sam Harris is a succinct refutation of Christianity as it's generally practiced in the US employing crystal-clear logic.

Augustus: The Life of Rome's First Emperor by Anthony Everitt is the best biography of one of the most interesting men in history, in my personal opinion.

Travels with Herodotus by Ryszard Kapuscinski is a jaw-dropping book on history, journalism, travel, contemporary events, philosophy.

A Short History of Nearly Everything by Bill Bryson is a great tome about... everything. Physics, history, biology, art... Plus he's funny as hell. (Check out his In a Sunburned Country for a side-splitting account of his trip to Australia).

The Annotated Mona Lisa by Carol Strickland is a thorough primer on art history. Get it before going to any major museum (Met, Louvre, Tate Modern, Prado, etc).

Not the Impossible Faith by Richard Carrier is a detailed refutation of the whole 'Christianity could not have survived the early years if it weren't for god's providence' argument.

Six Easy Pieces by Richard Feynman are six of the easier chapters from his '63 Lectures on Physics delivered at CalTech. If you like it and really want to be mind-fucked with science, his QED is a great book on quantum electrodynamics direct from the master.

Lucy's Legacy by Donald Johanson will give you a really great understanding of our family history (homo, australopithecus, ardipithecus, etc). Equally good are Before the Dawn: Recovering the Lost History of Our Ancestors by Nicholas Wade and Mapping Human History by Steve Olson, though I personally enjoyed Before the Dawn slightly more.

Memory and the Mediterranean by Fernand Braudel gives you context for all the Bible stories by detailing contemporaneous events from the Levant, Italy, Greece, Egypt, etc.

After the Prophet by Lesley Hazleton is an awesome read if you don't know much about Islam and its early history.

Happy reading!

edit: Also, check out the Reasonable Doubts podcast.

I'm also an xt6 owner.

For software, you can't go wrong with Stellarium. It's free, and it lets you choose your location as well as time and date. Very handy.

For reading material, these two books have served me well:

Nightwatch: contains loads of stargazing tips and general astronomy information. Also contains star charts, and detailed charts of select constellations.


Binocular Highlights: I find myself using this one all the time. Its focus is on binocular astronomy, but you can use it with a telescope as it's a sort of "best-of" of the night sky. Each object has a detailed, zoomed-in map and a brief description. Contains star charts for every season, with every object in the book marked on the charts.


For photography, you'll only really be able to take decent pictures of the Moon and the brighter planets. As others have pointed out, you'll need some fancier equipment to take good pictures of deep-sky objects.


Just for fun, here are some of my favorite objects:




The Orion Nebula (M42): under the heavily light-polluted skies of my backyard, still fuzzy and nebula-like. Glorious under dark skies, when the dusty arms and finer details become apparent.

Andromeda Galaxy (M31): Looks like a big hazy smudge through the eyepiece. Its companion (M32, I think) is also visible in the same field of view.

Ring Nebula (M57): Even under light-polluted skies, I can pick this one out pretty easily by star-hopping. Looks like a small, blue donut.

Double Cluster: absolutely brilliant collection of stars in a single field of view.

Pick up mathematics. Now if you have never done math past the high school and are an "average person" you probably cringed.

Math (an "actual kind") is nothing like the kind of shit you've seen back in grade school. To break into this incredible world all you need is to know math at the level of, say, 6th grade.

Intro to Math:

1. Book of Proof by Richard Hammack. This free book will show/teach you how mathematicians think. There are other such books out there. For example,
   
   

• How to Prove It: A Structured Approach by Daniel Velleman
  
  
• Mathematical Proofs: A Transition to Advanced Mathematics by Gary Chartrand et al
  
  
• Discrete Mathematics with Applications by Susanna Epp
  
  These books only serve as samplers because they don't even begin to scratch the surface of math. After you familiarized yourself with the basics of writing proofs you can get started with intro to the largest subsets of math like:
  
  Intro to Abstract Algebra:
  
  
• Linear Algebra: Step by Step by Singh
  
  
• Abstract Algebra: A Student-Friendly Approach by the Dos Reis
  
  
• Numbers and Symmetry: An Introduction to Algebra by Johnston/Richman
  
  
• Discovering Group Theory: A Transition to Advanced Mathematics by Barnard/Neil
  
  
• A Friendly Introduction to Group Theory by Nash
  
  
• Linear Algebra Done Right by Sheldon Axler
  
  There are tons more books on abstract/modern algebra. Just search them on Amazon. Some of the famous, but less accessible ones are
  
  
• Algebra: Chapter 0 by Aluffi
  
  
• Algebra by Maclane/Birkhoff
  
  
• Algebra by Lang
  
  
• Advanced Linear Algebra by Steven Roman
  
  Intro to Real Analysis:
  
  
• The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Grinberg
  
  
• Understanding Analysis by Abbot
  
  
• Writing Proofs in Analysis by Kane
  
  
• The Lebesgue Integral for Undergraduates by Johnston
  
  Again, there are tons of more famous and less accessible books on this subject. There are books by Rudin, Royden, Kolmogorov etc.
  
  Ideally, after this you would follow it up with a nice course on rigorous multivariable calculus. Easiest and most approachable and totally doable one at this point is
  
  
• Vector Calculus, Linear Algebra and Differential Forms: A Unified Approach by the Hubbards
  
  At this point it's clear there are tons of more famous and less accessible books on this subject :) I won't list them because if you are at this point of math development you can definitely find them yourself :)
  
  From here you can graduate to studying category theory, differential geometry, algebraic geometry, more advanced texts on combinatorics, graph theory, number theory, complex analysis, probability, topology, algorithms, functional analysis etc
  
  Most listed books and more can be found on libgen if you can't afford to buy them. If you are stuck on homework, you'll find help on [MathStackexchange] (https://math.stackexchange.com/questions).
  
  Good luck.

Perhaps it's time to move away from LDS specific arguments, and start questioning the God concept in general; especially as it relates to morality.

One argument I've always liked, is that even if there is a god, by far the strongest test of morality it could ask for is if a person will be moral while believing there is no such being, and no promise of reward or punishment.

If she is willing to read, I recommend the following:

• Start with The Demon Haunted World by Carl Sagan. It's much less confrontational than the stuff from more current atheist writers, and his argument is awesome. He basically debunks religion by dismantling the new age movement, and then showing that religion is basically the same.
  
  
• After reading that I would go with "The God Delusion" by Richard Dawkins, or "God is not Great" by Christopher Hitchens. Both are much more confrontational, and in my opinion, are not recommended unless someone is already close to on the fence. Both also deal heavily with the immorality of religion, but I think "God Is Not Great" probably puts more focus on that particular issue.
  
  YouTube is also a fantastic resource. Here are some of the video series that I found particularly convincing as I was going through my own transition:
  
  
• Why I Am No Longer a Christian
  
  
• Psychology of Belief
  
  
• Morality By QualiaSoup: 1 - Good Without Gods, 2 - Not So Good Books, 3 - Objectivity and Oughtness
  
  
• The Best Optical Illusion in the World
  
  I think it's also important to remember that there is are alternative worldviews out there which are not based on religion, which are just as rewarding and fulfilling, if not more so. Here are a few videos that have sparked that sense of wonder and that I used to associate with the spirit. Most of these are not direct attacks on religion, but rather are just inspiring ideas from a secular\scientific worldview. I recognize that these may not have universal appeal, but they spoke to me, and may do so for you and your wife as well:
  
  
• My Spirituality as an Atheist
  
  
• You are Here (Pale Blue Dot)
  
  
• The Sagan Series
  
  
• The Most Astounding Fact: Neil deGrasse Tyson
  
  
• We Stopped Dreaming: Episode 1, Episode 2
  
  
• Science Saved My Soul
  
  
• Why Didn't Anybody Tell Me?
  
  
• Instruction Manual for Life
  
  
• We Got Scared
  
  
• The Greatest Speech Ever Made
  
  

I don't have any old problem sets off hand, but I could point you towards all the topics you should know and be familiar with. It's basically the first 3 chapters of Griffiths -- by the end of the quarter you should know everything from these chapters extremely well.
As for an explicit list of things to do, I would recommend (in this order, more or less)

• get familiar with using probability distributions, complex numbers (i.e. integrating probability densities to find probabilities, means, standard deviations, complex conjugates, norm squared, normalization, etc.)
  
  
• try to grasp the idea of operators (e.g. position, momentum), observables/hermitian operators, commutation relations, and what is means when two observables commute or not (thing about eigenstates, sequential measurements, uncertainty principle,...)
  
  
• derive solution to infinite square well (0 < x < a ; -a < x < a)
  
  
• derive solution to harmonic oscillator (focus on algebraic derivation, raising and lowering operators are extremely
  important later on)
  
  
• calculate expectation values of x, x^2 for the oscillator using ladder operators (this is to highlight orthogonality of eigenstates)
  
  
• derive free particle, examine scattering (E > 0) and bound (E < 0) states
  
  
• derive delta well, finite square well and calculate transmission/reflection coefficients (and bound states for delta well)
  
  
• read up on and use Dirac notation until it is second nature. redo first bullet point with this notation (this could be useful to do first so that you can practice it)
  
  
• understand the level of abstraction for a ket and what it means to "multiply" by a bra and express an equation in the basis (as described by the bra)
  
  
• revisit the idea of operators in a specific basis
  
  
• derive generalized uncertainty principle, revisit non-commuting operators
  
  Hopefully, that gets you started off, but for 110A it may be worth the time to learn Einstein summation notation -- it'll come in handy.
  
  Good luck!
  
  Edit: formatting

Late to the game, but I feel like this is such a big idea that we don't hear enough about it needs to be mentioned here.

In my heart, I know (roughly sketched) the evolutionary incremental steps from apes to humans - how communication and conscious thought began.

It all starts with The Origin of Consciousness in the Breakdown of the Bicameral Mind which is a beautiful, but untestable theory. The shocking component of this theory is that humans developed the capacity for speech long before they were capable of maintaining a conscious train of thought in their minds. In fact, it's quite probable according to this theory that entire societies started to manifest themselves, agriculture was born, and fairly complex tools were being used - all without maintaining a modern conscious train of thought.

The theory goes like this - early man started as a tool maker and solver of survivalist problems. One early advantage was the development of speech to allow for transference of learned solutions to other members of the tribe and its descendants. None of this necessarily requires any kind of internal monologue.

Just imagine if any clever animal who devised a solution to a problem could effectively transmit that knowledge to another. None of that necessarily requires higher level modes of consciousness like self-awareness or recognition of self in a mirror. Even today, you conduct much of your day without maintaining a conscious thought about what you're doing. Often you are thinking about something completely different.

So imagine early humans speaking their early speech to their fellow tribes people teaching them how to make a fire. They speak out loud through the steps. Maybe when they're alone they speak out loud the steps as well - maybe speaking out loud was the only way to work through a problem. How many modern humans today find it easier to speak out loud to themselves while working through a particularly complicated task? It's almost as if the brain's wiring is "smoother" if the problem solving part of the brain goes out through the mouth, in through the ears, and back into the "doer" part of the brain. It doesn't seem like much of a stretch to think those two parts of the brain evolved independently and were only linked much later.

So then one day you don't speak the fire making steps out loud to yourself, but instead hear them in your head. How would you react if this was a novel experience? How would it be comprehended? "Whoa! What was that? Must have been the gods talking to me." Of course, it doesn't take place in such a "eureka!" like moment, but it's still a new novel brain connection that is created much later in our development from baby to teenager.

For proof, the book offers up early writings like the Illiad and Odyssey where characters at first take no action without the gods actively telling them to do something and then later on they see to have their own personas taking their own free will actions. Other things include modern day schizophrenics who can't distinguish their own thoughts from disembodied "voices". In fact, I just recently learned that new evidence shows that these "voices" are registered as activity in the part of the brain associated with speech production rather than language comprehension - that strongly implies the audio hallucinations are more about an inability to distinguish their internal voice as their own.

It's all completely not provable, but something I feel just "fits" so perfectly with how humans would have evolved from apes that it just has to be true.

This is just my perspective, but . . .

I think there are two separate concerns here: 1) the "process" of mathematics, or mathematical thinking; and 2) specific mathematical systems which are fundamental and help frame much of the world of mathematics.

​

Abstract algebra is one of those specific mathematical systems, and is very important to understand in order to really understand things like analysis (e.g. the real numbers are a field), linear algebra (e.g. vector spaces), topology (e.g. the fundamental group), etc.

​

I'd recommend these books, which are for the most part short and easy to read, on mathematical thinking:

​

How to Solve It, Polya ( https://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X ) covers basic strategies for problem solving in mathematics

Mathematics and Plausible Reasoning Vol 1 & 2, Polya ( https://www.amazon.com/Mathematics-Plausible-Reasoning-Induction-Analogy/dp/0691025096 ) does a great job of teaching you how to find/frame good mathematical conjectures that you can then attempt to prove or disprove.

Mathematical Proof, Chartrand ( https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094 ) does a good job of teaching how to prove mathematical conjectures.

​

As for really understanding the foundations of modern mathematics, I would start with Concepts of Modern Mathematics by Ian Steward ( https://www.amazon.com/Concepts-Modern-Mathematics-Dover-Books/dp/0486284247 ) . It will help conceptually relate the major branches of modern mathematics and build the motivation and intuition of the ideas behind these branches.

​

Abstract algebra and analysis are very fundamental to mathematics. There are books on each that I found gave a good conceptual introduction as well as still provided rigor (sometimes at the expense of full coverage of the topics). They are:

​

A Book of Abstract Algebra, Pinter ( https://www.amazon.com/Book-Abstract-Algebra-Second-Mathematics/dp/0486474178 )

​

Understanding Analysis, Abbott ( https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116 ).

​

If you read through these books in the order listed here, it might provide you with that level of understanding of mathematics you talked about.

For math you're going to need to know calculus, differential equations (partial and ordinary), and linear algebra.

For calculus, you're going to start with learning about differentiating and limits and whatnot. Then you're going to learn about integrating and series. Series is going to seem a little useless at first, but make sure you don't just skim it, because it becomes very important for physics. Once you learn integration, and integration techniques, you're going to want to go learn multi-variable calculus and vector calculus. Personally, this was the hardest thing for me to learn and I still have problems with it.

While you're learning calculus you can do some lower level physics. I personally liked Halliday, Resnik, and Walker, but I've also heard Giancoli is good. These will give you the basic, idealized world physics understandings, and not too much calculus is involved. You will go through mechanics, electromagnetism, thermodynamics, and "modern physics". You're going to go through these subjects again, but don't skip this part of the process, as you will need the grounding for later.

So, now you have the first two years of a physics degree done, it's time for the big boy stuff (that is the thing that separates the physicists from the engineers). You could get a differential equations and linear algebra books, and I highly suggest you do, but you could skip that and learn it from a physics reference book. Boaz will teach you the linear and the diffe q's you will need to know, along with almost every other post-calculus class math concept you will need for physics. I've also heard that Arfken, Weber, and Harris is a good reference book, but I have personally never used it, and I dont' know if it teaches linear and diffe q's. These are pretty much must-haves though, as they go through things like fourier series and calculus of variations (and a lot of other techniques), which are extremely important to know for what is about to come to you in the next paragraph.

Now that you have a solid mathematical basis, you can get deeper into what you learned in Halliday, Resnik, and Walker, or Giancoli, or whatever you used to get you basis down. You're going to do mechanics, E&M, Thermodynamis/Statistical Analysis, and quantum mechanics again! (yippee). These books will go way deeper into theses subjects, and need a lot more rigorous math. They take that you already know the lower-division stuff for granted, so they don't really teach those all that much. They're tough, very tough. Obvioulsy there are other texts you can go to, but these are the one I am most familiar with.

A few notes. These are just the core classes, anybody going through a physics program will also do labs, research, programming, astro, chemistry, biology, engineering, advanced math, and/or a variety of different things to supplement their degree. There a very few physicists that I know who took the exact same route/class.

These books all have practice problems. Do them. You don't learn physics by reading, you learn by doing. You don't have to do every problem, but you should do a fair amount. This means the theory questions and the math heavy questions. Your theory means nothing without the math to back it up.

Lastly, physics is very demanding. In my experience, most physics students have to pretty much dedicate almost all their time to the craft. This is with instructors, ta's, and tutors helping us along the way. When I say all their time, I mean up until at least midnight (often later) studying/doing work. I commend you on wanting to self-teach yourself, but if you want to learn physics, get into a classroom at your local junior college and start there (I think you'll need a half year of calculus though before you can start doing physics). Some of the concepts are hard (very hard) to understand properly, and the internet stops being very useful very quickly. Having an expert to guide you helps a lot.

Good luck on your journey!

I'm going to post my favorite videos that I grew up on. I could watch them over and over and not get sick of them. Dawkins is my hero.

Royal Institute Christmas Lectures - Richard Dawkins' "Growing Up in the Universe". Entertaining, engaging, and fascinating series of lectures for children on the basics of evolution in a way that makes a hell of a lot of sense. You will see fascinating stuff. I found some parts mind-blowing, and the demonstrations are just great (and here's proof!)

• Ep 1 - Waking Up in the Universe http://www.youtube.com/watch?v=jHoxZF3ZgTo
  
• Ep 2 - Design and Designoid Objects http://www.youtube.com/watch?v=xGyh1Qsw-Ak&feature=channel
  
• Ep 3 - Climbing Mount Improbable http://www.youtube.com/watch?v=YT1vXXMsYak&feature=channel
  
• Ep 4 - The Ultraviolet Garden http://www.youtube.com/watch?v=_igTWNidwnk&feature=channel
  
• Ep 5 - The Genesis of Purpose http://www.youtube.com/watch?v=qm-0Z0ceezQ&feature=channel
  
  BBC Horizon - Nice Guys Finish First (Part 1 of 5) - Documentary on Evolution and Altruism, as well as some basics of Game Theory
  
  
• http://www.youtube.com/watch?v=qFj0caNX1s0
  
  Documentary - The Blind Watchmaker (1 of 5)
  
  
• http://www.youtube.com/watch?v=VhJdai8eKic
  
  Book - The Greatest Show on Earth by Richard Dawkins.
  
  
• http://www.amazon.com/Greatest-Show-Earth-Evidence-Evolution/dp/1416594787
  Fantastic book that illustrates evolution very well. It's an easy read, but it manages to break down complex ideas in a very clear manner. I read it recently, and even though I thought I knew a lot, this really helped me get a better grasp on some of the basics. Dawkins' tone in the beginning might come off as unusually annoying in this book, but it gets better. The pictures and metaphors are beautiful, and there are some witty lines and funny stories. Some of the statistics will make you rage. The ending is surprisingly sad and powerful.
  
  
  Best of luck!

I. Sure, some forms of theism are coherent (Christianity is not one of those forms, for what it's worth; the Problem of Natural Evil and Euthyphro's Dilemma being a couple of big problems), but not all coherent ideas are true representations of the world; any introductory course in logic will demonstrate that.

II. The cosmological argument is a deductive argument. Deductive arguments are only as strong as their premises. The premises of the cosmological argument are not known to be true. Therefore, the cosmological argument should not be considered true. If you think you know a specific formulation of the cosmological argument that has true premises, please present it. I'm fully confident I can explain how we know such premises are not true.

III. There is no doubt that the teleological argument has strong persuasive force, but that's a very different thing than "being real evidence" or "something that should have strong persuasive force." I explain apparent cosmological fine-tuning as an entirely anthropic effect: if the constants were different, we wouldn't be here to observe them, therefore we observe them as they are.

IV. This statement is just false on its face. Lawrence Krauss has a whole book about the potential ex nihilo mechanisms (plural!) for the creation of the universe that are entirely consistent with the known laws of physics. (Note that the idea of God is not consistent with the known laws of physics, since he, by definition, supersedes them.)

V. This is just a worse version of argument III. Naturalistic evolution has far, far more explanatory power than theism. To name my favorite examples: the human blind spot is inexplicable from the standpoint of top-down design, but it makes perfect sense in the context of evolution; likewise, the path of the mammalian nerves for the tongue traveling below the heart makes no sense from the standpoint of top-down design, but it makes perfect sense in the context of evolution. Evolution routinely makes predictions that are tested to be true, whether it means predicting where fossils with specific characteristics will be found or how fruit fly mating behavior changes after populations have been separated and exposed to different environments for 30+ generations. It's worth emphasizing that it is totally normal to look at the complexity of the world and assume that it must have a designer...but it's also totally normal to think that electrons aren't waves. Intuition isn't a reliable way to discern truth. We must not be seduced by comfortable patterns of thought. We must think more carefully. When we think more carefully, it turns out that evolution is true and evolution requires no god.

VI. There are two points here: 1) the universe follows rules, and 2) humans can understand those rules. Point (1) is easily answered with the anthropic argument: rules are required for complex organization, humans are an example of complex organization, therefore humans can only exist in a physical reality that is governed by rules. Point (2) might not even be true. Wigner's argument is fun and interesting, but it's actually wrong! Mathematics are not able to describe the fundamental behavior of the physical world. As far as we know, Quantum Field Theory is the best possible representation of the fundamental physical world, and it is known to be an approximation, because, mathematically, it leads to an infinite regress. For a more concrete example, there is no analytic solution for the orbital path of the earth around the sun! (This is because it is subject to the gravitational attraction of more than one other object; its solution is calculated numerically, i.e. by sophisticated guess-and-check.)

VII. This is just baldly false. I recommend Dan Dennett's "Consciousness Explained" and Stanislas Dehaene's "Consciousness and the Brain" for a coherent model of a materialist mind and a wealth of evidence in support of the materialist mind.

VIII. First of all, the idea that morality comes from god runs into the Problem of Natural Evil and Euthyphro's Dilemma pretty hard. And the convergence of all cultures to universal ideas of right and wrong (murder is bad, stealing is bad, etc.) are rather easily explained by anthropology and evolutionary psychology. Anthropology and evolutionary psychology also predict that there would be cultural divergence on more subtle moral questions (like the Trolley Problem, for example)...and there is! I think that makes those theories better explanations for moral sentiments than theism.

IX. I'm a secular Buddhist. Through meditation, I transcend the mundane even though I deny the existence of any deity. Also, given the diversity of religious experience, it's insane to suggest that religious experience argues for the existence of the God of Catholicism.

X. Oh, boy. I'm trying to think of the best way to persuade you of all the problems with your argument, here. So, here's an exercise for you: take the argument you have written in the linked posts and reformat them into a sequence of syllogisms. Having done that, highlight each premise that is not a conclusion of a previous syllogism. Notice the large number of highlighted premises and ask yourself for each, "What is the proof for this premise?" I am confident that you will find the answer is almost always, "There is no proof for this premise."

XI. "...three days after his death, and against every predisposition to the contrary, individuals and groups had experiences that completely convinced them that they had met a physically resurrected Jesus." There is literally no evidence for this at all (keeping in mind that Christian sacred texts are not evidence for the same reason that Hindu sacred texts are not evidence). Hell, Richard Carrier's "On the Historicity of Christ" even has a strong argument that Jesus didn't exist! (I don't agree with the conclusion of the argument, though I found his methods and the evidence he gathered along the way to be worthy of consideration.)

-----

I don't think that I can dissuade you of your belief. But, I do hope to explain to you why, even if you find your arguments intuitively appealing, they do not conclusively demonstrate that your belief is true.

Personally, I think you would get great suggestions on /r/physics. But since you're here...

Since you seem like you're just dipping your toes in the water, you might want to start off with something basic like Hawking (A Brief History of Time, The Universe in a Nutshell).

I highly recommend Feynman's QED, it's short but there's really no other book like it. Anything else by Feynman is great too. I found this on Amazon and though I haven't read it, I can tell you that he was the greatest at explaining complex topics to a mass audience.

You'll probably want to read about relativity too, although my knowledge of books here is limited. Someone else can chime in, maybe. When I was a kid I read Einstein for Beginners and loved it, but that's a comic book so it might not be everyone's cup of tea.

If you really want to understand quantum mechanics and don't mind a little calculus (OK, a lot), try the textbook Introduction to Quantum Mechanics by Griffiths. Don't settle for hokey popular misconceptions of how QM works, this is the real thing and it will blow your mind.

Finally, the most recent popular physics book I read and really enjoyed was The Trouble with Physics by Smolin. It's ostensibly a book about how string theory is likely incorrect, but it also contains really great segments about the current state of particle physics and the standard model.

What this expressions says

First of all let's specify that the domain over which these statements operate is the set of all people say.
Let us give the two place predicate P(x,y) a concrete meaning. Let us say that P(x,y) signifies the relation x loves y.

This allows us to translate the statement:
∀x∀yP(x,y) -> ∀xP(x,x)

What does ∀x∀yP(x,y) mean?

This is saying that For all x, it is the case that For all y, x loves y.
So you can interpret it as saying something like everyone loves everyone.

What does ∀xP(x,x) mean?

This is saying that For all x it is the case that x loves x. So you can interpret this as saying something like everyone loves themselves.

So the statement is basically saying:
Given that it is the case that Everyone loves Everyone, this implies that everyone loves themselves.
This translation gives us the impression that the statement is true. But how to prove it?

Proof by contradiction

We can prove this statement with a technique called proof by contradiction. That is, let us assume that the conclusion is false, and show that this leads to a contradiction, which implies that the conclusion must be true.

So let's assume:
∀x∀yP(x,y) -> not ∀xP(x,x)

not ∀xP(x,x) is equivalent to ∃x not P(x,x).
In words this means It is not the case that For all x P(x,x) is true, is equivalent to saying there exists x such P(x,x) is false.

So let's instantiate this expression with something from the domain, let's call it a. Basically let's pick a person for whom we are saying a loves a is false.

not P(a,a)

Using the fact that ∀x∀yP(x,y) we can show a contradiction exists.

Let's instantiate the expression with the object a we have used previously (as a For all statement applies to all objects by definition) ∀x∀yP(x,y)

This happens in two stages:

First we instantiate y
∀xP(x,a)

Then we instantiate x
P(a,a)

The statements P(a,a) and not P(a,a) are contradictory, therefore we have shown that the statement:

∀x∀yP(x,y) -> not ∀xP(x,x) leads to a contradiction, which implies that
∀x∀yP(x,y) -> ∀xP(x,x) is true.

Hopefully that makes sense.

Recommended Resources

Wilfred Hodges - Logic

Peter Smith - An Introduction to Formal Logic

Chiswell and Hodges - Mathematical Logic

Velleman - How to Prove It

Solow - How to Read and Do Proofs

Chartand, Polimeni and Zhang - Mathematical Proofs: A Transition to Advanced Mathematics

I just want to point out one thing that everyone seems to be glossing over: when people say that you'll need to review classical mechanics, they aren't talking only about Newtonian Mechanics. The standard treatment of Quantum Mechanics draws heavily from an alternative formulation of classical mechanics known as Hamiltonian Mechanics that I'm willing to bet you didn't cover in your physics education. This field is a bit of a beast in its own right (one of those that can pretty much get as complicated/mathematically taxing as you let it) and it certainly isn't necessary to become an expert in order to understand quantum mechanics. I'm at a bit of a loss to recommend a good textbook for an introduction to this subject, though. I used Taylor in my first course on the subject, but I don't really like that book. Goldstein is a wonderful book and widely considered to be the bible of classical mechanics, but can be a bit of a struggle.

Also, your math education may stand you in better stead than you think. Quantum mechanics done (IMHO) right is a very algebraic beast with all the nasty integrals saved for the end. You're certainly better off than someone with a background only in calculus. If you know calculus in 3 dimensions along with linear algebra, I'd say find a place to get a feel for Hamiltonian mechanics and dive right in to Griffiths or Shankar. (I've never read Shankar, so I can't speak to its quality directly, but I've heard only good things. Griffiths is quite understandable, though, and not at all terse.) If you find that you want a bit more detail on some of the topics in math that are glossed over in those treatments (like properties of Hilbert Space) I'd recommend asking r/math for a recommendation for a functional analysis textbook. (Warning:functional analysis is a bit of a mindfuck. I'd recommend taking these results on faith unless you're really curious.) You might also look into Eisberg and Resnick if you want a more historical/experimentally motivated treatment.

All in all, I think its doable. It is my firm belief that anyone can understand quantum mechanics (at least to the extent that anyone understands quantum mechanics) provided they put in the effort. It will be a fair amount of effort though. Above all, DO THE PROBLEMS! You can't actually learn physics without applying it. Also, you should be warned that no matter how deep you delve into the subject, there's always farther to go. That's the wonderful thing about physics: you can never know it all. There just comes a point where the questions you ask are current research questions.

Good Luck!

That's perfect then, don't let me stop you :). When you're ready for the real stuff, the standard books on quantum mechanics are (in roughly increasing order of sophistication)

• Griffiths (the standard first course, and maybe the best one)
  
• Cohen-Tannoudji (another good one, similar to Griffiths and a bit more thorough)
  
• Shankar (sometimes used as a first course, sometimes used as graduate text; unless you are really good at linear algebra, you'd get more out of starting with the first two books instead of Shankar)
  
  By the time you get to Shankar, you'll also need some classical mechanics. The best text, especially for self-learning, is [Taylor's Classical Mechanics.] (http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X/ref=sr_1_1?s=books&ie=UTF8&qid=1372650839&sr=1-1&keywords=classical+mechanics)
  
  
  Those books will technically have all the math you need to solve the end-of-chapter problems, but a proper source will make your life easier and your understanding better. It's enough to use any one of
  
  
• Paul's Free Online Notes (the stuff after calculus, but without some of the specialized ways physicists use the material)
  
• Boas (the standard, focuses on problem-solving recipes)
  
• Nearing (very similar to Boas, but free and online!)
  
• Little Hassani (Boas done right, with all the recipes plus real explanations of the math behind them; after my math methods class taught from Boas, I immediately sold Boas and bought this with no regrets)
  
  When you have a good handle on that, and you really want to learn the language used by researchers like Dr. Greene, check out
  
  
• Sakurai (the standard graduate QM book; any of the other three QM texts will prepare you for this one, and this one will prepare you for your PhD qualifying exams)
  
• Big Hassani(this isn't just the tools used in theoretical physics, it's the content of mathematical physics. This is one of two math-for-physics books that I keep at my desk when I do my research, and the other is Little Hassani)
  
• Peskin and Schroeder (the standard book on quantum field theory, the relativistic quantum theory of particles and fields; either Sakurai or Shankar will prepare you for this)
  
  Aside from the above, the most relevant free online sources at this level are
  
  
• Khan Academy
  
• Leonard Susskind's Modern Physics lectures
  
• MIT's Open CourseWare

How the universe was made?

I think the real crux of the question you're asking is how can something come from nothing? (feel free to correct me if I'm wrong; I don't want to speak for you) Let me just start off by saying there is no definitive scientific answer to this question... yet. However, there are very prominent research scientists who have tackled the question and come up with very cogent theories (backed up by current mathematical models).

I won't pretend to understand most of these theories as I'm a biologist, not a physicist. There is one recent book written on the very topic called A Universe from Nothing by Lawrence Krauss (he is a published theoretical physicist and cosmologist). He posits that particles do in fact spontaneously come into existence and there is scientific proof and reasoning for how and why. I haven't gotten around to reading it myself (it was just published this year), but I've been told it's good for the layman on the topic.

Now let me move on to some of the problems with this question. Perhaps you yourself don't have this supposition, but the supposition many theists make with the question (where did the universe come from?), is that if it can't be answered than God must have done it. This is a logical leap that defies rational reasoning, and is a leap theists have been making for millenia. What makes the tides go in and out? We don't know; must be God. What causes disease? We don't know; must be God. Where did the universe come from? We don't know; must be God?

It's what's known as a God of the gaps; wherein anything that can't be explained is conveniently claimed to have a divine explanation. Until a rational scientific answer comes along and religion takes a step back. There will likely always be gaps in our knowledge base (most definitely in our liftetimes). That doesn't mean we should make the same mistake as our ancestors and attribute these gaps to God. It's okay to simply not know and strive to understand.

Another huge problem with your question is that the theist answer only serves to further complicate the original question.

1. How can something come from nothing?
   
2. Well it can't right? So God must have created that original something.
   
3. God is something. Go back to step 1.
   
   Theists tend to skip that third step, or explain it away as God just always existing. Yet the universe always existing is something that is logically unacceptable to them. If anything, throwing God into the equation only makes it more complicated. A sentient being capable of creating the initial state of the universe would be more complex than what it is creating (meaning God is more complex than the universe). Trying to explain than how God came into being is more complicated than the original question, so nothing has really been answered or solved.
   
   If you're really trying to stump atheists, the best common theist argument I've seen is the cosmological constants one (how are they so fine tuned?). No doubt there are answers, but that's one of the better arguments out there. I won't go into it here, just search for it.

Look into local chapters of the mycological society or mushroom hunting groups/clubs in your area. This site lists a few options. Looks like the one in Albion may be near-ish to you.

I've also found many of the links in the sidebar helpful, especially mushroom observer and the mushroom hunting and identification forum on The Shroomery. The Shroomery's ID forum is where I go to confirm my suspected ID's after keying out specimens on my own.

I use Mushrooms Demystified, by David Arora, as a my post collection ID book. It's both huge and dated (i think it's latest edition is from the early or mid 80's) so it's functionality as a field guide or the final word in ID is lacking. Even so, it is good to learn to work through dichotomous keys like the ones that it employs and it usually gets you headed in the right direction. Other guides like Rogers Mushrooms, All the Rain Promises and More, and The National Audubon Society Field Guide to North American Mushrooms are good resources, too (I'm sure other folks can add to this list, I'm just dropping the names that first come to mind).

As much as I clash with some of his professional/ethical decisions, Paul Stamets has contributed a ton to the accessibility of Mycology to the masses. Check out Mycelium Running and Growing Gourmet and Medicinal Mushrooms as introductions to the Fifth Kingdom.

I'm also really enjoying Tradd Cotter's new book, Organic Mushroom Farming and Mycoremediation

Fungi for the People and The Radical Mycology Collective have also been hugely influential in my personal growth as an amateur mycologist. If you ever get a chance to attend any of their events, I would recommend doing it.

Best of luck and enjoy your journey!

You should absolutely not give up.

• Axler is fairly advanced for a freshman course in linear algebra. The fact that it's making more sense the second time you go over it is much more important than failing to understand it the first time.
  
• Nobody can learn sophisticated math from a lecture if they haven't seen it before. Well, maybe geniuses can, but my guess is that the majority of successful mathematicians reach a point where the lecture medium becomes much less important. You have to read the textbook with a pencil in hand, proving lemmas yourself. Digest proofs at your own pace, there's nothing wrong or unusual with not understanding it the way your Professor presented it.
  
• About talking math with people - this just takes time. Hold off on judging yourself. You can also get practice by getting involved with math subreddits or math.stackexchange.
  
• It's pretty unlikely that you are "too stupid" to study math. I've seen people with a variety of natural ability learn a tremendous amount about math and related disciplines, just by working hard.
  
  None of this is groundbreaking, and a lot of it is pretty cliché, but it's true. Everyone struggles with math at some point. Einstein said something like "whatever your struggles with math are, I assure you that mine are greater."
  
  As for specific recommendations, make the most of this summer. The most important factor in learning math in my experience is "time spent actively doing math." My favorite math quote is "you don't learn math, you get used to it." I might recommend a book like How to Prove It. I read it the summer before I entered college, and it helped immensely with proofs in real analysis and abstract algebra. Give that a read, and I bet you will be able to prove most lemmas in undergraduate algebra and topology books, and solve many of their problems. Just keep at it!

Lots of love for you, here are some thoughts of mine...

• it is a mistake to believe that you should be asking the question "What is the purpose of my life?" it's not a question you ask, IT IS A QUESTION YOU ANSWER! and you answer it by living your life as ONLY you can, having the adventure that is your life experience, discovering the magical miracle that is ONLY YOU in all of this vast universe!
  
  
• After losing Mormonism and the understanding of the universe that goes with it, I find myself an atheist, which has made this little journey of life INFINITELY more precious to me. It's all and everything we have! (as far as we know).
  
  
• I have pulled in many helpful, empowering, peaceful ideas from Buddhism, Philosophy, Science that has helped me start to form a new, optimistic, and amazingly open minded new world-view. I no longer have to believe anything that doesn't make sense, I get to believe only sweet things now, and that is SO nice.
  
  Here are some resources that I have been really grateful for on my journey, which I am 12 months into...
  
  The Obstacle is the Way
  
  The Daily Stoic this is my new "daily bible" I read a page every morning
  
  Secular Buddhism podcast
  
  Waking Up podcast
  
  End of Faith
  
  The Demon Haunted World
  
  Philosophize This! podcast OR Partially Examined Life podcast
  
  I wish you the very best in your journey, be patient with yourself, you have EVERY reason to be! Start filling your mind with powerful positive ideas, keep the ones that help you find your way, set aside the ones that don't.
  
  And remember, you are young and free and the possibilities of what your life can become are boundless!

You do realize that there is guesswork but the extremes of the confidence interval are strictly positive right? In other words, no one is certain but what we are certain about is that optimum homework amount is positive. Maybe it's 4 hours, maybe it's 50 hours. But it's definitely not 0.

I don't like homework either when I was young. I dreaded it, and I skipped so many assignments, and I regularly skipped school. I hated school. In my senior year I had such severe senioritis that after I got accepted my grades basically crashed to D-ish levels. (By the way this isn't a good thing. It makes you lazy and trying to jumpstart again in your undergrad freshman year will feel like a huge, huge chore)

Now that I'm older I clearly see the benefits of homework. My advice to you is not to agree with me that homework is useful. My advice is to pursue your dreams, but when doing so be keenly aware of the pragmatical considerations. Theoretical physics demands a high level of understanding of theoretical mathematics: Lie groups, manifolds and differential algebraic topology, grad-level analysis, and so on. So get your arse and start studying math; you don't have to like your math homework, but you'd better be reading Spivak if you're truly serious about becoming a theoretical physicist. It's not easy. Life isn't easy. You want to be a theoretical physicist? Guess what, top PhD graduate programs often have acceptance rates lower than Harvard, Yale, Stanford etc. You want to stand out? Well everyone wants to stand out. But for every 100 wannabe 15-year-old theoretical physicists out there, only 1 has actually started on that route, started studying first year theoretical mathematics (analysis, vector space), started reading research papers, started really knowing what it takes. Do you want to be that 1? If you don't want to do homework, fine; but you need to be doing work that allows you to reach your dreams.

It can be explained, though not simply, nor accessibly. Luckily, I'm not just an atheist, I'm also a theoretical physics student. Keep in mind that this of course can not be demonstrated empirically (science is the study of our Universe, so we obviously can't study things outside it in time or space).

Lets go back to before the Universe exists. Let's call this state the Void. It's important to note that no true void exists in our Universe, even the stuff that looks empty is full of vacuum fluctuations and all kinds of other things that aren't relevant, but you can investigate in your own time if you want. In this state, the Void has zero energy, pretty much by definition. Now, the idea that a Void could be transforms into a Universe is not really controversial; stuff transforms by itself all the time. The "problem" with a Universe arising from a Void is that the Universe has more energy than the Void, and it there's not explanation for where all this energy came from. Upon further investigation, we'll actually see that the Universe has zero net energy, and this isn't actually a problem.

Now, let's think about a vase sitting on a table. One knock and it shatters, hardly any effort required. But it would take a significant amount of effort to put that vase back together. This is critically important. Stuff has a natural tendency to be spread out all over the place. You need to contribute energy to it in order to bring it together. We're going to call this positive energy.

Gravity is something different though. Gravity pulls everything together. Unlike the vase, you'd need to expend energy in order to overcome the natural tendency of gravity. Because it's the opposite, we're going to call gravity negative energy. In day to day life, the tendency of stuff to spread out overwhelms the tendency of gravity to clump together, simply because gravity is comparatively very weak. There's quite a few more factors at play here, but stuff and gravity are the important ones.

Amazingly, it turns out that it's possible for the Universe to have exactly as much negative energy as it does positive energy, which means that it would have zero total energy, meaning that it's perfectly possible for it to pop out of nowhere, by dumb luck, because no energy input is required. Furthermore, we know how to check if our Universe has this exact energy composition. And back in 1989, that's exactly what cosmologists did. And it turns out it does. We can empirically show, to an excellent margin of error, that our Universe has zero net energy. Think about that for a second. Lawrence Krauss has a great youtube video explaining the evidence for this pretty incredible claim.

The really incredible thing is, given that our Universe has zero net energy, it's not only possible that it could just pop into existence on day, it's inevitable. It's exactly what we'd expect. Hell, I'd be out looking for God's fingerprints if there wasn't a Universe, not the opposite.

If you want to read more about it, by people who've spent far more time investigating this than I have, I suggest The Fabric of the Cosmos by Brian Greene, and A Universe From Nothing: Why There Is Something Rather Than Nothing by Lawrence Krauss. Both go into detail about the subject, and don't require any prior physics knowledge.

tl;dr The Universe didn't need a "first cause". PHYSICS!

For Quantum Physics I cannot recommend Quantum Physics: A Beginner's Guide it has enough maths to make it worth reading, but the equations etc. are in supplemental boxes with explanations and investigations so you can ignore all the maths if you want. It tends to focus on the applications of quantum physics in semiconductors, superconductors which is good to learn about as it is easier to comprehend than the really tricky philosophical implications.

I would also recommend The Fabric of the Cosmos by Brian Greene, because it has more philosophical stuff in it, and although it is broader and not just about quantum physics but includes relativity and stuff too, it is an awesome book and you won't regret reading it.

For evolutionary biology I would recommend The Blind Watchmaker by Richard Dawkins, it is a Science book so don't worry if you don't like his aggressive atheism as if I recall correctly it doesn't rear it's head in the book at all. It is especially good if you enjoy Computer Science as he makes some analogies between life and programs which are obviously easier to appreciate if you have some experience (Dawkins was a programmer for many years).

I don't know what paleo-anthropology is so unfortunately I can't recommend anything there, but I would be extremely happy if you could enlighten me and perhaps recommend some texts. (Not terribly helpful, I know :P )

Answering your edit, time dilation does occur at the speed of light. So much so that at exactly the speed of light, no travel in time occurs. To a photon, this means it "feels like" it was born and dies at the same instant, if we're going to anthropomorphize here, even though to us we can see it existing in time.

EDIT: as u/Aliudnomen points out, "a frame traveling at c is not a valid inertial frame", which means it's not precise to say that time dilation is happening at the speed of light. Got a bit carried away with the explanation here :) You see infinity time dilation at the speed of light, but that's because the denominator trends to 0, which is a place that inertial objects can't get to. It doesn't really mean that time dilation is infinite, but rather nonexistent. This is why it's often said information is the only thing that can appear, to us, to travel at the speed of light: anything with an inertial reference frame can never get to the speed of light.

With you being in 10th grade, I'll use an analogy/projection that I find helpful. Imagine a Cartesian set of axes (the normal kind), where the y axis is time-velocity and the x axis is space-velocity. Draw a big circle of radius the speed of light, we'll call that "1 unit". Now, you need to replace the idea of "speed of light" (which implies movement of light in the space velocity coordinate frame) with c, the celerity constant: celerity means "rapidity of motion", but it was chosen specifically because it can mean speed in the 4 dimension coordinate system of spacetime. In other words, you can travel in space or you can travel in time, and both of these will be measured, not with mph, but with some fraction of c. With me so far?

OK, what relativity is saying here is that we are always traveling on a circle with radius c. If we don't travel along the space-velocity x axis (we're at rest), we travel along the time-velocity(y axis), and whenever we travel along the x axis, we rotate our point from (0, 1) around this circle clockwise toward (1, 0).

To see this, we can rearrange the time dilation equation:

t' = t / sqrt(1 - (v/c)^2) Original equation
t' / t = 1 / (sqrt(1 - v/c)^2) Move the t in the numerator over
t' / t = 1 / sqrt((c^2) - (v^2)) Multiply the guys under the sqrt by c^2
(t' / t)^2 = 1 / (c^2 - v^2) Square both sides
1 / (t' / t)^2 = c^2 - v^2 Invert both sides
1 / (t' / t)^2 + v^2 = c^2 Add v^2 to both sides
t^2/t'^2 + v^2 = c^2 Square under the first term denominator and invert.

This is an equation of a circle with radius c: the axes can be chosen so that the y axis is "ratio of time", which is what I'm calling "time velocity" and the x axis is "space velocity".

We are always traveling at c, and so we're always somewhere on this circle. This is why it's a constant: nothing in the universe travels faster or slower than this celerity, we can only change which coordinates add up to get us there. If we're perfectly at rest in the space-velocity dimension (x = 0), all of our travel is along the time dimension (y = 1): we're at (1, 0) on this point of the circle. With me so far?

This is what "spacetime" means: right here we're dropping the fact that space is 3 dimensional and considering all velocity to be along the one axis, but if you add in higher dimensions, this is spacetime: x, y, z, t all involved in the same equations. Events - which are used to describe "something that happens somewhere in spacetime" - always travel within a 4 dimensional hypersphere that relativistic folk call the light cone.

Back to our 2d example. As you start to increase your x dimension - that is, start moving - your celerity starts to rotate around the circle. When you travel half the speed of light, where x = 0.5, you can imagine the line drawn from the origin to the point on the circle that corresponds to this x coordinate slanting up and to the right, which happens to be solved by (x^2 ) + (y^2 ) = c^2. Solving for y, we get 0.866 - that is, we're traveling at 0.866 the normal rate of time flow.

Keep increasing space velocity, and you'll plot points like (0.6, 0.8), (0.7, 0.714), (0.8, 0.6), (0.9, 0.435), (0.95, 0.31), (0.99, 0.14), (0.999, 0.045), (0.9999, 0.014)

You see, we're putting more and more of our celerity into the space-velocity coordinate and taking it from the time-velocity coordinate. This is time dilation.

Finally, anything with mass requires energy to convert its travel in time to travel in space. As you keep attempting to get closer to (1, 0), it requires more energy to shift the angle around the circle, until the last little bit is infinite. This is why only massless particles (like photons) can travel at the speed of light.

You can also, then, intuitively grasp the other parts of this circle: what does it take to make time slow down? Well, we would have to move from the 1st quadrant (the top right quadrant) to the 3rd and 4th quadrants (the bottom quadrant). We don't really know for sure how to do this, but we do know that it seems possible that more exotic particles could behave just like matter, except progressing backwards. In other words, at rest, their velocity is (0, -1). What does it take to get from matter going forward in time to backwards? Well, you can't do it by increasing your space-velocity alone: no matter how much you increase your velocity, you can only ever get to almost (1, 0) with something that has mass. This is the "tachyon" idea: a massive particle that travels so fast that it loops around the coordinate frame into quadrant 4 (bottom right), that is, think about moving so fast that you move faster than the speed of light (perhaps you became massless for a second, then gained mass as you somehow started traveling in the negative time direction. This can't happen, AFAIK, because you'd have to travel through infinite energy to loop around, but you can imagine the symmetry here). Real particles can't do this, but it's theoretically possible that particles do exist that travel "faster than the speed of light", but only in a way that breaks what it means to have velocity: they're traveling backwards in time, so their motion is some fraction of c to them; they're not moving faster than the speed of light. To us observing them, they're moving faster than we can achieve with our motion on the x coordinate: their motion backwards in time makes them seem to us as if they're moving faster than c. They're not, remember: all of us are always moving at c.

If something has anti-mass, however (that is, antimatter), it seems possible to have it traveling at (0, -1) all on its own! It's hard to jump on something that has anti-mass, though, so this is still theoretical in many ways. That is, the equations say it should be moving backwards in time, but what that actually means is far more complicated: it maths out that way, but it's not like causality is broken (that is, when we create antimatter in particle accelerators, they don't appear "before" the collision, but they do get "younger" before they annihilate. What does "younger" mean to a particle? How do you define "younger" when it's getting "older in negative time"? What is the sound of one hand clapping?

Also interesting is the idea of time dilation with negative velocities: the 2nd (top-left) quadrant. What does it mean to move "backwards" in space? Does that even have a meaning? I mean if I walk down the street, I'm moving forward in a direction, but if I walk the opposite way, I'm moving forward in the opposite direction. I'm not aware of anything discussing "negative velocity", but that's just my ignorance: perhaps someone else can chime in if they know more.

Finally, Carl Sagan here to describe what life looks like as you approach the speed of light. You can start to see from his example what it would be like to travel so fast that no time passes for you at all.

Finally, one of the most accessible books I've ever read is Stephen Hawking's a brief history of time. If you're at all remotely curious about either relativity or quantum mechanics, this guy, along with being just about the most brilliant mind in these fields, has a fantastic way of explaining the concepts while still staying true to the equations involved.

I used to love all those new age books! Why not head down to the used bookstore and pick up half a dozen books that look fun out of that section? There's always something entertaining there. If she's a true believer, avoid anything that suggests people can survive by eating nothing but air.

Or, if she's not a true believer but just interested in the subject, have you considered getting her some non-fiction books that delve into the psychology behind ghost sightings and such? Like Investigating the Paranormal (less skeptical) or Demon-Haunted World (much more skeptical)?

Cows, Pigs, Wars, and Witches was a fascinating read and IIRC largely historical. She might also enjoy branching out into a book like The Predictioneer's Game, which is about game theory and how to use it effectively in modern life.

If she likes mysteries at all, I suggest Josephine Tey's The Daughter of Time. It's about a police officer who is laid up in hospital and decides to use the time to solve a famous historical mystery. You could also consider biographies of strong and active women who inspire -- Princess Diana, maybe, or Martha Stewart?

(Edited to add links)

Love your typo!

All That the Rain Promises and More: A Hip Pocket Guide to Western Mushrooms, by David Arora is definitely a good place to start. For people in the U.S.

There are good edible Russula, Lactarius and Amanita mushrooms, but the species you've listed are not commonly eaten. I do believe A. rubescens is edible, but I would not suggest anyone who is new to mushrooming even pretend to think about eating any species of Amanita until they have familiarized themselves with the genus and the Amanitas in their harvesting areas. Stick with the numerous other edible genera for a season or two, and learn all you can. Russula and Lactarius are great places to start; very delicious and often abundant.

Good luck. If you wanna come back and post pics of your finds, make sure to get them in focus and get shots of all parts, including the gills and their attachment to the stipe. Try to get into the habit of making spore prints of unknown specimens, as this can narrow down considerably the number of potential genera your specimen could belong to...

Have fun!

This has been my curse since college. In college I truly blossomed, it was a community college and the profs truly cared and were passionate about teaching. I was fascinated by every course I took, I read books related to the course material because I couldn't get enough. I was blessed by having not grown up religious, and I easily shed the sort of pseudo therapeutic deism I had in favor of physicalism, lifism, and humanism. Humans beings and life on Earth are the things of the most value we have ever experienced. However with the knowledge I gained, I realized the nature of social reality that we all do here: we live in a humanity-destroying doomsday device called capitalism, politics was utter bullshit, and nothing was there to prevent the apocalypse. My greatest fear was and is humanity destroying itself via its own stupidity. This became my Focus, my core query, and the essential dilemma between what I valued most and its utter negation destroyed me. And so I went under, and how I went under. Imagine everyone you love dying at the same time, over and over, with you helpless to stop it; I felt this for years. I tried distractions, to "simply be happy" and seek escapism in video games and the internet (which led me to Second Life and my business there which made me $9000 a month at my peak) and to hide myself from the world. I became a hermit in my own apartment, (later a room in my Mother's house) and have been ever since, until now.

It was also during college (2001-2004, broken up due to life circumstances) that I discovered Richard Dawkins' phenomenal work, along with many others in philosophy and science. I envisioned a science of creativity, of a way to augment people's innate creativity instead of the shitty definition of "memetic engineering" which is essentially engineering propaganda. I imagined an explosion of human creative experience known as the Memetic Singularity. I didn't realize it, but after making this my Focus I subconsciously sought it, and to the solution of my core query of how to prevent the death of humanity. Eventually, this led me here. And so here I am.

There are many that share my core queries of an expanding fractal of human experience / life-as-art and art-as life, and to prevent the destruction of humanity. Our synchronicity is us working along separate lines of inquiry that converge in very precise ways, the precision having increased until the memetic singularity was realized sometime in the last few months. The War on Nihilism, the War on Zero is over, we are in a post-war period of reconstruction. A really awesome Christmas (metaphorically) is coming where many gifts will be revealed that will allow humanity to reach its true potential that we all know deep down is our birthright.

I like your diagram and it is a good way to visualize and organize your mental schema on these topics. I'm not sure what sort of diagram I would make, but it would probably involve bubbles with topics with sub-bubbles branching off with sub-topics and a whole lot of cross-crossing lines of relations between them.

If you haven't already, I strongly recommend watching my special blends in order, without skipping anything (the whole is other than the sum of their parts.) The true message is in the interrelationships of the media used, both between blends and within them.

Carl Sagan is also one of my biggest role models, in the midst of the total chaos (parents, family, high school) of my teenage years I discovered amateur astronomy. I learned to love the cosmos, I built my own 10" Dobsonian Newtonian reflector, the night sky became a home to me. I had previously had a deep fear of the dark which vanished from this, which is why this book is so meaningful to me. What initiated my interest in astronomy was the movie Contact based on his book I had previously read. This scene in the movie describes the holy experience of astronomy that I felt many times just as strongly as the movie depicts. The scene isn't about aliens, it's about humanity and the universe, which has a sort of intrinsic quality of love to it, which it must to have created something as wonderful as life, love, and consciousness. We truly are the means by which the universe experiences itself.

Materialism isn't the problem, it's incomplete materialism that is Cartesian Dualism in disguise. The perception and not mere belief of holistic physicalism gives a sense of interconnectedness and wonder to all existence.

I can think of a few

• Paul Kennedy's "The Rise and Fall of the Great Powers" - WHY and how whole empires fall
  
  
• Niall Ferguson's "The Ascent of Money" - How money rules the world - here's how.
  
  
• Jarred Diamond's "Guns, Germs and Steel" - his thesis might not be entirely correct - but it's a VERY fair look at how our history was influenced by these factors.
  
  
• Bruce Bueno De Mesquita's - "The Predictioneer's Game" - - How quantitative models are SCARILY accurate
  
  
• Emanuel Derman's "Models Behaving Badly" - And how sometimes quantitative models are totally wrong.
  
  
• Paul Roberts - "The End of Oil" - Probably the most serious and balanced read on what could be one of the most important economic problems facing our modern civilization in the next 20 years.
  
  
• Frank & Cook's "Winner Take All Society" - and why things are a problem.
  
  
• Richard Florida's "The Great Reset" - Florida is a pretty good author all around - far better than some others in the pitch.
  
  
• James Bamford's amazing "Body of Secrets" - Not all our enemies are external, and sometimes our allies turn out to actually be thuggish & deadly enemies.
  
  
• Iris Chang's "The Rape of Nanking" - Nobody here is exactly as they appear.
  
  
• Carl Sagan's "A Demon Haunted World"
  
  
• Robin Marantz Henig's "A Monk in the Garden" - Yeah - the priest that proved Darwin's theory, in 1865.....oh yeah and he invented statistics along the way.
  
  
• Brian Sykes' "The seven Daughters of Eve"
  
  
• Douglas Hofstadter's "Metamagical Themas" - Every page is practically amazing - a collection of amazing old articles from Dr. H's work
  
  
• Kristina Borjesson's edit of "Into the Buzzsaw" - the hard truth about a couple of things in the US media
  
  
• Richard Dawkins' "Climbing Mount Improbable" - a great work about such an amazing idea.
  
  
• Kim Sterelny's "Dawkins vs. Gould" - this is a REAL debate about evolution!
  

The Book

The Review of The Book:

~~

OK... Deep breaths everybody...

It is not possible to overstate how good this book is. I tried to give it uncountably many stars but they only have five. Five is an insult. I'm sorry Dr. Rudin...

This book is a good reference but let me tell you what its really good for. You have taken all the lower division courses. You have taken that "transition to proof writing" class in number theory, or linear algebra, or logic, or discrete math, or whatever they do at your institution of higher learning. You can tell a contrapositive from a proof by contradiction. You can explain to your grandma why there are more real numbers than rationals. Now its time to get serious.

Get this book. Start at page one. Read until you come to the word Theorem. Do not read the proof. Prove it yourself. Or at least try. If you get stuck read a line or two until you see what to do.

Thrust, repeat.

If you make it through the first six or seven chaptors like this then there shall be no power in the verse that can stop you. Enjoy graduate school. You half way there.

Now some people complain about this book being too hard. Don't listen to them. They are just trying to pull you down and keep you from your true destiny. They are the same people who try to sell you TV's and lobodemies.

"The material is not motivated." Not motivated? Judas just stick a dagger in my heart. This material needs no motivation. Just do it. Faith will come. He's teaching you analysis. Not selling you a used car. By the time you are ready to read this book you should not need motivation from the author as to why you need to know analysis. You should just feel a burning in you chest that can only be quenched by arguments involving an arbitrary sequence {x_n} that converges to x in X.

Finally, some people complain about the level of abstraction, which let me just say is not that high. If you want to see abstraction grab a copy of Spanier's 'Algebraic Topology' and stare at it for about an hour. Then open 'Baby Rudin' up again. I promise you the feeling you get when you sit in a hottub for like twenty minutes and then jump back in the pool. Invigorating.

No but really. Anyone who passes you an analysis book that does not say the words metric space, and have the chaptor on topology before the chapter on limits is doing you no favors. You need to know what compactness is when you get out of an analysis course. And it's lunacy to start talking about differentiation without it. It's possible, sure, but it's a waste of time and energy. To say a continuous function is one where the inverse image of open sets is open is way cooler than that epsilon delta stuff. Then you prove the epsilon delta thing as a theorem. Hows that for motivation?

Anyway, if this review comes off a combative that's because it is. It's unethical to use another text for an undergraduate real analysis class. It insults and short changes the students. Sure it was OK before Rudin wrote the thing, but now? Why spit on your luck? And if you'r a student and find the book too hard? Try harder. That's the point. If you did not crave intellectual work why are you sitting in an analysis course? Dig in. It will make you a better person. Trust me.

Or you could just change your major back to engineering. It's more money and the books always have lots of nice pictures.

In conclusion: Thank you Dr. Rudin for your wonderfull book on analysis. You made a man of me.

> Hovind does a great job of sounding convincing to somebody who doesnt have the facts.

... or someone who is not scientifically literate. I don't have all the facts either, but there are heuristics I use to determine whether someone is feeding me a line of BS or not. If you think your scientific literacy could improve, check out Carl Sagan's book The Demon-Haunted World. It's an excellent manual for learning critical thinking and skepticism. You can usually find a copy at used bookstores.

> So anyway that example you gave their pushes it to 50,000 years but what about older than that?

Right, since we're only speaking about radiocarbon dating here, 50,000 years is sort of the limit, since the half-life of C-14 is around 5700 years, after tens of thousands of years, there's so little C-14 left that it's increasingly difficult to use it as a means of dating.

If you want to date something older than that, you have to use methods other than radiocarbon.

One method is paleomagnetic dating.

Ice core dating is another. In this technique, not only can years be counted, but atmospheric gases can be sampled in these layers, and sometimes, these gases can be dated radiometrically. Years where there were large volcanic eruptions can be recorded, as that sediment is found in specific layers of the cores. I seem to recall that this method is good for up to 160,000 years ago.

Radiometric dating (as distinct from radiocarbon dating) are fairly widely-used methods. One example of this sort of dating is uranium-lead dating, and is the method used my Clair Patterson when he determined the age of the Earth back in 1956. There are a bunch of methods that are used, and in some cases, when using multiple methods to date something, we get results that are very close. In short: independent methods agree with each other.

If you've not seen any of it, you might enjoy Cosmos: A Spacetime Odyssey. In episode 7, titled The Clean Room, they detail how Clair Patterson, in his quest to discover the true age of the Earth, discovers something else rather unsettling. I won't spoil it for you - if you want to watch that specific episode, DailyMotion has a link here. It's a decent overview of radiometric dating. The whole series is pretty good, if you're looking to update your knowledge on modern science.

If you want a post-graduate level of understanding, it will be hard to learn the math past calculus that you will need with no instruction. Maybe impossible unless you are very gifted or studious. You'll need to learn more advanced math (taylor expansions, more advanced integration methods not always taught in calc I, multi-variable calculus, ordinary differential equations and linear algebra for starters). A layperson's understanding wouldn't require that much (maybe reading Sagan and Co. would be enough?), but it sounds like you aren't content with that. Maybe it would be good to start reading some journal articles and seeing what you can glean from them (introductions mostly), especially reviews of subjects you find interesting. If those are opaque, check a local university library for textbooks like Introduction to Modern Astrophysics, Padmanabhan's astrophysics I-III, Binney and Tremaine and things like that. There are text books more focused on specific subjects as well, but that's more a matter of personal interest. For me, Lewin and van der Klis is good, and so is Accretion Power in Astrophysics and the "CV Bible." You might notice Cambridge Astrophysics publishes quite a lot of quality astrophysics textbooks.

None of those are going to be legible without the math, though. There's not really anything between the "popular science" and "so you're taking a graduate course in astrophysics..." level texts that I've seen.

When I've got a clear aim in view for where I want to get to with a self-study project, I tend to work backwards.

Now, I don't know quantum mechanics, but here's how I might approach it if I decided I was going to learn (which, BTW, I'd love to get to one day):

First choose the book you'd like to read. For the sake of argument, say you've picked Griffiths, Introduction to Quantum Mechanics.

Now have a look at the preface / introduction and see if the author says what they assume of their readers. This often happens in university-level maths books. Griffiths says this:

> The reader must be familiar with the rudiments of linear algebra (as summarized in the Appendix), complex numbers, and calculus up to partial derivatives; some acquaintance with Fourier analysis and the Dirac delta function would help. Elementary classical mechanics is essential, of course, and a little electrodynamics would be useful in places.

So now you have a list of things you need to know. Assuming you don't know any of them, the next step would be to find out what are the standard "first course" textbooks on these subjects: examples might be Poole's Linear Algebra: A Modern Introduction and Stewart's Calculus: Early Transcendentals (though Griffiths tells us we don't need all of it, just "up to partial derivatives"). There are lots of books on classical mechanics; for self-study I would pick a modern textbook with lots of examples, pictures and exercises with solutions.

We also need something on "complex numbers", but Griffiths is a bit vague on what's required; if I didn't know what a complex number is than I'd be inclined to look at some basic material on them in the web rather than diving into a 500-page complex analysis book right away.

There's a lot to work on here, but it fits together into a "programme" that you can probably carry through in about 6 months with a bit of determination, maybe even less. Then take a run at Griffiths and see how tough it is; probably you'll get into difficulties and have to go away and read something else, but probably by this stage you'll be able to figure out what to read for yourself (or come back here and ask!).

With some projects you may have to do "another level" of background reading (e.g., you might need to read a precalculus book if the opening chapters of Stewart were incomprehensible). That's OK, just organise everything in dependency order and you should be fine.

I'll repeat my caveat: I don't know QM, and don't know whether Griffiths is a good book to use. This is just intended as an example of one way of working.

[EDIT: A trap for the unwary: authors don't always mention everything you need to know to read their book. For example, on p.2 Griffiths talks about the Schrodinger wave equation as a probability distribution. If you'd literally never seen continuous probability before, that's where you'd run aground even though he doesn't mention that in the preface.

But like I say, once you've taken care of the definite prerequisites you take a run at it, fall somewhere, pick yourself up and go away to fill in whatever caused a problem. Also, having more than one book on the subject is often valuable, because one author's explanation might be completely baffling to you whereas another puts it a different way that "clicks".]

I'll take a stab at a few :)

3) How do i get an empirical measurement of seeing/light polution etc so i can record the data during taking the subs?

Couple of ways you can do this. You could use a "sky quality meter" like this guy or, apparently, build your own.

Otherwise, you could use the work by Tony Flanders to collect data over a few weeks and measure your skyglow with your camera. This method is, obviously, a good bit less expensive, but clearly impractical for any area you're not at for an extended period of time.

Either of those methods would give you a quantitative analysis of the skyglow in your area.

4) What are the books every newbie should read to understand/learn about this awesome hobby?


IMO, Patrick Moore's PRactical Astronomy Series is a pretty solid place to start. You'll want to read descriptions/reviews thoroughly since some of them are limited to a particular hemisphere, or visual work only, etc. But in general, if it's in that series, it's likely to be good information packaged in an enjoyable read.

Finally, Turn left At Orion is, arguably, the beginners' Bible for any sort of amateur astronomy.

5) What are some good videos that are a great source of learning?

Probably can't go wrong with /u/forresttanaka's videos on YouTube as a starting point.

6) (For the people on the Northern side of the equator) If you could image 1 object in the Southern hemisphere, What would it be?

NGC 3372

omfg, NGC 3372

7) What is the difference between J2000 and JNOW, What are the benefits/drawbacks of each one?

The Earth's precession (wobble...1 wobble every ~26,000 years) means that objects in the night sky do "move" over long periods of time.

J2000 is the coordinates of a given object on the date of epoch (Julian date, hence the J) specifically, in this case, 12h on 1 JAN 2000. This gives us a uniform, unchanging reference for our current epic. We can say "Object X is at coordinates Y" and have everyone in agreement.

Of course, precession means it won't be EXACTLY there...how far off depends, obviously, on the date. So, to be precise about where the object is at this given time and date, we use "now"...hence, JNOW.

Which you use typically won't matter...most software/mounts/etc will know the difference, or calculate the difference, and be able to find whatever it is they're looking for.

Where it will matter most is when you're using 2 or ore pieces of equipment/software/etc, and they're talking to each other (For example, using Stellarium to control your Atlas mount via EQMOD). In that case you simply want to be certain you're using the SAME
system for everything.

Of course! :)

Here are a few of my favorite youtube channels that cover our universe.

These guys do a good job of giving excellent and creditable facts while keeping the video short and sweet.

https://www.youtube.com/user/scishowspace

This channel covers more than just space, but again they give good facts while still keeping the videos not too lengthy.

https://www.youtube.com/user/Kurzgesagt

And of course, nothing gets more credibility than the big guys themselves, NASA. These videos are a bit long, but are just loaded with a ton of real world space Q&A's.

https://www.youtube.com/user/NASAtelevision/videos

The few magazines I have lying around my house right now are all related to space, and they are a great read for any of my guests! Heres a link for the planetary society (main source of my reading material)
http://planetary.org/

and here are a few books that every curious mind should take a good long glance at when it comes to our universe.

http://www.barnesandnoble.com/w/pale-blue-dot-carl-sagan/1103141155

https://www.amazon.com/Brief-History-Time-Stephen-Hawking/dp/0553380168/ref=asap_bc?ie=UTF8

(this one is a MUST READ!)---> https://www.amazon.com/Science-Interstellar-Kip-Thorne/dp/0393351378

The main podcast I listen to is Star Talk with Neil DeGrasse Tyson. He has a plethora of different guests on at all times talking about new and fascinating topics. Here's a link for his show

https://www.startalkradio.net/

And when it comes to articles, most of them come from Reddit! I am subscribed to a ton of different space related subreddits which post countless numbers of interesting articles all the time. Here is a small list just to name a few

r/space r/astronomy r/astrophysics r/astrophotography r/science r/spaceporn

I hope this helps!

Little mental trick you can do to show off to some people:

any number * 11 is easy. Even in the 2 digits.

Let's do 32 again.

*32 11

Separate 32 into two digits, add them, and then put that number between those two digits. For example:

3 + 2 = 5

place between the two original digits:

352

-----

This works with three digits as well (but I have to go figure out how to do that one again). There is a book on the Apple Store that is an awesome read if you're into it. All of the things I am showing you are possible to do mentally. I can currently square 4 digit numbers in my head sorta reliably, and can square 3 and 2 digit numbers without fail. It is really fun and I enjoy doing it.

-----

EDIT:

PLEASE PLEASE PLEASE support this guy and do not download a pdf of the book. He is absolutely incredible with what he can do and is sharing it with people so they can do it too. Give him credit!

Book on Amazon

Book on iBooks

-----

Youtube video of this guy

I think the advice given in the rest of the thread is pretty good, though some of it a little naive. The suggestion that differential equations or applied math somehow should not be of interest is silly. A lot of it builds the motivation for some of the abstract stuff which is pretty cool, and a lot of it has very pure problems associated with it. In addition I think after (or rather alongside) your initial calculus education is a good time to look at some other things before moving onto more difficult topics like abstract algebra, topology, analysis etc.

The first course I took in undergrad was a course that introduced logic, writing proofs, as well as basic number theory. The latter was surprisingly useful as it built modular arithmetic which gave us a lot of groups and rings to play with in subsequent algebra courses. Unfortunately the textbook was god awful. I've heard good things about the following two sources and together they seem to cover the content:

How to prove it

Number theory

After this I would take a look at linear algebra. This a field with a large amount of uses in both pure and applied math. It is useful as it will get you used to doing algebraic proofs, it takes a look at some common themes in algebra, matrices (one of the objects studied) are also used thoroughly in physics and applied mathematics and the knowledge is useful for numerical approximations of ordinary and partial differential equations. The book I used Linear Algebra by Friedberg, Insel and Spence, but I've heard there are better.

At this point I think it would be good to move onto Abstract Algebra, Analysis and Topology. I think Farmerje gave a good list.

There's many more topics that you could possibly cover, ODEs and PDEs are very applicable and have a rich theory associated with them, Complex Analysis is a beautiful subject, but I think there's plenty to keep you busy for the time being.

I may be in the minority here, but I think that high school students should be exposed to statistics and probability. I don't think that it would be possible to exposed them to full mathematical statistics (like the CLT, regression, multivariate etc) but they should have a basic understanding of descriptive statistics. I would emphasize things like the normal distribution, random variables, chance, averages and standard deviations. This could improve numerical literacy, and help people evaluate news reports and polls critically. It could also cut down on some issues like the gambler's fallacy, or causation vs correlation.

It would be nice if we could teach everyone mathematical statistics, the CLT, and programming in R. But for the majority of the population a basic understanding of the key concepts would be an improvement, and would be useful.

Edit At the other end of the spectrum, I would like to see more access to an elective class that covers the basics of mathematical thinking. I would target this at upperclassmen who are sincerely interested in mathematics, and feel that the standard trig-precalculus-calculus is not enough. It would be based off of a freshman math course at my university, that strives to teach the basics of proofs and mathematical thinking using examples from different fields of math, but mostly set theory and discrete math. Maybe use Velleman's book or something similar as a text.

First off, I'd recommend looking into a book like this.

Second, when doing something like multiplication, it always helps to break a problem down into easier steps. Typically, you want to be working with multiples of 10/100/1000s etc.

For multiplying 32 by 32, I would break it into two problems: (32 x 30) + (32 x 2). With a moderate amount of practice, you should quickly be able to see that the first term is 960, and the second is 64. Adding them together gives the answer: 1024. It can be tricky to keep all these numbers in your head at once, but that honestly just comes down to practice.

Also, that same question can be expressed as 32^2 . These types of problems have a whole bunch of neat tricks. One that I recall from the book I linked above has to do with squaring any number ending in a 5, like 15 or 145. First, the number will always end in 25. For the leading digits, take the last 5 off the number, and multiply the remaining digits by their value +1. So, for 15 we just have 1x2=2. For 145, we have 14x15=210. Finally, tack 25 on the end of that, so you have 15^2 = (1x2)25 = 225, and 145^2 = (14x15)25 = 21025. Boom! Now you can square any number ending in 5 really quick.

Edit: Wanted to add some additional comments that have helped me out through the years. First, realize that

(1) Addition is easier than subtraction,

(2) Addition and subtraction are easier than multiplication,

(3) Multiplication is easier than division.

Let's go through these one by one. For (1), try to rewrite a subtraction problem as addition. Say you're given 31 - 14; then rephrase the question as, what plus 14 equals 31? You can immediately see that the ones digit is 7, since 4+7 = 11. We have to remember that we are carrying the ten over to the next digit, and solve 1 + (1 carried over) + what = 3. Obviously the tens digit for our answer is 1, and the answer is 17. I hope I didn't explain that too poorly.

For (2), that's pretty much what I was originally explaining at the start. Try to break a multiplication problem down to a problem of simple multiplication plus addition or subtraction. One more example: 37 x 40. Here, 40 looks nice and simple to work with; 37 is also pretty close to it, so let's add 3 to it and just make sure to subtract it later. That way, you end up with 40 x 40 - (3 x 40) = 1600 - 120 = 1480.

I don't really have any hints with division, unfortunately. I don't really run into it too often, and when I do, I just resort to some mental long division.

I applaud your skepticism! I do take issue with a few statements:

>My younger brother (19), however, is a hardcore skeptic. He claims to have seen a cup levitate and move in front of him in the bathroom one night, and [...] I know that he is definitely not the type of person to do any investigating whatsoever and will just automatically assume that it was a ghost.

Your brother is not a skeptic.

>I always ridicule him for his insane belief.

That's not very nice.

>As an atheist, I can't help but look down upon people who hold religious beliefs because it all seems so absurd to me.

That doesn't help foster communication. I think you might benefit greatly from this half-hour talk from "bad astronomer" Phil Plait. The general idea behind the talk is: when have you ever changed your beliefs just because someone told you that they were stupid? Instead of helping your case, you are hurting it. You'll only cause them to reinforce their beliefs, even if your confirmed evidence directly disproves their beliefs.

>me being the logical person I am, I choose the side of "you're crazy and you imagined it", while he takes the "it was definitely a ghost" side.

You two should work on your communication, because this approach is going to go nowhere.

>It took my brother a little longer to come around to the fact that there is no god.

It is not a fact that there is no god.

>I consider myself atheist while I consider him to be agnostic.

It's a common misconception, but that's not how it works.

If you found confirmation bias [edit: interesting] (and all of the other names we have for the ways our brains will innately fool us), I'd highly recommend that you read Carl Sagan's The Demon-Haunted World: Science As A Candle In The Dark. I would suggest that you read it first, in private. Then I would suggest lending it to your brother to read, and asking him to recommend that you read a book of his recommendation. Afterwards, talk about your thoughts together.

Don't be mean to him, or dismissive. Sometimes, critical thinking has to be taught, or self-learned after experience. It's not a slight on my aunt's intelligence, for instance, that she believes that some forms of homeopathy is effective. I could tell her all day that we know that homeopathy doesn't work. I could give her thousands of pages of scientific journals explaining, in great and meticulous detail, why this is the case. She would likely dismiss "mainstream science," though, because it isn't supporting her worldview and/or belief system. That doesn't mean my aunt is a moron. It means, more than anything else, that she doesn't understand what a useful standard of evidence is in order to determine truths about our world.

>I don't believe in ghosts. Please tell me some experiences, give insight and opinions. Try to help me understand.

I've made similar posts searching for similar truths, like:

• Addressing The Most Common Paranormal Claims
  
• Considering how easy it is to fake photo/video/audio footage, can they still be accepted as forms of paranormal evidence?
  
• Carl Sagan said "Extraordinary claims require extraordinary evidence." - What are your thoughts on this?
  
  From my own observations, what it really seems to come down to is a combination of: the person's standards of evidence, their relationship with their pre-existing beliefs, their upbringing, and a near-complete misunderstanding of what science is and how science works. I see examples of these four issues every day on /r/Paranormal, as well as /r/UFOs, which I've also probed for truths:
  
  
• Why attribute ancient structures and complex crop circles to extraterrestrials?
  
• My thoughts on Ancient Aliens (TV), Erich von Däniken, and Zecharia Sitchin. What are yours?
  
• UFO experience from one of your resident subscribing skeptics
  
  The bottom line is: there is no proof of ghosts like what you are looking for. The best thing we have, so far, isn't from a digital photograph or an EVP. We've got neuroscience. We're getting better and better at watching the brain work. We can watch brain activity related to our consciousness happen, and we can do it all the time, every time. We've also noticed that once a human body is dead, there is no activity related to our consciousness or anything else occurring within our brains. So, based on the evidence so far, consciousness seems to die with the body. This, more than anything else, speaks to the existence of ghosts, if the belief is, in fact, that ghosts are the souls/consciousness/manifestation of dead people.
  
  But that says nothing about the experience a person goes through when they believe that they've seen a ghost. The experience is real, even if self-deception is involved. That includes your brother. I wish you the very best of luck. Try to be more tolerant of him!

I'm only a high school sophomore, so I can't really help you with most of your questions, but if you want to improve your mental math, buy "Secrets of Mental Math" by Arthur Benjamin.

It's written in a way that makes sitting in your room doing mental calculations seem fun and it is very accessible. I have only gotten through 3 chapters (the addition/subtraction/multiplication chapters) and I can confidently add and subtract 3-digit numbers in seconds. I can even mentally cube two-digit numbers in a few minutes.

[Anyway, here's a link to the book] (http://www.amazon.com/Secrets-Mental-Math-Mathemagicians-Calculation/dp/0307338401/ref=sr_1_1?s=books&ie=UTF8&qid=1381633585&sr=1-1&keywords=mental+math)

[If you don't want to buy it, you can use this PDF version of the book] (http://www.uowm.gr/mathslife/images/fbfiles/files/Secrets_of_Mental_Math___Michael_Shermer___Arthur_Benjamin.pdf)

[And here is the author, Arthur Benjamin, performing what he likes to call "Mathemagics"] (http://www.youtube.com/watch?v=e4PTvXtz4GM)

I hope this has been helpful and you succeed in whatever uni you go to :)

>evolution is based around the fact that existence is random and chaotic.

>random system

Evolution is the opposite of random. It's natural selection, not natural shit happens (no offense). It's a pattern: the things likely to be reproduced are reproduced the most, and there end up being the most of those things, until they completely overpower the others and they're all that's left and they're the new standard. (To answer your questions: The hornier humans made more babies. Then there were more horny babies and humans. Today, all the humans are horny (inclined to mate), to paraphrase.)

We're not naked all the time because it snows. (I'm simplifying, but do you see my point?) Also, culture. That's been around, in anthropological terms, fo eva. (Shyness is something else. This is all extremely complex.)

>And if you take into account that that would accelerate reproduction too much, food supply would diminish and natural selection would kick in.

Looks like you answered your own question there. It's like trees: being taller (mating more) gets them an advantage; but being too tall costs too many resources (we eat too much) and they even out.

I hate to sound insulting, but there are soo many things wrong with your post; you don't understand evolution at all. I think you should read up on it a little. If you're willing to read a book, Richard Dawkins's The Greatest Show on Earth is amazing. Not only will it give you a wonderful understanding, but it's just a brilliant read, and I plan on rereading it for the fun of it. And I got the tree thing from Chapter 12. (Dawkins explains it much better.)

But if you don't want to read a whole book, maybe find some articles or something.

Anyway, good luck.

There are essentially "two types" of math: that for mathematicians and everyone else. When you see the sequence Calculus(1, 2, 3) -> Linear Algebra -> DiffEq (in that order) thrown around, you can be sure they are talking about non-rigorous, non-proof based kind that's good for nothing, imo of course. Calculus in this sequence is Analysis with all its important bits chopped off, so that everyone not into math can get that outta way quick and concentrate on where their passion lies. The same goes for Linear Algebra. LA in the sequence above is absolutely butchered so that non-math majors can pass and move on. Besides, you don't take LA or Calculus or other math subjects just once as a math major and move on: you take a rigorous/proof-based intro as an undergrad, then more advanced kind as a grad student etc.

To illustrate my point:

Linear Algebra:

1. Here's Linear Algebra described in the sequence above: I'll just leave it blank because I hate pointing fingers.
   
   
2. Here's a more serious intro to Linear Algebra:
   
   Linear Algebra Through Geometry by Banchoff and Wermer
   
   3. Here's more rigorous/abstract Linear Algebra for undergrads:
   
   Linear Algebra Done Right by Axler
   
   4. Here's more advanced grad level Linear Algebra:
   
   Advanced Linear Algebra by Steven Roman
   
   -----------------------------------------------------------
   
   Calculus:
   
   
3. Here's non-serious Calculus described in the sequence above: I won't name names, but I assume a lot of people are familiar with these expensive door-stops from their freshman year.
   
   
4. Here's an intro to proper, rigorous Calculus:
   
   Calulus by Spivak
   
   3. Full-blown undergrad level Analysis(proof-based):
   
   Analysis by Rudin
   
   4. More advanced Calculus for advance undergrads and grad students:
   
   Advanced Calculus by Sternberg and Loomis
   
   The same holds true for just about any subject in math. Btw, I am not saying you should study these books. The point and truth is you can start learning math right now, right this moment instead of reading lame and useless books designed to extract money out of students. Besides, there are so many more math subjects that are so much more interesting than the tired old Calculus: combinatorics, number theory, probability etc. Each of those have intros you can get started with right this moment.
   
   Here's how you start studying real math NOW:
   
   Learning to Reason: An Introduction to Logic, Sets, and Relations by Rodgers. Essentially, this book is about the language that you need to be able to understand mathematicians, read and write proofs. It's not terribly comprehensive, but the amount of info it packs beats the usual first two years of math undergrad 1000x over. Books like this should be taught in high school. For alternatives, look into
   
   Discrete Math by Susanna Epp
   
   How To prove It by Velleman
   
   Intro To Category Theory by Lawvere and Schnauel
   
   There are TONS great, quality books out there, you just need to get yourself a liitle familiar with what real math looks like, so that you can explore further on your own instead of reading garbage and never getting even one step closer to mathematics.
   
   If you want to consolidate your knowledge you get from books like those of Rodgers and Velleman and take it many, many steps further:
   
   Basic Language of Math by Schaffer. It's a much more advanced book than those listed above, but contains all the basic tools of math you'll need.
   
   I'd like to say soooooooooo much more, but I am sue you're bored by now, so I'll stop here.
   
   Good Luck, buddyroo.

Depends what kind of math you're interested in. If you're looking for an introduction to higher (college) math, then How to Prove It is probably your best bet. It generally goes over how proofs work, different ways of proving stuff, and then some.

If you already know about proofs (i.e. you are comfortable with at least direct proofs, induction, and contradiction) then the world is kind of your oyster. Almost anything you pick up is at least accessible. I don't really know what to recommend in this case since it's highly dependent on what you like.

If you don't really know the basics about proofs and don't care enough to yet, then anything by Dover is around your speed. My favorites are Excursions in Number Theory and Excursions in Geometry. Those two books use pretty simple high school math to give a relatively broad look at each of those fields (both are very interesting, but the number theory one is much easier to understand).

If you're looking for high school math, then /u/ben1996123 is probably right that /r/learnmath is best for that.

If you want more specific suggestions, tell me what you have enjoyed learning about the most and I'd be happy to oblige.

I agree with all the suggestions to start with How to Prove It by Velleman. It's a great start for going deeper into mathematics, for which rigor is a sine qua non.

As you seem to enjoy calculus, might I also suggest doing some introductory real analysis? For the level you seem to be at, I recommend Understanding Analysis by Abbott. It helped me bridge the gap between my calculus courses and my first analysis course, together with Velleman. (Abbott here has the advantage of being more advanced and concise than Spivak, but more gentle and detailed than baby Rudin -- two eminent texts.)

Alternatively, you can start exploring some other fascinating areas of mathematics. The suggestion to study Topology by Munkres is sound. You can also get a friendly introduction to abstract algebra by way of A Book of Abstract Algebra by Pinter.

If you're more interested in going into a field of science or engineering than math, another popular approach for advanced high schoolers to start multivariable calculus (as you are), linear algebra, and ordinary differential equations.

Well, one of the books I read that really got me started in cosmology and physics is Brian Greene's The Fabric of the Cosmos. I think it is his best book and talks a lot about the fundamentals of our universe. Brian Greene studies string theory and those bits are interesting, but just know that the theory is far from complete or proven. This one is definitely the most physics heavy suggestion.

Another book that I really enjoy is A Short History of Nearly Everything by Bill Bryson. It is essentially a history of science, and he covers a lot of topics. Many of which I knew almost nothing about when I read it. It puts into perspective how all the things we know came to be.

The next two recommendations are not books, but they still have a lot of great information in them. This first is a Youtube series called Crash Course Astronomy. The host is Phil Plait, one of the programmers involved with the Hubble Space Telescope. There are a lot of videos, so it would keep you busy and learning for a while.

The last recommendation is as close to the upper level undergraduate astronomy courses that I have taken without actually doing any math. It is a bunch of class lectures from Ohio State University that were recorded and released as a podcast about stellar astronomy and planetary astronomy. I found the lecturer's voice a little whiny at first, but I soon got past that because the content was so good. I kid you not, I listened to this ahead of my ASTRO 346 Stellar Astronomy class at my university, and I felt like the class concepts were almost a review.

All of those recommendations require you to do no math, but you only get a glimpse of the concepts that way. If you want to dive in more, you'll need to take a class or read a textbook on your own.

I hope that helps. Let me know if you have any other questions about astronomy as a subject or as a course of study in school :)

Check out the Foundational Falsehoods of Creationism.

Check out a copy of the books The Greatest Show on Earth or Why Evolution is True from a library. You can also get one of them for free on Audible, but you will miss out on the citations and diagrams.

See if you can watch or read The Grand Design by Stephen Hawking. I watched the miniseries, it's pretty good. It used to be on Netflix but no longer is.

Cosmos is great, and is on Netflix. If you want to watch videos about Cosmology just type in one of the popular physicist's names, Brian Greene, Neil deGrasse Tyson, Lawrence Krauss (his Universe from Nothing book is really great, so are his lectures about it), Sean Carroll etc.

Let me know if you want to talk, I'm always up for it.

To put this in a slightly different light than other commenters, there's one simple answer: the laws of physics should work no matter what you're doing (this is what Einstein focused on). You can't go exactly the speed of light, but even if you blasted off from Earth at 0.999c (very close to it!) your spaceships headlights, disco ball, and christmas light would still beam light away from you at the speed of light. Whaaat? Why?

Speed and velocity are relative. In this case, your ship is moving relative to Earth, and off to Neptune or some dank, misty moon like Titan. If you're in empty space and a spaceship goes floating by, it's difficult to tell if she's the one whizzing past, or you. Inside you're own ship, like when you're in a smoothly cruising car, it's almost like you're standing still. Hence, when you turn on a flashlight, or your headlights, they work just like normal and the light travels at the speed of light. If this seems weird - it is a bit weird! It's where all the cool stuff that happens in relativity comes from (twin paradox time dilation, E= mc^2). To learn more, I seriously recommend checking out shows like Cosmos or books like "The Elegant Universe." Hopefully they will blow your mind like they did mine. :)

"A Book of Abstract Algebra" by Charles C. Pinter is nice, from what I've seen of it--which is about the first third. I'm going through it in an attempt to relearn the abstract algebra I've forgotten.

I was using Herstein (which was what I learned from the first time), and was doing fine, but saw the Pinter book at Barnes & Noble. I've found it is often helpful when relearning a subject to use a different book from the original, just to get a different approach, so gave it a try (it's a Dover, so was only ten bucks).

What is nice about the Pinter book is that it goes at a pretty relaxed pace, with a good variety of examples. A lot of the exercises apply abstract algebra to interesting things, like error correcting codes, and some of these things are developed over the exercises in several chapters.

You don't have to be a prodigy to be able to understand some real mathematics in middle school or early high school. By 9th grade, after a summer of reading calculus books from the local public library, I was able to follow things like Niven's proof that pi is irrational, for instance, and I was nowhere near a prodigy.

The Z10 would be a great scope. I have the Z12, and I love it. It's a lot to handle though. The Z10 would give you some more mobility and wouldn't take up too much space. A 10 is still a great light bucket and will give you wonderful views of lots of fun objects.

There are myriad resources to get you going on what to see and when to see it. You can check out earthsky.org for a day-by-day update on what's happening in the sky. Telescopius is another great resource. Also, grab yourself a copy of Turn Left at Orion. It'll help you get acquainted with the night sky.

The Bahamian sky should treat you quite nicely. Just be patient with the equipment and the hobby. Learning takes time.

For a good starter into critical analysis and the scientific method, along with general topics on not getting suckered into things, I recommend Demon Haunted World by Carl Sagan:

https://www.amazon.com/Demon-Haunted-World-Science-Candle-Dark/dp/0345409469

To help start thinking about balanced critical awareness you can try some little workbooks like this: https://www.amazon.com/Do-You-Think-What-Philosophical/dp/0452288657

That book isn't very in depth but I found it a good way to start exercising skepticism and logic.

To learn how to step back and pay attention to what is happening, including thought patterns, emotions and body states with a critical but calm eye, I recommend mindfulness practice in the insight meditation tradition, it is quite secular, rational and will be useful for anyone.

6 part introduction to mindfulness:

http://www.audiodharma.org/series/1/talk/1762/

To dampen the irrational negativity I recommend the practice of metta which is something like purposefully practicing compassion, forgiveness and support.

For specific info on Metta(loving kindness) practice just ctrl+f on "metta" on this page: http://www.audiodharma.org/recommended_talks/

Then, I recommend two practical philosophies that both teach how to deal with internal dialogue and experience in rational and practical methods.

Secular Buddhism
https://secularbuddhism.com/category/podcast/

Stoicism
https://immoderatestoic.com/good-fortune/

You should start with the oldest episodes.

On the Stoicism side it would be helpful to read through Epictetus Enchiridion and Marcus Aurelius Meditations as starters. Try to find some modern translations to make it a bit easier unless you like the old language stuff.

I know that is a lot, I'd say start with either the mindfulness practice or Carl Sagan's book. Keep it simple and take your time.

Well... Not really? I'd probably word it more as experiencing the passage of time faster/slower as opposed to moving through time faster/slower, as the latter (at least to me) seems to imply time as an absolute, but that may just be a wording issue on my part.

Honestly we're moving toward areas I don't feel as confident explaining, but I'll give it a try. As far as I understand, basically if two observers are at rest with respect to each other in the same inertial reference frame, they will experience the same passage of time. If the two observers are in motion with respect to each other (outside of a major gravitational field), each will observe the other's clock as going slower than his own. Each observer's experience of his own passage of time also never changes.

Clocks near significant gravitational masses also move more slowly than those farther away, which isn't reciprocal like the relative velocity time dilation. An observer farther away from the mass and one closer will both agree that the farther away observer's clock is moving faster and the closer observer's clock is moving slower.

If all this fascinates you and you want to read about it from someone who actually knows what they're talking about, I'd recommend Stephen Hawking's "A Brief History of Time". You can also check out the Wikipedia pages on the theory of relativity and time dilation, but I think it helps a lot to have a whole book to explore the ideas rather than just a couple Wikipedia pages. Also, Hawking is really good at explaining all of it in a way that normal people like us can understand while still keeping the ideas intact.

A good book that is fun to read and has tons of anecdotes about scientific history is A Short History of Nearly Everything by Bill Bryson

In a similar vein, you can ponder the more mind-bending aspects of our Universe with Stephen Hawkings A Brief History of Time

Other than that you may find some interesting things in the works of Carl Sagan or Richard Dawkins (I personally recommend Dawkins's The Selfish Gene)

If you are sick of scientific titles you can also check out Freakonomics or The Worldly Philosphers

These Books are all written for a general audience so they go down pretty easy.

Deciding which major in College can be tricky - I was lucky since I knew exactly what I wanted to study before I left High School, but maybe some ideas in these books will pique your interest. My parents always told me to go to school to study something I love, and not to train for a job. I'm not so sure this advice carries through in "recovering" economy. You may want to factor in the usefulness of your degree post-college (but don't let that be the only thing you consider!).

Good Luck, and enjoy!

I've posted this elsewhere but here ya go...

> Avoid the Audubon guide. The Audubon guide is pretty terribad (bad photos, pithy descriptions, not user-friendly.)

> There are much better nationwide guides out there (like the Falcon Guide), but quite honestly you're better off with a regional guide.

> My recs for regional field guides:

> Alaska

> - Common Interior Alaska Cryptogams

> Western US

> - All The Rain Promises and More

• Mushrooms of the Pacific Northwest
  
  >Midwestern US
  >
  
• Mushrooms of the Midwest
  
• Edible Wild Mushrooms of Illinois and Surrounding States
  
• Mushrooms of the Upper Midwest
  
  >Southern US
  >
  
• Texas Mushrooms: A Field Guide
  >
  Eastern US
  >
  
• Mushrooms of West Virginia and the Cental Appalachians
  
• Mushrooms of Northeast North America
  
• Macrofungi Associated with Oaks of Eastern North America
  
  > As an aside, books like Mushrooms Demystified, Lichens of North America, Mushrooms of Northeastern North America, and Mushrooms of the Southeastern United States are too large and cumbersome to take out in the field, but are all excellent references to have at home for ID after a foray.

I would not recommend the Audubon guide it is very out of date (this can range from outdated taxonomy all the way to toxicology that has changed over the years). It is useful because it lists species other guides lacks but you'll learn to hate it.

Buy a location specific guide. It depends on where you live. If you get really into field hunting buy some specific guides that give you a more in depth understanding and help you not to die. Joining a local mycological society is also an extremely valuable resource in understanding mycology.

Here's a bit of everything

Regional guides

Alaska

Common Interior Alaska Cryptogams

Western US

All The Rain Promises and More
Mushrooms of the Pacific Northwest

Mushrooms Demystified This is an old book, while still useful it definitely needs updating.

The New Savory Wild Mushroom Also dated but made for the PNW

Midwestern US

Mushrooms of the Midwest

Edible Wild Mushrooms of Illinois and Surrounding States

Mushrooms of the Upper Midwest

Southern US

Texas Mushrooms: A Field Guide

Mushrooms of the Southeastern United States

Common Mushrooms of Florida

A Field Guide to Southern Mushrooms It's old so you'll need to learn new names.

Eastern US

Mushrooms of West Virginia and the Central Appalachians

Mushrooms of Northeast North America (This was out of print for awhile but it's they're supposed to be reprinting so the price will be normal again)

Mushrooms of Northeastern North America

Macrofungi Associated with Oaks of Eastern North America(Macrofungi Associated with Oaks of Eastern North America)

Mushrooms of Cape Cod and the National Seashore

More specific (Advanced) guides

Psilocybin Mushrooms of the World

North American Boletes

Tricholomas of North America

Milk Mushrooms of North America

Waxcap Mushrooms of North America

Ascomycete of North America

Ascomycete in colour

Fungi of Switzerland: Vol. 1 Ascomycetes A series of 6 books.

Fungi Europaei A collection of 14 books.

PDFs and online Guides

For Pholiota

For Chlorophyllum

American species of Crepidotus

Guide to Australian Fungi If this is useful consider donating to this excellent set of guides.

Websites that aren't in the sidebar

For Amanita

For coprinoids

For Ascos

MycoQuebec: they have a kickass app but it's In French

Messiah college this has a lot of weird species for polypores and other things

For Hypomyces

Cultivation

The Mushroom Cultivator: A Practical Guide to Growing Mushrooms at Home (If your home is a 50,000 sq ft warehouse)

Organic Mushroom Farming and Mycoremediation: Simple to Advanced and Experimental Techniques for Indoor and Outdoor Cultivation

Growing Gourmet and Medicinal Mushrooms

Mycology

The fifth kingdom beginner book, I would recommend this. It goes over fungal taxonomy Oomycota, Zygomycota and Eumycota. It also has ecology and fungi as food.

The kingdom fungi coffee table book it has general taxonomy of the kingdom but also very nice pictures.

Introduction to fungi Depends on your definition of beginner, this is bio and orgo heavy. Remember the fungi you see pop out of the ground (ascos and basidios) are only a tiny fraction of the kingdom.

NAMA affiliated clubs

For a pocket guide I'd recommend All That the Rain Promises and More. It has a little bit of a bias towards species in western North America, but it's still very useful in the east (I'm in New England and I love it). Mushrooms Demystified is pretty big for taking into the field, but it is a great companion to ATtRPaM, and it is the best all around field guide for North America, in my opinion.

I didn't take any lower division classes here but the upper division classes are pretty great. I haven't really had any bad professors and they seem to be a lot better at teaching than the professors in my upper division physics courses were.

The quarter system isn't bad. I think it's actually a good pace and the courses that have more than 10 weeks of content are 2 or 3 quarters long, which is great because it means you're not stuck in a class that you hate for very long.

The difficulty depends entirely on the professor, but I haven't had a class that was super difficult and uncurved. Curves always seem fair for the difficulty of the class. Finals are usually fair but midterms really suck because they're only 50 minutes long. You will probably do horrible on a few of them before you figure out a way to make it work. We have a much cushier path to upper division than most schools. Instead of being dumped into linear algebra or real analysis and having to learning how to do proofs, we have an intro to proofs and logic prerequisite and another class where you essentially just practice proof techniques that you will use in analysis later. I loved it because it let me focus on the material in my more challenging classes without having to figure out the mechanics and techniques of general proof writing.

One thing to keep in mind is that upper division math is nothing whatsoever like the math that you're probably used to. You essentially start over and learn things correctly, and you usually have to pretend that you don't know anything that you've learned over the past 14 years of math classes outside of basic arithmetic and algebra. You will be writing paragraphs in plain English with occasional math symbols. It's all about taking definitions and theorems that you know and using them to argue that other theorems are true. It's a lot more fun than it sounds. If you want to get a feel for what it's going to be like, check out this book:

http://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995/

It's easy to find elsewhere. You don't need to know anything to get started and it's actually really fun to work through. This was the textbook for my intro to proofs class.

I use printouts and books much more than apps. Printouts especially are great because you can mark them up and plan what you want to look for.

I mostly use http://www.skymaps.com/downloads.html to get the map of what's up this month, and it includes locations of the planets. Easy two page printout. Of course, planets are bright enough that you don't even need dark skies to find them, so you can try pointing your funscope at them right now.

Currently, the planets are coming up later at night, with Jupiter coming up after mindight, mars after 2:00am, and venus at 4:00am. So if you want to see them, I'd recommend getting up early in the morning. I'd recommending practicing finding them in the sky with an App before you leave. They are super easy to find once you've done it a couple of times, and follow the path of the sun.

Since your scope and binoculars are relative low on magnification, you'll probably want to look for big bright nebula's, star clusters, and galaxies. If you've never seen any of them before, look for the bright ones: the Orion Nebula and Andromeda galaxy are huge and going to be high in the sky in the evening. They are both bright enough to see a little bit of even in light polluted skies, so I'd practice finding them before you leave on vacation.

For traveling recently, I just brought binoculars and a tripod. I have cheap sets of 7x50 and 15x70. Your funscope has a 76mm mirror, about the size of my big binoculars.

Personally, I think it's a great idea to bring both the scope and the binoculars. You'll get a feel for what you like to look through more once you're out there.

I am not an expert on taking pictures through telescopes, but I do know that if you don't have a tracking equatorial mount, it's really tough to get anything in the sky because you have to take brief pictures. And the funscope doesn't have a parabolic mirror, which makes goop pictures very difficult, too.

If you're just starting out and want to get into the hobby, I really recommend the book Left Turn at Orion. Truly a great guide to getting started when you have no idea where to start in this hobby. And it's the best guide for finding stuff for the first time.

> If there isnt a creator then how did all this life get here?

Abiogenesis is our best working guess for now, but there's a lot of work left to be done. The key thing here though is to be honest and admit that we don't have all the answers rather than wave our hands and say that it was a magical sky faerie.

> I under stand the big bang, at one point all the matter in Universe was compact then it all expanded outwards, well from school I learned that matter cannot be created nor destroyed. How did all that compact matter get there in the first place? I dont know.

It's ok to not know - that's honesty. This excellent book by Lawrence Krauss is fascinating. If you don't have access to it, there's also a talk he gave a few years back.

> I guess I'm getting old enough where my own opinions are forming I'm just trying to decide what I want those opinions to be.

Remember that ultimately our opinions are just that - opinions. The universe is as it is regardless of what we may wish to be true and what we may believe.

I agree. :-) I figured I'd pick a fairly strong example of easily shot down attributes. (On the other hand, the fact that at least 1/3 of the voters in my country agree with the easily shot down version is quite scary, but that's a rant for another day ;-)

The reasons I reject Christianity as a whole are much larger, and not really applicable here, but since you brought it up:

I was born and raised an evangelical Christian, and remained so for ~25 years after my decision at 7 to accept Jesus's death as atonement for my sins and follow him with my whole life.

I am no longer for many reasons, starting with accepting evolution and the lack of an historical Adam, moving into biblical criticism and archeological study, studying other world religions and cultures and their similar claims to Christianity, studying cosmology, psychology, sociology, and cognitive science of religion, and ending at philosophy and specifically epistemology. I tried really hard to maintain my faith, but there is no grounding for it that I can find, and I gave it up with much grief.

Christianity is in no way exceptional to all the other religions. In that way I agree with Spong's 12 points of reform. If you don't know why Spong talks like that, his book Why Christianity Must Change or Die speaks at least as strongly as the atheist polemics. In addition, as I understand the reasons for apparent teleology and cognitive basis for religion which arose by co-opting the social mechanisms of our brain given by natural selection, and think there is a rising case for the universe spontaneously springing out of a quantum foam which is a much less problematic thing to pre-exist than a conscious, changeless entity of incredible knowledge, power, and perfection. Not to mention the issues of causality and intentionality existing in such a creature outside space-time and the entropic arrow of time, without which causality is incoherent. It is for this reason that much of the most interesting theology in the journals these days is on time issues.

Because of all these things we now have much simpler answers for than a supreme being, I see absolutely no reason to posit even a panenthesitic, pantheistic, or deistic god. The later two, even if existant, would by definition have absolutely no impact on my life, and the first no measurable impact.

In the end, if all religion can possibly discover is that we should to be nice to each other and feel awe of the universe and love, I'll take other moral theories that give me the same and yet come from grounding in the observable universe, thanks. Desire utilitarian theory is one of the more interesting ones.

I think the Atheist's Guide to Reality linked above is perhaps the most important book I've ever read which argues strongly goes against the typical arguments of the apologists, and I'm anxious to see more people critique it. Krauss's book linked above is one of very few I've ever pre-ordered, as his video with the same title was quite interesting. If he has a good basis for his claims, it might be the most important scientific theory since Darwin in relation to understanding ourselves.

RPCV checking in. This is a good idea... you're going to have a lot of downtime and it's a great opportunity to read all the things you've wanted to but haven't yet found the time for. That could mean math, or languages, or just old novels.

When I was learning functional analysis, if found this book by Bollobas to be incredibly helpful. Of course, the only real analysis reference you need is Baby Rudin, but if you want to learn measure theory you may want his Real & Complex Analysis instead.

For texts on the other subjects, take a look at this list. You should be able to find anything you need there.

If you have any questions about Peace Corps, feel free to PM me. Good luck!

When you say everyday calculations I'm assuming you're talking about arithmetic, and if that's the case you're probably just better off using you're phone if it's too complex to do in you're head, though you may be interested in this book by Arthur Benjamin.

I'm majoring in math and electrical engineering so the math classes I take do help with my "everyday" calculations, but have never really helped me with anything non-technical. That said, the more math you know the more you can find it just about everywhere. I mean, you don't have to work at NASA to see the technical results of math, speech recognition applications like Siri or Ok Google on you're phone are insanely complex and far from a "solved" problem.

Definitely a ton of math in the medical field. MRIs and CT scanners use a lot of physics in combination with computational algorithms to create images, both of which require some pretty high level math. There's actually an example in one of my probability books that shows how important statistics can be in testing patients. It turns out that even if a test has a really high accuracy, if the condition is extremely rare there is a very high probability that a positive result for the test is a false positive. The book states that ~80% of doctors who were presented this question answered incorrectly.

For a more in-depth look at String Theory I recommend The Elegant Universe.

You undoubtedly already know the part of the theory that posits everything boils down to these fundamental "string" objects, and the way they vibrate (both in terms of the typical wave vibration, but also the way where the whole object moves back and forth) determines how it behaves in the universe. And that's influenced and constrained by the type of space in which the strings can move, etc.

But how might that help resolve QM and GR? Well, because strings have a little bit of length.

When we think about particles, we treat them as points with zero dimensions. That works all right in the framework of QM, but when you apply the equations of GR to those points, you end up with some fun, indeterminate divide by zero issues. Any nonzero length at all, like something on the scale of the Planck Length, can bridge the connection and produce a meaningful result.

Now, that's not to say that's all there is to it or everything has been solved (far from it), but that may shed some light on why it's an attractive theory to pursue. There are then many types of String Theory, which may just be different facets of one larger one, but finding connections between them is difficult. And experimental confirmation of strings is completely out of reach of our current technology. So, much remains to figure out.

Nothing about your claims of "self-evidence" is true in my case.

> These beliefs are ones you cannot help but believe; for example, the belief that you exist.

Descartes? "I think, therefore I am?" That's evidence, not self-evidence (though it is evidence for self.) I find it convincing; but then I have a strong bias. This isn't about sufficiency of evidence though; it's about evidence vs. self-evidence.

But how do you take it beyond that? How do you extend it to observations, to the universe, to reality? There are two choices there:

> Most of us also posses pragmatism as a self-evident belief.

"Most" people don't think about it at all. "Most" people are content to think their smartphones are magic. Scientists aren't most people. I'm no most people. And if you're thinking about this topic enough to have this conversation, you're not most people in this respect either. So let's look beyond the pragmatism of "not thinking about epistemology and empiricism won't get me eaten by a tiger, so why bother" and get on with the conversation.

I do consider the possibility the universe is a simulation, or that I'm a brain in a jar being fed stimulus (Actually it's hard to distinguish that testably from surfing reddit, but I digress.) Why not? But those avenues of thought don't lead very far; I feel I've considered them sufficiently. They haven't lead to useful insights yet (saving perhaps the holographic principle), but I remain open to the possibility. Pragmatism has it's place; you can't philosophies if you don't pay attention to things like not dying, but that's evidence for its necessity, not its sufficiency. Think further.

> Why is the sky blue? Because you see it as blue. How do you know that it actually is blue? You don't, but you [presumably] find it self-evidently more rational to assume that what you see is representative of reality, via pragmatism, or a similar philosophy.

And this is where I differ vastly from your preconceived notions of me. I believe the sky is blue because, when I was nine, I built a crude spectroscope and measured it (It's actually mostly white, by the way, with a small but significant increase in the intensity of blue light over what is expected of black-body radiation. Not counting sunset of course. And neglecting absorption lines - I was in third grade, the thing wasn't precise enough for that!)

So that's evidence the sky is blue (and that I was an unusual kid), not "self-evidence." Although in this case, actually observing the sky with your eyes is still evidence; our eyes may be flawed in many ways, but they are sufficient for distinguishing between at least a few million gradations between 390-700 nm wavelengths. That's quite sufficient for narrowing it down to "blue."

That's exactly what I mean about what people consider "self-evidence" actually being evidence they've seen so often they've forgotten it's evidence. You note the approximate visible wavelength of the sky many times a day; it's actually quite well established by repeated observation that (barring systematic errors in our visual processes) it's blue.

> But, if someone did not share this self-evident belief, they would find it quite irrational to assume that the sky is indeed blue in reality, as opposed to merely in your perception of it.

So let's say this happened - let's say someone said the sky was green. Well, there are two possibilities, and we can distinguish between them by showing them other objects with similar emission or reflection spectra. One is that they see these other purportedly blue objects as green. No problem! They simply use "green" to mean "blue." Half a billion people use azul instead, so this is no big deal.

The other possibility is that every other blue thing we can test looks blue to this person, but they still insist the sky is green. This again leads to two possibilities. One is that the sky really is green just for this individual and most of what we have determined about reality is false. The other is that this person has a psychological condition that makes him believe the sky is green. Do we have to accept that the sky is simply self-evidently green to him? Nope! Science!

Put him in a room, and through one slit allow in natural sunlight, and through another match the spectrum of solar light with artificial light as closely as possible. Vary which slit is which. Can this person regularly identify the "green" sky? (specifically compared to control groups?) If not, we can conclude he sees the sky as green due to a psychological condition, not something indicative of reality. This is surprisingly common - just read up on dowsing for instance. There are people convinced they can detect water with sticks, but every one of them fail in tests to do so at rates above random chance. (Dowsers got away with this in old days because when you dug a well, you'd only have to hit a state-sized aquifer.)

The alternative, if he can regularly identify the sky slit as green, and assuming that other possibilities have been excluded, is that reality really doesn't work the way we think it does. Maybe he's a separate brain in a separate jar. Maybe light waves like certain people better. Maybe what we thought were photons were just faeries and they're screwing with us for fun. Whatever the case, though, we'd now have evidence for it. Not "self-evidence" but actual evidence.

Now, you can argue that maybe reality doesn't matter - maybe that person's psychological condition that makes him see a green sky is just as important as the blue sky. Maybe it makes him happier or donate to charity more or whatever, so we should leave him alone. All fine arguments, but they would be separate discussions.

From your other link:

> I also concluded that by logic, existence itself is uncaused.

That remains to be seen. Well-tested theories still leave open other possibilities; though obviously we haven't yet tested these possibilities. But since your basis for belief, according to the other thread, was on the necessity of an uncaused creation in violation of natural laws, I thought you might be interested to know that there are some hypothesis regarding said creation that fit within those laws.

There's a lot of fun and interesting physics and astronomy that can be understood with little more than solid algebra skills. Add a little bit of introductory calculus, and there's a lot to keep you busy. If you're brave enough to dive into calc, I recommend this book.

Since you expressed particular interest in Astronomy, I would suggest using that as an anchor point. Get a good Astrophysics text like An Introduction to Modern Astrophysics by Carroll and start there. Inevitably, you will come upon concepts that you're shaky on-- luckily this is the age of the internet! I find HyperPhysics is a great resource (which appears to be down at the moment).

If you find that Newtonian physics is tripping you up, I recommend Basic Physics: A Self-Teaching Guide to fill in the gaps.

Audio Books are your friend, like seriously pick up something to listen to.

Surely You're Joking, Mr. Feynman! (Adventures of a Curious Character) by Richard P. Feynman


The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman

"What Do You Care What Other People Think?": Further Adventures of a Curious Character


The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory by Brian Greene


The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene


The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos by Brian Greene


Physics of the Impossible: A Scientific Exploration by Michio Kaku

Einstein's Cosmos: How Albert Einstein's Vision Transformed Our Understanding of Space and Time: Great Discoveries by Michio Kaku


The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics by Leonard Susskind (This one I recommend on the highest degree, personally I have read it 3 times)


A Brief History of Time by Stephen Hawking

The Theory of Everything: The Origin and Fate of the Universe by Stephen W. Hawking


Pale Blue Dot: A Vision of the Human Future in Space by Carl Sagan


Contact by Carl Sagan


Billions & Billions: Thoughts on Life and Death at the Brink of the Millennium by Carl Sagan

All these books I've listened to or read, and I recommend all of them some more then others, I have tons more about Quantum Mechanics, Physics, Biology, Cosmology, Astronomy, Math etc. But I'm to lazy to list all of them here.

"An elegant universe" by Brian Greene is a good read. It leans more towards string/superstring theory. "The science of interstellar" also touches on some concepts related to quantum mechanics.

I know that you asked for books but "PBS Spacetime" is a YouTube channel that does a great job explaining quantum mechanics. "Veritasium" is another great channel with a few videos explaining phenomena as well. I posted links below. Physics is dope. Happy hunting!

An elegant universe:
https://www.amazon.com/Elegant-Universe-Superstrings-Dimensions-Ultimate/dp/039333810X

The science of interstellar:
https://www.amazon.com/gp/aw/d/0393351378/ref=mp_s_a_1_1?ie=UTF8&qid=1502885214&sr=8-1&pi=AC_SX236_SY340_FMwebp_QL65&keywords=the+physics+of+interstellar&dpPl=1&dpID=41Ii8OmMy0L&ref=plSrch

PBS Spacetime:
https://m.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g

Veritasium:
https://m.youtube.com/user/1veritasium

I'm a physics student excited to take astrophysics this fall semester. We're using the Big Orange Book (Intro to Modern Astrophysics by Carroll and Ostlie, 2nd ed.), which, according to many around here, seems to be a great text. My copy came in the mail today but I'm wondering if I got a counterfeit.

There are a few reasons I am suspicious. The cover is a faded and uneven shade of orange, the print appears low quality on close inspection, the binding is glued, and the overall feel of the book falls short of most textbooks I've used. Additionally, the book shipped new, from Malaysia (with a customs value of $25).

I bought the book from Abebooks (specifically not an international edition) and am hoping for a refund. Just to be sure though, would anyone be willing to take pictures of their copy for me to compare? I am specifically interested in color, the binding as seen while the book is closed, and how well the print on the cover aligns with the spine.

I'm hoping this is a book I keep for a while, so I want to make sure I have a copy that will last! Thanks for your help!

The foundation of probability is measure theory, not nonstandard analysis (the topic that includes the hyperreals). So, when dealing with statements about probability, we deal with probability measures, which assign numbers in the real interval [0, 1] to subsets of the space of possible events. (Perhaps someone has studied a variant of measure theory that substitutes the hyperreals for the reals, but if so, it's sufficiently obscure that I've never heard of it.)

Also, nowhere in all this is anyone "raising a real number to the power of infinity". There are formal statements of the following sort:

>(*) The limit of 1/2^N as N approaches infinity is zero.

However, this is a statement about the limit of a sequence of real numbers, which is most definitely a real number, and is also formally defined in a way that makes no reference to "infinity". The expression "as N approaches infinity" is just a mildly informal (but much more readable) way of expressing that formal definition.

If you care to parse the formal statement, here it is:

>For any real number ε > 0, there exists a natural number N such that for all natural numbers n ≥ N, we have |1/2^(N) - 0| < ε.

This is how we precisely formalize statement (*).

For more information on limits of sequences, I recommend reading a book on mathematical analysis. Spivak's Calculus has a good chapter on this; it's an excellent book, so it's worth reading anyway.

> Cultural beliefs do actually influence ways of thought, scientific method included

The scientific method is not a "way of thought". It's a method. You're not providing any evidence to support that claim. The fact that different cultures have different patterns of thought is well-established, the idea that this makes science culturally relative is not. Are you saying logic is culturally dependent as well?

> Westerners tend to rely more on formal logic and insist on correctness of one belief over another when investigating conflicting opinions or theories, while easterners consider all the interacting environmental relationships,

A vague and unsubstantiated orientalist over-generalization if I ever heard one.

> One can even argue the Scientific Method is actually an invention of the western tradition

The automobile is a western invention too, and yet the Japanese understand them just the same way as we do.

>TL;DR: read something like The Geography of Thought for intriguing trends in how your Asian lab partner interprets data differently from you.

I've never run across a case where he did. Read a good book on philosophy of science to understand why natural science strives to eliminate bias, including cultural bias. It's not contingent on it but the exact opposite.

>Difference being Goswami was a quantum physics professor

There's no such thing as a 'quantum physics professor' or really a 'quantum physicist'. All physicists study quantum mechanics and nearly all use it, to different extents. Goswami's actual expertise is apparently nuclear physics, which does not imply any greater understanding of the foundations of quantum mechanics than that of most physicists.

> who wrote respected college textbooks

As far as I can tell, he's written one textbook on introductory quantum mechanics. I've never heard of him or his textbook before, and I see little reason to believe it's 'well-respected' or popular, as it only has 5 amazon reviews, as compared to 70 for Griffiths, an actual well-regarded textbook. Sakurai's "Modern QM" and Shankar's "Principles of QM" are popular and well-respected as well. Griffith's is also known for the consistent-histories interpretation of quantum mechanics, while the latter two are 'Easterners', yet don't subscribe to any of this kind of nonsense.

> My background is not in quantum physics, but sooner or later you guys will have to (you should?) reconcile your understanding of reality with how different cultural traditions interpret reality.

You haven't shown any depth of knowledge about 'cultural traditions'. You've made gross generalizations and outright false statements about these things. Calling Western philosophy 'materialist' while 'eastern' is supposedly uniformly 'idealist' (both terms are from Western philosophy) is flat-out wrong.

> Furthermore, the jump is discontinuous in that the electron is never in any orbit not defined by one of the probability clouds.

That's saying that mixed states and quantum superpositions do not exist. It's wrong, and introductory level understanding of formal quantum mechanics is enough to know it.

>Can you please point me to a more accurate description?

Show that the eigenfunctions of the electronic Hamiltonian are no longer eigenfunctions under the action of a perturbing external electromagnetic field.

> What is the interesting part of the delayed-choice experiment then if it's not that what we observe depends on how we measure it?

Did you make any effort at all to find out on your own, such as reading the wikipedia article? I don't see why I should spend time explaining it otherwise. The fact that "what we observe depends on how we measure it" is already evident in the double-slit experiment.

> the most interesting scientific discoveries come when interpretations of science and philosophy butt up against each other.

No, they don't. The most interesting scientific discoveries come when a well-established theory is proven wrong. Metaphysics has nothing to do with science. The Bell test is not philosophy, it's science. It's an empirical test of an empirically-testable thing.

> it appears that a non-local signal (that is, a deliberate faster-than-light transmission) is impossible

It's not the Bell test that says that, it's special relativity.

> Help me understand reality as you interpret it.

Now why the heck would I spend any time on doing that? There's a huge number of good, factual popular-scientific books on quantum mechanics and modern physics. There are plenty of good textbooks. There are good books on science and philosophy of science as well. But instead you waste your time on reading Goswami's nonsense, which would clearly be out of the mainstream to anyone who'd bothered to do a modicum of web searching beforehand. Then you defend it all, basically by stating that you know better than an actual scientist how science works.

You haven't shown that you've made even the slightest bit of a good-faith effort to understand either science, the scientific method and mindset, or established quantum physics. To me it appears that you came here seeking confirmation of what you'd already decided you wanted to believe.

Stephen Hawking, Brian Greene, Carl Sagan, Richard Feynman, Neil Tyson, Stephen Weinberg and Murray Gell-Mann, among others, have all written good popular-scientific books on modern physics. Just about all of them say something about quantum mechanics and the more popular interpretations of it. And for a more in-depth study of the philosophy of science surrounding quantum mechanics, read e.g. Omnes' "Quantum philosophy".

>maybe higher iq correlates to being right

You have the right idea. Having a solid foundation in logic correlates to "being right", and thankfully using logic is a learnable skill.

When it comes to understanding the world, you have two practical choices. You can rely on emotion and follow only what "feels good" (like you said, wanting to feel special and having the world make sense to you exclusively rather than learning how to make sense of the world, big difference). Here you risk being manipulated and fooled by emotionally controlling groups or individuals. You also risk being very wrong about how things in the world work.

Or, you can rely on reason and follow the path that corresponds logically with what you already know. It's not easy or fun at times, but if you really want to be able to understand how the world works then it's the only option. The best thing is that, once you establish a good system of logical checks, you develop a sense of true pride and confidence knowing that you can see past bullshit and even anticipate how things will happen. You become a better informed person, and that in itself is special.

If you're serious about this, I would recommend reading this book. It's a great introduction into analysing the world from a logical perspective.

No particular order:

Blind Descent by James M. Tabor. It is a great book about cave exploration and the race to discover the worlds deepest supercave.

A Brief History of Time by Stephen Hawking. Are you interested in the universe and how it all happened? This gives some pretty insightful answers.

From Eternity To Here by Sean Carrol. A really interesting view on the nature and concept of time and how it relates to the us and the universe. It can get a bit deep from time to time, but I found it fascinating.

Adventures Among Ants by Mark W. Moffet. It's about ants. Seriously. Ants.

The Worst Journey in the World by Apsley Cherry-Garrard. A first hand account of the ill-fated Scott expedition to the south pole in 1911-1912. Even after reading the book I cannot imagine what those men went through.

Bonus book: The Dragons of Eden by Carl Sagan. Human intelligence and how it evolved. Some really interesting stuff about the brain and how it works. A very enjoyable read.

So here are some options I recommend:

• (Advanced) Go through a few chapters of Spivak's Calculus. This is the MAT157 textbook and will over prepare you for the course and you will probably do very well. This will require a lot of self motivation, but I think is worth it (I went through a bit of Spivak's after 137). Keep in mind that this material is more rigorous than what you will see in MAT137
  
  
• (Computer Science) If you're a CS student, grab How to Prove It. You will be dealing with a lot of proofs in MAT137, CSC165, 236/240, etc. This is a more broad approach and is not directly calculus, though what you learn will help for 137. Also, get familiar with epsilon-delta proofs.
  
  
• (At your own pace: videos) Khan Academy tries to build an intuitive knowledge of calculus, which is something that MAT137 also tries to do. The videos are well done and you get points and achievements for watching them (gamification is great), you can watch the videos in your free time and it's fun(?).
  
  
• (At your own pace: reading) One of the (previous?) instructors for MAT137 has some really good lecture notes, which you can read/download here. This is essentially the exact content of the course, if you go through it, you will do well. Try to read at least up to page 50 (the end of limits chapter), and do the exercises.
  
  You can find all the textbooks I mentioned online, if you know what I mean. All of these assume you haven't seen math in a while, and they all start from the very basics. Take your time with the material, play around with it a bit, and enjoy your summer :D
  
  EditL this article describes one way you can go about your studies

I actually see a lot of parallels between your situation and where I found myself at your age. It was 14 or 15 that I really developed an interest in science, because before that I hadn't really been properly exposed before that. Fast forward 6 or 7 years, I'm now a third year university student studying physics and I love it; I'll be applying to PhD programs next fall.

Like you, astronomy (by which I broadly mean astronomy, astrophysics, cosmology, etc.) was what really caught my attention. In school, I liked all the sciences and had always been good at math (calculus was by far one of my favorite high school courses because the science can be pretty watered down).

If you're interested in learning more about astrophysics, I would recommend any one of a number of books. The first book on the topic that I read was Simon Singh's Big Bang; I read a couple Brian Greene books, namely The Elegant Universe and Fabric of the Cosmos; I read Roger Penrose's Cycles of Time, and finally Bill Bryson's A Short History of Nearly Everything. Also, I bought a book by Hawking and one by Michio Kaku that, to this day, sit on a shelf at my parents' house unread. I would recommend Singh's book as a nice book that should be at your level, and in fact it was the one recommended to me by some professors who I bugged with questions about the universe when I was around your age. Also, Bryson's book is a good survey look at a lot of different scientific topics, not just astrophysics/cosmology specific; I enjoyed it quite a lot.

As far as reaching out to people, I would recommend trying to connect with some scientists via email. That's what I did, and they were more responsive than I expected (realize that some of the people will simply not respond, probably because your email will get buried in their inbox, not out of any ill-will towards you).

At this point, I'll just stop writing because you've more than likely stopped reading, but if you are still reading this, I'd be more than happy to talk with you about science, what parts interest(ed) me, etc.

>good sources on Darwinism?

So far as I know "Darwinism" isn't actually a thing. I know this is mostly semantics, but really the only people who say "Darwinism" are creationists who wish to portray evolution as an ideology, and of course over-inflate Darwin's relevance in the contemporary theory of biological evolution. Hes he was the first to lay out the idea of evolution by natural selection, but we know oh so much more about it now than what his observations revealed, so painting Darwin as the final word in evolutionary theory is also just as misguided as trying to portray it as an ideology.

As for where to start, though, as a few others in this thread have suggested I'd say take a look at Richard Dawkins' The Greatest Show On Earth. He does a wonderful job of explaining many of the major points in what is currently known about evolution and how we know it all in language that regular laypersons like most of us here are quite capable of understanding.

Here's my list of the classics:

General Computing

• But How Do It Know? - The Basic Principles of Computers for Everyone
  
  
• The Elements of Computing Systems: Building a Modern Computer from First Principles
  
  
• Code: The Hidden Language of Computer Hardware and Software
  
  
• Gödel, Escher, Bach: An Eternal Golden Braid
  
  Computer Science
  
  
• The New Turing Omnibus: Sixty-Six Excursions in Computer Science
  
  
• Compilers: Principles, Techniques, and Tools, 2nd Edition (aka The Dragon Book)
  
  
• The Art of Computer Programming
  
  
• Algorithms, 4th Edition
  
  
• Introduction to Algorithms, 3rd Edition (aka CLRS)
  
  
• Essential Algorithms: A Practical Approach to Computer Algorithms Using Python and C#, 2nd Edition
  
  
• Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People
  
  
• Structure and Interpretation of Computer Programs, 2nd Edition (aka SICP, available for free on the MIT website)
  
  
• Discrete Mathematics with Applications, 4th Edition
  
  Software Development
  
  
• Designing Data-Intensive Applications: The Big Ideas Behind Reliable, Scalable, and Maintainable Systems by Martin Kleppmann
  
  
• Design Patterns: Elements of Reusable Object-Oriented Software (aka The Gang of Four)
  
  
• Think Like a Programmer: An Introduction to Creative Problem Solving
  
  
• The Pragmatic Programmer: your journey to mastery, 20th Anniversary Edition, 2nd Edition
  
  
• The Mythical Man-Month: Essays on Software Engineering
  
  
• Code Complete: A Practical Handbook of Software Construction, 2nd Edition
  
  
• The Design of Everyday Things
  
  
• Clean Code: A Handbook of Agile Software Craftsmanship
  
  
• Programming Pearls, 2nd Edition
  
  
• Soft Skills: The Software Developer's Life Manual
  
  
• Hello, Startup: A Programmer's Guide to Building Products, Technologies, and Teams
  
  
• Hacker's Delight, 2nd Edition
  
  
• Peopleware: Productive Projects and Teams, 3rd Edition
  
  Case Studies
  
  
• The Soul of a New Machine
  
  
• Masters of Doom: How Two Guys Created an Empire and Transformed Pop Culture
  
  
• Hackers: Heroes of the Computer Revolution
  
  
• Where Wizards Stay Up Late: The Origins Of The Internet
  
  
• Fire in the Valley: The Birth and Death of the Personal Computer, 3rd Edition
  
  Employment
  
  
• Cracking the Coding Interview: 189 Programming Questions and Solutions, 6th Edition
  
  
• The Complete Software Developer's Career Guide: How to Learn Programming Languages Quickly, Ace Your Programming Interview, and Land Your Software Developer Dream Job
  
  
• The Self-Taught Programmer: The Definitive Guide to Programming Professionally
  
  
• The Passionate Programmer: Creating a Remarkable Career in Software Development
  
  Language-Specific
  
  C
  
  
• The C Programming Language, 2nd Edition
  
  Python
  
  
• Automate the Boring Stuff with Python: Practical Programming for Total Beginners, 2nd Edition
  
  
• Python Crash Course: A Hands-On, Project-Based Introduction to Programming
  
  
• Python Programming: An Introduction to Computer Science, 3rd Edition
  
  
• Effective Python: 59 Specific Ways to Write Better Python
  
  C#
  
  
• The C# Player's Guide, 3rd Edition
  
  C++
  
  
• The C++ Programming Language, 4th Edition
  
  
• Starting Out with C++: from Control Structures to Objects, 9th Edition
  
  Java
  
  
• Introduction to Java Programming and Data Structures: Comprehensive Version, 11th Edition
  
  
• [Java: A Beginner's Guide](https://www.amazon.com/Java-Beginners-Seventh-Herbert-Schildt/dp/1259589315/, 7th Edition)
  
  
• Java: The Complete Reference, 11th Edition
  
  
• Core Java Volume I - Fundamentals, 11th Edition
  
  
• Starting Out with Java: From Control Structures through Objects, 6th Edition
  
  
• Effective Java, 3rd Edition
  
  Linux Shell Scripts
  
  
• The Linux Command Line: A Complete Introduction, 2nd Edition
  
  
• Wicked Cool Shell Scripts: 101 Scripts for Linux, OS X, and UNIX Systems, 2nd Edition
  
  
• Linux Command Line and Shell Scripting Bible
  
  
• Mastering Linux Shell Scripting
  
  Web Development
  
  
• Learning Web Design: A Beginner's Guide to HTML, CSS, JavaScript, and Web Graphics, 5th Edition
  
  
• Eloquent JavaScript: A Modern Introduction to Programming, 3rd Edition (also available for free on the author's website)
  
  
• JavaScript and JQuery: Interactive Front-End Web Development
  
  
• HTML and CSS: Design and Build Websites
  
  
• You Don't Know JS: Up & Going
  
  Ruby and Rails
  
  
• Ruby on Rails Tutorial: Learn Web Development with Rails, 4th Edition (Note: this book is somewhat out of date compared to the live version on the author's website.)
  
  
• The Well Grounded Rubyist, 3rd Edition
  
  
• Practical Object-Oriented Design in Ruby: An Agile Primer
  
  
• Agile Web Development with Rails 5.1
  
  
• Programming Ruby 1.9 & 2.0: The Pragmatic Programmers' Guide, 4th Edition
  
  
• Eloquent Ruby
  
  Assembly
  
  
• Assembly Language for x86 Processors, 8th Edition

Hmm. Well, I really like Codyslab on youtube. He has some intersting stuff. Vihart uses to make some creative math videos back in the day.

If you want books, Richard Feynman wrote a bunch that are great. My favorite is "Surely you must be joking, Mr Feynman!" Which covers such adventutes as cracking the safes of the Manhattan project, sleeping on a bench the first day of his professorship, and his eureka moment with quantum electrodynamics!

A good textbook for a little light reading is the Big Orange Book, or the BOB. https://www.amazon.com/Introduction-Modern-Astrophysics-2nd/dp/0805304029 It is a good intro to all different subjects on astrophysics, and if you take it in college, this may be one of the books you need to get. Some solutions can be found online for it too ;)

Some here will disagree, yet I think your cause is a noble one.

My suggestion would be to keep encouraging her to be a freethinker, question everything, and learn all she can about science. If she can be at a point where she understands that "science is more than a body of knowledge, it is a way of thinking" (Carl Sagan), if she can fall in love with the wonders of the creation of the universe and the evolution of life on this world, then you'll be done, as those things will show any thinking person the absurdity of religion as a moral compass.

If she likes to read, here are some books you might consider getting for her:

• The Demon-Haunted World by Carl Sagan. An amazing argument for the use the scientific way of thinking in every aspect of our lives.
  
  
• A Universe from Nothing by Lawrence Krauss. How math and science can fully explain the creation of the universe, and a powerful argument against the universe needing a creator.
  
  
• The Greatest Show on Earth by Richard Dawkins. The subtitle is The Evidence for Evolution. Meant as a book for readers your sister's age. Big plus is that if she likes it, she may want to read The God Delusion and/or The Magic of Reality.
  
  Edit: grammar

Go slow. There are some good resources available to help you out. For your personal experience level etc, I can't recommend the book Nightwatch by Terrance Dickinson highly enough! It covers everything from basic astrophysics (like the scale of the universe, how big those stars really are out there, the life cycle of stars, some basics of why orbits are the way they are) to super basic star charts (identifying major constellations) and observing tips (what cool objects easy to find objects are in each constellation) to what the differences between telescope designs are. Nothing is above a 12th grade science level and it'd be really easy to slow things up for an 8y.o. + be a handy reference for her deeper curiosity for at least a while (I know I am a voracious consumer of knowledge... aka, a huge nerd, myself). You might even luck out and find a copy in your local library! My tiny rural college town's local library had a copy.

There is also a nice little youtube series called "Eye in the Sky" which are little, entertaining 10 minute segments about what interesting objects are in the sky for this week.

Others have already mentioned it but join an astronomy club and download Stellarium. Here's a couple book suggestions:
Turn Left at Orion will get you familiar with some of the more interesting objects to look at in the night's sky. This is definitely a good place to start. You also want to pick up a star atlas to help you navigate the sky and find some of the dimmer objects in the sky. A favorite is Sky and Telescope's Pocket Star Atlas. Another favorite for new astronomers is Nightwatch which will educate you a bit more about astronomical bodies and the night sky.

>You seem to be saying entirely different things each time you comment on this point.

I am saying the same thing. Philosophers, particularly before the advent of modern science, have often become so dedicated to concepts that they make faulty assertions about the natural world. Concepts derived from a limited understanding become impediments. Grand metaphysical systems of the past may impress with their internal consistency and complexity, but they do not describe the natural world with the accuracy or usefulness of modern scientific theories.

>but rather whether it is sound.

Soundness implies truth of the propositions used as premises in the argument. How would one test the premises of metaphysical arguments about prime movers and such? While I admit that such arguments may be interesting or internally consistent or even valid to the extent that they do not violate the rules of deduction, they are still built on definitions that do not allow for testing against the natural world and are thus not sound.

>No, physics doesn't suggest anything like this.

Lawrence Krauss would disagree.

>The ontological argument...

Depends on the definition of 'great' and whether such definition does or does not include existence. Descartes' goes on to include 'clear and distinct' ideas of supreme beings. These are very muddy concepts and to say 'well I guess god exists because this proof is valid' just seems silly by the standards of modern science. Grenlins exist because I have defined them as the 'greenest thing' and it is greener to exist than not to.

>science of course relying on the methods of logic.

Science relies on observation. Such observation has at times shown a world that does not conform with traditional notions of logic. It is the strength of science that it adapts to what is observed rather than attempting to squeeze the data into an accepted dogma.

>you seem to regard the meaning of time as being limited to physics

The OP asked about time in regard to cosmology which I believe is best dealt with by physics for reasons stated. If you mean by the 'meaning of time' how one experiences time, how it relates to human affairs, etc., then 'yes' other disciplines, from art to sociology, may have something to say.

You might try here: http://www.reddit.com/r/askscience/search?q=fact&restrict_sr=on

and then ctr+F for "evolution" for a few previous instances of this question, or here:


http://www.reddit.com/r/askscience/search?q=evolution+fact&sort=top&restrict_sr=on

or other variations thereupon.

Anyways, we don't make a habit of letting these questions out all that often, as they never really do well, and when they do attract attention it's mostly people who don't really understand evolution all that well, trying to explain evolution to people who definitely don't understand it that well, and it just never really winds up being productive (while those of us who do know something about evolution squirm in agony at even attempting to undue all the damage this whole "fact vs theory" thing in a somewhat concise manner).

I'm keeping it spammed (you could also try searching in /r/evolution), but my honest suggestion would be to have her read something like Jerry Coyne's Why Evolution is True, if she's willing to (and perhaps you could sit down and read it yourself first, to be able to give it an honest recommendation). Alternatively Dawkins's The Greatest Show on Earth is supposed to be good (I haven't read it myself), although Coyne's writing style might be more appealing for the non-academic, and some people are allergic to Richard Dawkins, for obvious reasons if you know who he is.

What's her angle. Presumably she is of the faithful? If that's really her angle, then you might be hard pressed to convince her with a short paragraph or two that I could provide.

If your interested in the special diversity of Earth, I strongly recommend The Greatest Show On Earth, which does a truly marvelous job of putting a couple hundred years of initial speculation, exciting research, and modern evidence for evolution, and the basis of life on Earth into an easy to read book. It can be a little daunting at time, but I love the book, and recommend it fondly.

For compsci you need to study tons and tons and tons of discrete math. That means you don't need much of analysis business(too continuous). Instead you want to study combinatorics, graph theory, number theory, abstract algebra and the like.

Intro to math language(several of several million existing books on the topic). You want to study several books because what's overlooked by one author will be covered by another:

Discrete Mathematics with Applications by Susanna Epp

Mathematical Proofs: A Transition to Advanced Mathematics by Gary Chartrand, Albert D. Polimeni, Ping Zhang

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers

Numbers and Proofs by Allenby

Mathematics: A Discrete Introduction by Edward Scheinerman

How to Prove It: A Structured Approach by Daniel Velleman

Theorems, Corollaries, Lemmas, and Methods of Proof by Richard Rossi

Some special topics(elementary treatment):

Rings, Fields and Groups: An Introduction to Abstract Algebra by R. B. J. T. Allenby

A Friendly Introduction to Number Theory Joseph Silverman

Elements of Number Theory by John Stillwell

A Primer in Combinatorics by Kheyfits

Counting by Khee Meng Koh

Combinatorics: A Guided Tour by David Mazur


Just a nice bunch of related books great to have read:

generatingfunctionology by Herbert Wilf

The Concrete Tetrahedron: Symbolic Sums, Recurrence Equations, Generating Functions, Asymptotic Estimates by by Manuel Kauers, Peter Paule

A = B by Marko Petkovsek, Herbert S Wilf, Doron Zeilberger

If you wanna do graphics stuff, you wanna do some applied Linear Algebra:

Linear Algebra by Allenby

Linear Algebra Through Geometry by Thomas Banchoff, John Wermer

Linear Algebra by Richard Bronson, Gabriel B. Costa, John T. Saccoman

Best of Luck.

Find a used version of Carroll & Ostlie and read it cover to cover. Bits of it might get too in-depth depending on your experience, but then you can branch off and find other resources for those areas that interest you. The NED Knowledgebase is also fun to read and I recommend AstroBites to keep up on current literature until you feel comfortable delving directly into publications. Have fun! :)

Nice! Well, I would definitely recommend he read some Carl Sagan (Cosmos and Pale Blue Dot) and Steven Hawking (Brief History of Time, The Grand Design, etc.). Looks like there's a really good book out since 3 days ago called, The Science of Interstellar by Kip Thorne. This would be a really good book to get him. I picked up a pretty old Astronomy textbook a while ago for a really cheap price that I'm going to look over a bit, but I don't know of any specific ones to recommend. Here's an awesome PDF I got from a redditor who was offering an eBook and PDF of his book for free to anyone who asked: http://docdroid.net/kyjz

This is - in dept - a difficult question for me to answer. Time itself is very hard to define as an isolated concept and books, like for example written by the great mind of our time Stephen Hawking, are written about it. This is a quote from the book 'Ibn 'Arabi - Time and Cosmology', (page 24):

>"...time is one of the most fundamental issues in philosophy and cosmology, since the whole of existence is nothing but consecutive series of events in time. Everybody feels time, but most people do not question it because it is commonly experienced every day in many things and is so familiar. However, it is far more difficult to understand the philosophical nature of time and its characteristics.

>Throughout the history of philosophy, many opposing views have emerged to discuss and describe the different aspects of time, and some novel hypotheses have eventually emerged in modern cosmology. However, it is still the dream of every physicist to unveil the reality of time, especially since all modern theories have come to the conclusion that time is the key."

When I would try to explain the concept of time to anyone, I would first of all state that we humans have our limitations. We do not know, other than that what we perceive. I would not have known that time is relative, if it were not for Einstein and Hawking to back-up their theories. Note that we are still scratching the surface, since I try to answer your question, without going into matters like what CERN does and what the effects of their assumptions and conclusions will have on widely accepted theories in modern day science, or for example the Higgs boson (he named it the 'God particle') and what this means for our basic understanding of concepts like cosmos and time.

I think that your question originates from not understanding the concept that Allah is not his creation. So everything that we observe, is within the creation of Allah and it is very hard (it would seem impossible, if not for the mercy - of knowing him - that he send down upon us) to define anything that is outside of his creation.

A chemistry professor in Stuttgard, which is a converted Christian himself, said about time: "Allah creates all of his creation again in every small instant". The same professor said that modern western scientists only recently made a shift in thinking about time, while 'Ibn 'Arabi (which I mentioned earlier) expressed such theories in his time already. The professor could make this conclusion, because he is an active member of fora where his peers post, discuss and promote the newest theories, and for example the papers they write, on these subjects.

You need some grounding in foundational topics like Propositional Logic, Proofs, Sets and Functions for higher math. If you've seen some of that in your Discrete Math class, you can jump straight into Abstract Algebra, Rigorous Linear Algebra (if you know some LA) and even Real Analysis. If thats not the case, the most expository and clearly written book on the above topics I have ever seen is Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers.

Some user friendly books on Real Analysis:

1. Understanding Analysis by Steve Abbot
   
   
2. Yet Another Introduction to Analysis by Victor Bryant
   
   
3. Elementary Analysis: The Theory of Calculus by Kenneth Ross
   
   
4. Real Mathematical Analysis by Charles Pugh
   
   
5. A Primer of Real Functions by Ralph Boas
   
   
6. A Radical Approach to Real Analysis by David Bressoud
   
   
7. The Way of Analysis by Robert Strichartz
   
   
8. Foundations of Analysis by Edmund Landau
   
   
9. A Problem Book in Real Analysis by Asuman Aksoy and Mohamed Khamzi
   
   
10. Calculus by Spivak
    
    
11. Real Analysis: A Constructive Approach by Mark Bridger
    
    
12. Differential and Integral Calculus by Richard Courant, Edward McShane, Sam Sloan and Marvin Greenberg
    
    
13. You can find tons more if you search the internet. There are more superstars of advanced Calculus like Calculus, Vol. 1: One-Variable Calculus, with an Introduction to Linear Algebra by Tom Apostol, Advanced Calculus by Shlomo Sternberg and Lynn Loomis... there are also more down to earth titles like Limits, Limits Everywhere:The Tools of Mathematical Analysis by david Appelbaum, Analysis: A Gateway to Understanding Mathematics by Sean Dineen...I just dont have time to list them all.
    
    Some user friendly books on Linear/Abstract Algebra:
    
    
14. A Book of Abstract Algebra by Charles Pinter
    
    
15. Matrix Analysis and Applied Linear Algebra Book and Solutions Manual by Carl Meyer
    
    
16. Groups and Their Graphs by Israel Grossman and Wilhelm Magnus
    
    
17. Linear Algebra Done Wrong by Sergei Treil-FREE
    
    
18. Elements of Algebra: Geometry, Numbers, Equations by John Stilwell
    
    Topology(even high school students can manage the first two titles):
    
    
19. Intuitive Topology by V.V. Prasolov
    
    
20. First Concepts of Topology by William G. Chinn, N. E. Steenrod and George H. Buehler
    
    
21. Topology Without Tears by Sydney Morris- FREE
    
    
22. Elementary Topology by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev and and V. M. Kharlamov
    
    Some transitional books:
    
    
23. Tools of the Trade by Paul Sally
    
    
24. A Concise Introduction to Pure Mathematics by Martin Liebeck
    
    
25. How to Think Like a Mathematician: A Companion to Undergraduate Mathematics by Kevin Houston
    
    
26. Introductory Mathematics: Algebra and Analysis by Geoffrey Smith
    
    
27. Elements of Logic via Numbers and Sets by D.L Johnson
    
    Plus many more- just scour your local library and the internet.
    
    Good Luck, Dude/Dudette.

Math is essential the art pf careful reasoning and abstraction.
Do yes, definitely.
But it may be difficult at first, like training anything that’s not been worked.

Note: there are many varieties of math. I definitely recommend trying different ones.

A couple good books:

An Illustrated Theory of Numbers

Foolproof (first chapter is math history, but you can skip it to get to math)

A Book of Abstract Algebra

Also, formal logic is really fun, imk. And excellent st teaching solid thinking. I don’t know a good intro book, but I’m sure others do.

For whichever professor you have for Math 42, I highly recommend you get this book: https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995
It definitely saved me a ton. It’s straight to the point, and not as dry as most textbooks can be. Math 32 will be a bit more work, but in my experience just start homework early and don’t be afraid to go to professor office hours and ask questions. Even if they seem distant during class, most professors do appreciate students who make the effort to ask questions. If you need free tutoring in any of your classes, contact Peer Connections. Specifically for math, I believe MacQuarrie Hall room 221 offers drop-in tutoring for free as well! And for physics, Science building room 319 has free drop-in tutoring.

Square one...

You should have a solid base in math:

Introduction to Calculus and Analysis, Vol. 1 by Courant and John. Gotta have some basic knowledge of calculus.

Mathematical Methods in the Physical Sciences by Mary Boas. This is pretty high-level applied math, but it's the kind of stuff you deal with in serious physics/astrophysics.

You should have a solid base in physics:

They Feynman Lectures on Physics. Might be worth checking out. I think they're available free online.

You should have a solid base in astronomy/astrophysics:

The Physical Universe: An Introduction to Astronomy by Frank Shu. A bit outdated but a good textbook.

An Introduction to Modern Astrophysics by Carroll and Ostlie.

Astrophysics: A Very Short Introduction by James Binney. I haven't read this and there are no reviews, I think it was very recently published, but it looks promising.

It also might be worth checking out something like Coursera. They have free classes on math, physics, astrophysics, etc.

> Especially considering my limited knowledge on physics, but I would like some kind of introduction to string theory.

Okay, the first thing you should do is read a classic in the field on a level you can understand now. I recommend The Elegant Universe. After that I would read books like it until you have taken some calculus and linear algebra.

After you have learned some calculus and linear algebra, I think you could work through this book which to be honest is the most approachable string theory book out there. You learn a lot of complex topics written so that anyone with the basic math skills I described could work through them. Literally every step in derivations and examples are spelled out or you with explanations.

After that, I recommend David Tong's lectures that are as advanced as any graduate text but are much more readable than any other graduate text.

I just read it last week. You're pretty well right about. If you're looking for an introductory book which covers evolution, I recommend The Greatest Show On Earth also by Dawkins.

Look, Dawkins is definitely one of the most pedantic authors I've ever read, but his work is strong and arguments are presented very clearly but if the subject isn't what you're interested in, then what can you do. That said, yes the book will contain valuable information that you will gain if you finish it. Any book that has stood as long as the Selfish Gene will leave you with something. But it is an old book. Much of what he says was pretty cutting edge at first edition, but it was released in the 70's (I think). Read the 30th Anniversary Edition if you decide to move forward with it, if not, move on to something that interests you more. It's only a book. It won't get mad.

TL;DR If you don't like it, don't read it.

On evolution:

I urge you to read some books on the issue that aren't written with a fundamentalist Christian slant. The science is decisive, and the distinction between "macro" and "micro" is itself a religious confusion. (as others have already pointed out).

On the Big Bang: The biggest problem with the Big Bang is that we don't know how it happened. That is a problem, and scientists are working obsessively to solve it. But saying "God did it" buys you a whole host of new problems. How did God happen? Who created God? Why did he create the universe? You haven't answered anything by saying "God did it": you've just kicked the can down the road and added an additional unfalsifiable and unsupported assumption.

Also, the evidence for the Big Bang is all around you: look up background microwave radiation,distribution and evolution of galaxies, the abundance of light elements, and the expansion of space.

On the supernatural:

Any thinking that starts with "Do you think it's possible that..." is a HUGE RED FLAG. Almost anything is possible, but usually the sort of logic that must be defended with a "Well, it's possible..." is absurdly improbable. This is a good example. Yeah, it's possible that an entire other world could be layered on our own - but it's more improbable than winning the lottery, and I don't buy lottery tickets.

If I had to explain the fundamental difference between the way I think about the spiritual and the way you think about the spiritual, it would be this. You ask "Is it possible that..." and "Do you think that maybe..."

I ask "Is there empirical support for..." and "Does the evidence support the assertion that..."

As for the hope that human consciousness continues on....

Nope. This is it. That sucks, and I'm sorry. It's among the hardest pills to swallow about being an atheist - but it's true whether you believe it or not.

Watch The Rubin Report on YouTube. Dave Rubin interviewed both Ben Shapiro and Jordan Peterson, as well as MANY of the other names I see posted by others here. He interviews people from different political, social, and economic philosophies. I even fund him on Patreon because his channel is great (and important).

 

If I had to pick three people that made the most dramatic impact on my life in terms of how I think, seek and evaluate evidence, and use reason, these people would be at the top. While the people on my list did not always agree on everything, I do believe that they are/were intellectually honest:

 

Thomas Sowell

• One of many interviews
  
  
• Basic Economics
  
  
• Black Rednecks and White Liberals - this book changed the way I think quite a bit
  
  Carl Sagan (Science-related things aside, he wrote a bit on Philosophy of thought)
  
  
• MUST WATCH - Great excerpt read by him in his book Pale Blue Dot
  
  
• The Demon-Haunted World
  
  Ayn Rand
  
  
• Interview with Mike Wallace
  
  
• The Fountainhead
  
  
• Read Atlas Shrugged after Fountainhead - this book honestly changed my life
  
  I hope that helps! :)

If you want a rigorous basic understanding of astrophysics, you need a couple of years of college-level math and physics. If you are the sort who can learn difficult material on your own, they have textbooks at libraries. These topics go into it:

Math: Presumably you had the full track of algebra and trigonometry, so then you need single and multivariable calculus, differential equations, and linear algebra.

Physics: Newtonian mechanics, heat and electromagnetism, relativity, and quantum mechanics.

You also need statistics, which I would advise learning the basics of before trying to learn quantum mechanics. Chemistry is nice to have too, but isn't essential except for certain topics.

Once you have this background, there are introductory astrophysics textbooks you can read. In fact, you might just want to browse through one at a library just to see what it's like. The one I learned from in college was pretty great:

https://www.amazon.com/Introduction-Modern-Astrophysics-2nd/dp/0805304029

Even without completing the entire background knowledge, you can pick up some fascinating things reading a book like that.