(Part 3) Reddit mentions: The best science & math books

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.

Thank you for the effort! I'll try to do you justice with a thorough response.

----

> 1. God says what he needs to say to us through the Bible.

Sure it's the Bible and not Harry Potter? To anyone without your obvious bias, the Bible looks like a collection of fanciful but poorly edited fiction. God's message hasn't reached me and it hasn't reached 5 billion other humans alone among the living. In other words, if this is an omnipotent's idea of effective communication, God sucks as a communicator.

> 2. God is not inert, he sometimes does miracles

Prove this and I'll leave you alone. Has God ever healed an amputee? Has God ever accomplished a miracle that has no natural explanation?

No wait, references to the work of fiction mentioned in #1 don't count. There is not the slightest bit of evidence that your precious Bible is anything more than a stack of useful rolling papers. I've addressed this before. J.K. Rowling has Harry Potter performing scores of miracles in her books, it's really easy to create a miracle with pen and paper.

> 3. The evidence is not inadequate. If you want evidence of his existence, there is evidence everywhere, and in sheer necessity, it is pointed out that God must exist.

So you say. Your following arguments are... sorely lacking. Here we go:

> 3.1 The need of a creator
If you saw a car in the forest, you wouldn't say it randomly came into existence and over time came together by itself, because it is too complex for that to have happened.

Correct. That's easy for me to say because I know exactly what a car is and how it's made.

> In the same way, this universe and everything in it is far too complex to randomly explode into existence and come together by itself, a creator is needed and that creator is God.

Your analogy doesn't hold. The universe is not very complex conceptually, it's been satisfactorily explained how all heavenly bodies resulted from the expansion of space followed by the clumping of clouds of primeval hydrogen. Suns and the nuclear process in them? A natural consequence of packing a lot of hydrogen with gravity. Heavy elements? The ashes of nuclear fusion. Planets circling around suns? That's what happens when heavenly bodies nearly collide in a vacuum, influenced only by each other's gravity. Finally, the complexity of life on earth is neatly explained by evolution from very primitive beginnings from substances that occur -naturally- in the void of lifeless space. No magic is required to explain any of this. But I see we get to talk about this in greater depth in #4.

Still, for your interest, this video refutes Craig's Kalam Cosmological argument and is thoroughly captivating while presenting modern cosmology. Highly recommended!

> 3.2 The need for an original mover/causer
You know nothing moves by itself correct?

No, I don't know this, because I have a solid education in physics. Atomic nuclei spontaneously explode and particles fly from them - movement without a mover. Plato's Prime Mover argument dates back to a time when people didn't know anything about physics and science was done by sitting on your butt, guessing and thinking.

> 3.3 The need of a standard
When you call something, for instance let's say "good", there has to be a standard upon which good is based.

This response of yours -so far- is sounding suspiciously like a copy of a William Lane Craig debate argument. Please note that all of his arguments have been successfully refuted - though not necessarily within one debate or only within debates. But regardless, I can easily address your arguments on my own.

Now then. Basic moral behavior has been shown to emerge naturally as a result of evolution. Yes, this is why theists hate evolution so much. It explains a lot of stuff that used to be attributed to God. Animals in the wild show moral behavior such as altruism, fairness, love, cooperation, justice and so forth. Even robot simulations, given only the most minimal initial instructions, develop "moral" behavior because that turns out to be a successful selection criteria for survival.

If you try to point out that humans display and think about much more complex moral situations than animals, I'll agree. But you know who invented those extensions of purely survival-oriented moral behavior? Humans did, not God. Humans look at the behaviors that promote survival and well-being in animals and humans and call it "good." They see behavior that hurts and kills animals and people and makes them suffer, and they call it "bad." Your five year old kid can grasp this concept - you insult your god when you claim this is so difficult it necessarily requires divine intervention. I recommend Peter Singer's book Practical Ethics, a thoughtful and thorough discussion of morals far more nuanced and acceptable to a modern society than the barbaric postulates of scripture. Rape a virgin, buy her as a wife for 50 shekels, indeed!

> 4.1 About the Origin of Life/Finely tuning a killer cosmos

> Anyway, for life to come together even by accident, you would need matter

Correct.

> now the universe is not infinite and even scientists know that.

I'm not sure that's certain, but it's probably irrelevant. Let's move on.

> that scientists say made the universe would need matter present.

Correct. We certainly observe a helluva lot of matter in the present-day universe (to the extent we can observe it).

> Where do you expect that matter to have come from?

An empty geometry and some very basic laws of physics (including quantum physics). This is very un-intuitive, which is why people restricted to Platonic thinking have trouble with it. But you know that matter and energy are equivalent, via E=mc^2 , right? Given the raw physics of the very early universe, matter could be created from energy and vice versa. OK, that still doesn't explain where the (matter+energy) came from. Here's the fun part: it turns out that the universe contains not just the conventional "positive" energy we're familiar with, but also negative energy. And it turns out that the sum of (matter + positive energy) on one hand and (negative energy) on the other are exactly equal and cancel out. In other words, and this is important, the creation of the universe incurred no net "cost" in matter or energy. This being the case, it becomes similarly plausible for for the entire universe to have spontaneously popped into existence just like those sub-atomic particles that cause the Casimir Effect. Stephen Hawking has explained this eloquently in his book The Grand Design but you may prefer Lawrence Krauss' engaging lecture A Universe From Nothing.

> I know for a fact that people are smarter than an explosion and even they have been unsuccessful in making organic life forms from scratch

Wrong again. It took them 15 years, but Craig Venter and his project recently succeeded in constructing the first self-replicating synthetic bacterial cell.

By way of interest, people making the kind of claims you do were similarly amazed when Friedrich Wöhler, in 1828, synthesized the first chemical compound, urea, that is otherwise only created by living beings. This achievement torpedoed the Vital Force theory dating back to Galen. Yet another job taken off God's hands.

> let alone have them survive the forming of a planet.

Now this is just dumb. First the planet formed, then it cooled down a bit, then life developed.

> Because of that, I doubt an explosion could do it either.

So you're right there: The explosion just created the planet and the raw materials. Life later arose on the planet.

> Chance doesn't make matter pop into existence.

Yes it does. The effect I was mentioning earlier is called quantum fluctuation.

> 4.2 The human brain

(skipping the comparison of man with god. I don't see it contributing anything. All of this postulating doesn't make God plausible in any way)

> 4.3 The Original Christian Cosmos

> 4.3.1. Maybe because we are after the fall, we have already lost that perfect original cosmos Paul imagined.

Wait, this contradicts your next point.

> 4.3.2 You have to give Paul some credit for trying. He didn't have any the information or technology we have today.

Thank you, this confirms my assertion that the Bible and its authors contain no divinely inspired knowledge. The Bible is a collection of writings by people who thought you could cleanse leprosy by killing a couple of pigeons.

Now, about that original cosmos: either Paul was too uneducated to conceive the cosmos as it really exists, or what he imagined is irrelevant. In any case, what you consider the "after loss" cosmos is trillions of times larger than Paul imagined; it would be silly to call this a loss.

The fact remains that the world as described in the Bible is a pitiful caricature of the world as it is known today. And Carrier's main point remains that our cosmos is incredibly hostile to life; and if man were indeed God's favorite creation, the immensity of the cosmos would be a complete waste if it only served as a backdrop for our tiny little planet.

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.

It's great that you want to study particle physics and String Theory! It's a really interesting subject. Getting a degree in physics can often make you a useful person so long as you make sure you get some transferable skills (like programming and whatnot). I'll reiterate the standard advice for going further in physics, and in particular in theoretical physics, in the hope that you will take it to heart. Only go into theoretical physics if you really enjoy it. Do it for no other reason. If you want to become a professor, there are other areas of physics which are far easier to accomplish that in. If you want to be famous, become an actor or a writer or go into science communication and become the new Bill Nye. I'm not saying the only reason to do it is if you're obsessed with it, but you've got to really enjoy it and find it fulfilling for it's own sake as the likelihood of becoming a professor in it is so slim. Then, if your academic dreams don't work out, you won't regret the time you spent, and you'll always have the drive to keep learning and doing more, whatever happens to you academically.

With that out of the way, the biggest chunk of learning you'll do as a theorist is math. A decent book (which I used in my undergraduate degree) which covers the majority of the math you need to understand basic physics, e.g. Classical Mechanics, Quantum Mechanics, Special Relativity, Thermodynamics, Statistical Mechanics and Electromagnetism. Is this guy: Maths It's not a textbook you can read cover to cover, but it's a really good reference, and undoubtably, should you go and do a physics degree, you'll end up owning something like it. If you like maths now and want to learn more of it, then it's a good book to do it with.

The rest of the books I'll recommend to you have a minimal number of equations, but explain a lot of concepts and other interesting goodies. To really understand the subjects you need textbooks, but you need the math to understand them first and it's unlikely you're there yet. If you want textbook suggestions let me know, but if you haven't read the books below they're good anyway.

First, particle physics. This book Deep Down Things is a really great book about the history and ideas behind modern particles physics and the standard model. I can't recommend it enough.

Next, General Relativity. If you're interested in String Theory you're going to need to become an expert in General Relativity. This book: General Relativity from A to B explains the ideas behind GR without a lot of math, but it does so in a precise way. It's a really good book.

Next, Quantum Mechanics. This book: In Search of Schrodinger's Cat is a great introduction to the people and ideas of Quantum Mechanics. I like it a lot.

For general physics knowledge. Lots of people really like the
Feynman Lectures They cover everything and so have quite a bit of math in them. As a taster you can get a couple of books: Six Easy Pieces and Six Not So Easy Pieces, though the not so easy pieces are a bit more mathematically minded.

Now I'll take the opportunity to recommend my own pet favourite book. The Road to Reality. Roger Penrose wrote this to prove that anyone could understand all of theoretical physics, as such it's one of the hardest books you can read, but it is fascinating and tells you about concepts all the way up to String Theory. If you've got time to think and work on the exercises I found it well worth the time. All the math that's needed is explained in the book, which is good, but it's certainly not easy!

Lastly, for understanding more of the ideas which underlie theoretical physics, this is a good book: Philsophy of Physics: Space and Time It's not the best, but the ideas behind theoretical physics thought are important and this is an interesting and subtle book. I'd put it last on the reading list though.

Anyway, I hope that helps, keep learning about physics and asking questions! If there's anything else you want to know, feel free to ask.

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

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.

****

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!

Yes, I do believe it is by chance and I don't believe one needs to posit a god as the creator of the universe to explain its existence. And if one does, then where did that god come from?

E.g., one could explain the existence of the universe as the eminent theoretical physicist and cosmologist Steven Hawking did in The Grand Design.

>In his latest book, The Grand Design, an extract of which is published in Eureka magazine in The Times, Hawking said: “Because there is a law such as gravity, the Universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the Universe exists, why we exist.”
>
>He added: “It is not necessary to invoke God to light the blue touch paper and set the Universe going.”

Source: Stephen Hawking: God was not needed to create the Universe

I know it is hard for many people to accept that chance is involved in our existence. The theoretical physicist Albert Einstein is reputed to have remarked about God in relation to quantum mechanics that "I, at any rate, am convinced that He does not throw dice", which is commonly paraphrased as "God does not play dice with the universe." Supposedly, either Neils Bohr or Enrico Fermi remarked "Stop telling God what to do with his dice." - Source. And, Stephen Hawking remarked in a 1994 debate with Roger Penrose that "Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can't be seen." Source.

Note: One shouldn't assume that the use of "God" by any of them means the notion of God commonly held by Christians today. But, their remarks do show that there has been much disagreement among eminent physicists regarding the role that chance plays in the universe.

If by chance most species of dinosaurs on earth had not been wiped out by a cataclysmic event, such as an asteroid strike on earth, 65 million years ago, the creatures posing the question "Do you really think that our existence is owed just to chance" might look something like one of the creatures depicted here.

We may simply be like that puddle mentioned by Douglas Adams.

>This is rather as if you imagine a puddle waking up one morning and thinking, 'This is an interesting world I find myself in - an interesting hole I find myself in - fits me rather neatly, doesn't it? In fact it fits me staggeringly well, must have been made to have me in it!' This is such a powerful idea that as the sun rises in the sky and the air heats up and as, gradually, the puddle gets smaller and smaller, it's still frantically hanging on to the notion that everything's going to be alright, because this world was meant to have him in it, was built to have him in it; so the moment he disappears catches him rather by surprise. I think this may be something we need to be on the watch out for. We all know that at some point in the future the Universe will come to an end and at some other point, considerably in advance from that but still not immediately pressing, the sun will explode. We feel there's plenty of time to worry about that, but on the other hand that's a very dangerous thing to say.

Source: Is there an Artificial God?

As to why humans tend to find certain environmental features beautiful, well natural selection offers an explanation.

>One of the most important considerations in the survival of any organism is habitat selection. Until the development of cities 10,000 years ago, human life was mostly nomadic. Finding desirable conditions for survival, particularly with an eye towards potential food and predators, would have selectively affected the human response to landscape—the capacity of landscape types to evoke positive emotions, rejection, inquisitiveness, and a desire to explore, or a general sense of comfort. Responses to landscape types have been tested in an experiment in which standardized photographs of landscape types were shown to people of different ages and in different countries: deciduous forest, tropical forest, open savannah with trees, coniferous forest, and desert. Among adults, no category stood out as preferred (except that the desert landscape fell slightly below the preference rating of the others). However, when the experiment was applied to young children, it was found that they showed a marked preference for savannahs with trees-exactly the East African landscape where much early human evolution took place (Orians and Heerwagen 1992). Beyond a liking for savannahs, there is a general preference for landscapes with water; a variety of open and wooded space (indicating places to hide and places for game to hide); trees that fork near the ground (provide escape possibilities) with fruiting potential a metre or two from the ground; vistas that recede in the distance, including a path or river that bends out of view but invites exploration; the direct presence or implication of game animals; and variegated cloud patterns. The savannah environment is in fact a singularly food-rich environment (calculated in terms of kilograms of protein per square kilometre), and highly desirable for a hunter-gatherer way of life. Not surprisingly, these are the very elements we see repeated endlessly in both calendar art and in the design of public parks worldwide.

Source: Aesthetics and Evolutionary Psychology

Or see Survival of the Beautiful: Art, Science, and Evolution by David Rothenberg

No, you certainly don't seem arrogant to me. I wouldn't assume just because someone has a different opinion on such matters that means he or she is arrogant. Nor do I downvote people just because their views don't match my own as I noticed someone did to your comments.

One of the reasons I visit reddit is to expose myself to others' viewpoints so that I can, hopefully, learn from doing so.

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.

>The song is a wave of vibrating air molecules

The "song" is not a vibrating air molecule. I can sing the same song back to you and it would be different vibrations, but the same song. The song can sung be a different person, but it is still the same song. The song can be stored as a series of 1's and 0's but when played will still be the same song but the vibrations of the air molecules will be different because it was stored digitally.
Songs and words can be represented physically, but this does not mean they are physical themselves. Is the "law" is a physical object? Are "crimes" physical objects? Can you point out where scientists have discovered the crime atom? Concepts, abstractions are not physical and it is childish to pretend they are.

>Beauty is mathematical patterns loosely related to the golden ratio.

Wow, and people say us scientists are cold and unpoetic. There's really no way for me to go here if you truly believe this.

>It is called "materialism"

Materialism does not dictate that abstract concepts must be physical. What materialism does say is that there is only nature. There is no supernatural or unnatural. What exists exists. The physical universe is entirely physical.

>However, what you're talking about is not abstraction. It is closer to the theory of the "universals."

A 'universal' is an abstraction. Just as a word is not a physical object neither is a property of such a word.

>I do not have a belief on this matter.

If you honestly can't comprehend the difference between something real and something abstract then you do have a belief on the matter and my arguements will fall on deaf ears since they presuppose abstractions.

>No, you are not. If you were taking your information straight from the OT, you would know that you speak absolutely nonsense.

It is helpful to point specifically what I said was wrong rather than just declare it. Did god or did he not flood the earth? Was this a real flood and not a 'metaphorical' flood? Were Noah and his family the only human surivors? Simple yes or no questions.

>Anyway, prove your statement that God had to break the laws of physics to cause the flood.

You need to answer what the flood is first. I can ask this question to a hundred different christians and get a hundred different answers, which version are you subscribing to?

>Yes, but it is not my job to figure out how God did it.

You can start by telling me what he did first, then we can deduce the possible ways of doing this.

>I don't know what you mean by clear exchange of mass

Electrons have mass. Also energy is mass.

>No. The word 'universe' is defined to encompass all that is physically real,

Then you and I and astrophysics are using different definitions. The universe is defined to be everything that exists.

>Your argument falls flat on the fact that many scientists defend (and are attempting to prove with good chance) the existence of the multiverse,

The argument doesn't fall flat because scientists are not infalliable. Also, good luck to them searching for a multiverse (though it would be undetectable by definition), Copenhagen interpretation FTW.

>it is certainly not a strange idea for science that something outside of our Universe exists.

It is a strange idea precisely because there is no evidence for it. Even the string theorists have yet to make an experimental prediction. They are like the aetherists of yesteryear.

>Aging is measurable. If they are not aging, then they are immortal. It is verifiable.

And what if they are aging so slowly that it cannot be verified above uncertainty that they are aging? Better to put a hard limit on it, say 500 years?

>No more hunger and preventable diseases...

Well this is your version of utopia though it hits pretty close to any mark that I would measure to be a good interpretation. One world government though? I doubt tea-party activists would call that utopia.
But whatever it's a workable definition. I don't think it'll ever be achieved, not because there is no supernatural but because of human nature. Maybe we could do it with a bigger planet and a lot of robots. Or mind control, would that count?

>Yes. I do not consider it true resurrection because we have very little control over the outcome

We'll have very little outcome over the football results but it's still football. Certain techniques make the outcome more likely, but there is no such thing as certainty and it certainly isn't random that using, say, a defibrillator has a better chance of starting someone's heart than not.

>I want an absence of time-limit.

We'll we've advanced to the point of minutes.

>As long as there is a body left, in reasonable condition, it should be doable 100% of the time.

The devil is in the details, define 'reasonable'. Right now a limiting factor is nerve tissue damage which is currently impossible to reverse.
Still though, the techique is only getting better.

>Supernatural souls do not exist. It is greek pagan mythology.

So there are no souls or spirits in christian mythology? If your body doesn't go heaven then what does?

>As long as it is not a machine.

Details, devil, what is a 'machine'? If a machine is that which is created by man then the task is impossible by definition.
Would you allow a new form of bacterial life created artificially in a lab as an acceptable result?

>They are achievable and measurable. They are not easy.

They are getting close to being measurable, clearly defined conditions need to be stated from the beginning or else these definitions could change and we could never acheive the result.

>This has been found multiple times. And whenever it happens, they find an excuse to why the dating doesn't match.

This can't be true. There is a nobel prize out there waiting for anyone who can disprove along standing scientific theory. Einstein got one for disproving Newtonian physics.
If I had such evidence that evolution was false I would be shouting it from the rooftops because it would be one of the greatest discoveries ever and would advance our knowledge.
If by 'excuse' do you perhaps mean 'reason'? Show me the best three pieces of such evidence.

>No, it is not true, sorry

Roman examples aside. Do we not celebrate winter solstice? Have we not named our days of the week after Norse and pagan gods? Do you have a starsign?
Our culture is a melting pot of those that came before it.

>Your argument is basically, "if something doesn't exist already, then it cannot ever exist."

Not something, but basically yes as applies to time and space. You cannot say there was nothing and then there was time because 'then' is a temporal concept that cannot exist without time and you may as well say 'always'.

>Citation needed.

Well you can start with Gravitation is you want the details, or you could probably find it all in some of Hawkings pop-sci books

>No. Answer the question. By 'evolution' you mean M.E.S. or the basic premise of the theory?

You're confusing two arguments here. I was using evolution as analogy for something you know to true, this was before I knew I was talking to a creationist.
So instead of biology lets use geology. Just to double check, you know the Earth is an oblate spheriod yes? OK, imagine you are talking to a flat-earther and he demands absolute proof that the Earth has no edge, what do you say to him?

>...there is demonstrable evidence that M.E.S. is wrong.

Another topic for another day.

>It is the Bell's Theorem.

Just Bell's theorem not 'the', and it is a rival idea to the probability interpretation of quantum mechanics so hated by Einstein. In every experiment so far, QM holds perfectly. Though there are some limitations on what experiments can be done and it will be interesting to see if anything comes of this.
(Here's](http://www.springerlink.com/content/r23275410u4p5q72/) a good paper on the incompatibility will non-local realism theories like Bell's and QM

>I wouldn't go as far as saying that such important premise of QM 'doesn't make any sense.'

What doesn't make sense is something being both non-local and non-casual in the same experiment at the same time.

>Virtual particles are only demonstrably non-causal if locality is assumed to be true. The problem is that locality is independently demonstrably not true.

Yes, and non-locality depends on classical causality being true, which it demonstrably isn't at the QM scale.

>First, it is possible to prove a negative.

You can never prove the non-existence of something, you can only show where it doesn't exist

>You should not attempt to prove him wrong. You should request of him the proof that he is right.

Yes!

>There is a wall behind me.

I never said how far behind you, or how large the elephant was, or whether the elephant can go through walls. Here is the problem in proving a negative. All you can say at this point is there is no visible evidence of an elephant behind you, but is absense of evidence really evidence of absense?

>Virtual particles only violate causality is locality is assumed as true, as far as I know. Unfortunately I don't have access to the journal.

Well this is splitting hairs a little. Newtonian physics only works if you assume locality is true or causality is true (and you usually assume both). Virtual particles exist, they do not on their own violate locality but they do violate classical causality.

It's a pretty difficult question to answer because only you know what you want out of this (or maybe, you don't know yourself!)

"I want to see what kind of mathematics is out there"

Try The Joy Of X. This is a super fun "guided tour" of mathematics. Each chapter surveys a different mathematical topic with examples, intutions, and fun thought experiments. You won't learn to "do the math", but you should have more of an idea of the kinds of things mathematicians think about, and some of the history of mathematics. This is easy and enjoyable, even though no mathematical background.

There's a "Hard mode" version of this called Concepts Of Modern Mathematics. The language is still light and informal, but the concepts are dealt with in more depth and abstraction -- there are fewer "real life" examples, and you will have to follow some real mathematical arguments in your head or on paper. This is more difficult, but still requires no formal mathematical background.

The other place to check of course is YouTube. 3Blue1Brown, Mathologer, Numberphile and many other channels have great exposés of mathematical concepts for the general audience, with 3Blue1Brown being my favourite for his wonderful animations.

"I want to actually improve my mathematical knowledge and skill"

This is difficult, but doable. I'm a mature mathematics student, and I was only really in with a shot of university owing to the kindness of my then fiancée supporting me while I knuckled down and learned the basics. The first step will be to brush up on what you should know from school. I'm not really sure what to recommend here; most texts targeted at this level of mathematics are targeted at... well, bored teenagers who don't want to learn mathematics, rather than keen adults possessing of some degree of patience and perseverance. I suppose Serge Lang, probably the most prolific mathematics textbook author of all time, can offer "Basic Mathematics", but this means paying Springer textbook prices, unless you enjoy marauding on the high seas. Khan Academy is a website with dozens (hundreds?) of free videos, articles, and exercises on basic mathematics

After you're up to speed on your basic algebra and geometry, the two most widely applied and important topics in mathematics beyond school-level are calculus and linear algebra (other than maybe statistics and probability). Calculus is typically learned first, but actually, it doesn't really matter which order you do these in. Exactly how to learn these topics is also a pretty difficult question, and depends what you want to get out of it. I guess post back here if "step 1" (recovering all your school-level maths) goes well?

Maths is hard, but fun. You have to do exercises and practice. You have to think deeply about difficult and abstract concepts. If you do choose the "improve actual skill" route, I'd still recommend supplementing your learning with the books and YouTube videos from the first half of this reply. Being exposed to fun new ideas regularly helps motivate you to push through the technical difficulties of learning it "properly".

> 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.

I was in your position just a couple of years ago, here's what I did.

Start with a mechanics course if you haven't already, it's crucial that you have a solid understanding of physics before you try to learn the advanced stuff.

Learn calc all the way through vector calc. A great resource for this is Professor Leonard (this is calc 3, but he has all of them).

Here's where I learned physics Electricity and Magnetism, I also learned special relativity and basic quantum mechanics at this point (QM is optional, but fun)

I learned linear algebra and diff eqs at this point. I used Khan Academy for this, though I'm not sure it's the best resource out there.

Next, I would recommend trying to take a class on mathematical proofs, when you are reading papers rather than watching videos you will appreciate it. I watched this series because I'm a comp sci major, but if you aren't a comp sci person, just look for a methods of proofs class.

Now it's time for the fun stuff.

Tensor Calculus is what General Relativity is founded on, I found this series to be helpful

So now it's time to get into GR.

This series from PBS Space Time is a great introduction into accurate GR. Their other stuff is great too.

This video from DrPhysicsA steps through the thoughts behind each part of the EFEs and is not the best video, but it helped me.

And that's where I couldn't find any more videos, so I used some text resources.

The book gravitation is the most commonly used textbook for GR as far as I know.

I found this article on wikipedia to be ENORMOUSLY helpful in understanding how to work a general relativity problem. It took me a few times going through it to follow it all the way, but it is great.

Where you go after this really depends on what you are trying to do with GR, personally I find Kaluza-Klein theory to be very intriguing and that leads down the road to string theory.

Good luck

There are a lot of good classics on /u/thebenson's list. I want to highlight the books that are good for what you'll be learning, and give you a sense of how the sequence works. And I'll add a few.


Calculus books: Thomas' Calculus, Calculus by James Stewart (not multivariable), and this cheap easy read by Morris Kline.

Have you learned calculus in the past? It sounds like you'll need it for at least one of those courses, but either way, it will definitely help you conceptually for the others. You should really try to get solid on this before you need to use it.



Intro physics books: Fundamentals of Physics (Halliday & Resnick), Physics for Scientists and Engineers (Serway & Jewett), Physics for Scientists and Engineers (Tipler & Mosca), University Physics (Young), and Physics for Scientists and Engineers (Knight) are all good. Gee, they get really unoriginal with the names, huh?

Each of these books assumes no background in physics, but you do need to use calculus. If you're going to take a class in basic mechanics that doesn't involve any calculus, you may find it more useful to get a book at that level. The only such book that I'm familiar with is Physics: Principles with Applications by Giancoli. I know there are many others, but I can't speak for them.



Mathematical methods: Greenberg is way more than you need here. I think you would find Engineering Mathematics by Stroud & Booth more useful as a reference, since it covers a lot of the less advanced stuff that you may need a refresher on.



Sequence: it's typical to start learning physics by learning about Newtonian mechanics, with or without calculus. After that, one often goes on to thermodynamics or to electricity and magnetism. It sounds like this is roughly how your program is going to work.

If you are learning mechanics with calculus, you can expect E&M to be even heavier on the calculus and thermodynamics to be less so. More calculus is not a bad thing. People often get scared of it, but it actually makes things easier to understand.

It is very typical that you will use only one book (from the intro books above) for all of these topics. You shouldn't need to get any books on specific topics.

**

The other books on /u/thebenson's list are all great textbooks, but I think you should avoid them for now. They generally assume a healthy background in basic physics, and they may not be very relevant to the physics you'll be studying.

But I do want to give some mention to Spacetime Physics* by Taylor and Wheeler, since I don't want to imply that this is a background-heavy book. On the contrary, this is one of the most beginner-friendly physics books ever written, and it is my favorite introduction to special relativity. Special relativity is probably not something you need to learn about right now, but if you have any interest, I seriously recommend finding an old used copy of this book—it's a fun read aside from any other uses!

Beyond the obvious choices, Watts' The Book, Ram Dass' Be Here Now, Huxley's Doors of Perception, Leary’s The Psychedelic Experience, and of course Fear and Loathing (all of these should be on the list without question; they’re classics), here are a some others from a few different perspectives:

From a Secular Contemporary Perspective

Godel Escher Bach by Douglass Hofstadter -- This is a classic for anyone, but man is it food for psychedelic thought. It's a giant book, but even just reading the dialogues in between chapters is worth it.

The Mind’s Eye edited by Douglass Hofstadter and Daniel Dennett – This is an anthology with a bunch of great essays and short fictional works on the self.

From an Eastern Religious Perspective

The Tao is Silent by Raymond Smullyan -- This is a very fun and amusing exploration of Taoist thought from one of the best living logicians (he's 94 and still writing logic books!).

Religion and Nothingness by Keiji Nishitani – This one is a bit dense, but it is full of some of the most exciting philosophical and theological thought I’ve ever come across. Nishitani, an Eastern Buddhist brings together thought from Buddhist thinkers, Christian mystics, and the existentialists like Neitzsche and Heidegger to try to bridge some of the philosophical gaps between the east and the west.

The Fundamental Wisdom of the Middle Way by Nagarjuna (and Garfield's translation/commentary is very good as well) -- This is the classic work from Nagarjuna, who lived around the turn of the millennium and is arguably the most important Buddhist thinker after the Buddha himself.

From a Western Religious Perspective

I and Thou by Martin Buber – Buber wouldn’t approve of this book being on this list, but it’s a profound book, and there’s not much quite like it. Buber is a mystical Jewish Philosopher who argues, in beautiful and poetic prose, that we get glimpses of the Divine from interpersonal moments with others which transcend what he calls “I-it” experience.

The Interior Castle by St. Teresa of Avila – this is an old book (from the 1500s) and it is very steeped in Christian language, so it might not be everyone’s favorite, but it is perhaps the seminal work of medieval Christian mysticism.

From an Existentialist Perspective

Nausea by Jean Paul Sartre – Not for the light of heart, this existential novel talks about existential nausea a strange perception of the absurdity of existence.

The Myth of Sisyphus by Albert Camus – a classic essay that discusses the struggle one faces in a world inherently devoid of meaning.

----
I’ll add more if I think of anything else that needs to be thrown in there!

"We are going to die, and that makes us the lucky ones. Most people are never going to die because they are never going to be born. The potential people who could have been here in my place but who will in fact never see the light of day outnumber the sand grains of Sahara. Certainly those unborn ghosts include greater poets than Keats, scientists greater than Newton. We know this because the set of possible people allowed by our DNA so massively outnumbers the set of actual people. In the teeth of these stupefying odds it is you and I, in our ordinariness, that are here. We privileged few, who won the lottery of birth against all odds, how dare we whine at our inevitable return to that prior state from which the vast majority have never stirred?" -Richard Dawkins, Unweaving the Rainbow

"I do not fear death. I had been dead for billions and billions of years before I was born, and had not suffered the slightest inconvenience from it." -attributed to Mark Twain (source unknown)

"I believe that when I die I shall rot, and nothing of my ego will survive. I am not young and I love life. But I should scorn to shiver with terror at the thought of annihilation. Happiness is nonetheless true happiness because it must come to an end, nor do thought and love lose their value because they are not everlasting. Many a man has borne himself proudly on the scaffold; surely the same pride should teach us to think truly about man's place in the world. Even if the open windows of science at first make us shiver after the cosy indoor warmth of traditional humanizing myths, in the end the fresh air brings vigour, and the great spaces have a splendour of their own." -Bertrand Russell, What I Believe (essay)

[TED Talk: "Dan Dennett: The illusion of consciousness"](https://www.ted.com/talks /dan_dennett_on_our_consciousness)

I recommend Dennett's Consciousness Explained

Christopher Hitchens (Cartoon) - The Never Ending Party

There's also the cyclic model; there's also a Wikipedia article on the cyclic model. That model seems to mesh better with Hinduism.

>If you are a Hindu philosopher, none of the above should surprise you. Hindu philosophy has always accepted the notion of an alternately expanding and contracting universe. In his book Cosmos, Carl Sagan pointed out how, in Hindu cosmology, the universe undergoes an infinite number of deaths and rebirths, and its timescales are in the same ballpark as those of modern cosmology. Here is a quote from Cosmos:
>
>"There is the deep and appealing notion that the universe is but a dream of the god who, after a hundred Brahma years, dissolves himself into a dreamless sleep. The universe dissolves with him - until, after another Brahma century, he stirs, recomposes himself and begins again to dream the cosmic dream.
>
>Meanwhile, elsewhere, there are an infinite number of universes, each with its own god dreaming the cosmic dream. These great ideas are tempered by another, perhaps greater. It is said that men may not be the dreams of gods, but rather that the gods are the dreams of men."

Reference: The Conscious Universe: Brahma's Dream

Or for the Big Bang model, one might address the question as Steven Hawking has in his book The Grand Design.

>He adds: "Because there is a law such as gravity, the universe can and will create itself from nothing.
>
>"Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist.
>
>"It is not necessary to invoke God to light the blue touch paper and set the universe going."

Reference: Stephen Hawking: God did not create Universe

In any case, one can ask "where did God" come from as well. One can say "God has always existed", but one can say the universe always existed or there were other universes before this one, etc., also. Our limited intellects and knowledge of the universe may keep humans from truly knowing the answer indefinitely.

let me give you a shortcut.

You want to know how partial derivatives work? Consider a function with two variables: f(x,y) = x^2 y^3, for a simple example.

here's what you do. Let's take the partial derivative with respect to x. What you do, is you consider all the other variables to be constant, and just take the standard derivative with respect to x. In this case, the partial derivative with respect to x is: 2xy^3. That's it, it's really that easy.

What about taking with respect to y? Same thing, now x is constant, and your answer is 3x^2 y^2.

This is an incredibly deep topic, but getting enough of an understanding to tackle gradient descent is really pretty simple. If you want to full on jump in though and get some exposure to way more than you need, check out div curl and grad and all that. It covers a lot, including a fair amount that you won't need for any ML algorithm I've ever seen (curl, divergence theorem, etc) but the intro section on the gradient at the beginning might be helpful... maybe see if you can find a pdf or something. There's probably other good intros too, but seriously... the mechanics of actually performing a partial derivative really are that easy. If you can do a derivative in one dimension, you can handle partial derivatives.

edit: I misread, didn't see you were a junior in highschool. Disregard div curl grad and all that, I highly recommend it, but you should be up through calc 3 and linear algebra first.

To change my advice to be slightly more relevant, learn how normal derivatives work. Go through the Kahn Academy calc stuff if the format appeals to you. Doesn't matter what course you go through though, you just need to go through a few dozen exercises (or a few hundred, depending on your patience and interest) and you'll get there. Derivatives aren't too complicated really, if you understand the limit definition of the derivative (taking the slope over a vanishingly small interval) then the rest is just learning special cases. How do you take the derivative of f(x)g(x)? f(g(x))? There's really not too many rules, so just spend a while practicing and you'll be right where you need to be. Once you're there, going up to understanding partial derivatives is as simple as I described above... if you can take a standard derivative, you can take a partial derivative.

Also: props for wading into the deep end yourself! I know some of this stuff might seem intimidating, but if you do what you're doing (make sure you understand as much as you can instead of blowing ahead) you'll be able to follow this trail as far as you want to go. Good luck, and feel free to hit me up if you have any specific questions, I'd be happy to share.

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!

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.

> Why is a photon massless and still has momentum?

Because momentum isn’t actually p = mv, as in Newtonian mechanics, but it’s really

p = ( E/c^2 ) v

For objects with a non-zero mass m, moving non-relativistically, E is approximately equal to mc^2 and then p is approximately equal to mv, the Newtonian value.

However, photons are intrinsically relativistic. They have energy even though they don’t have mass (their energy is proportional to their frequency, E = hf, where h is Planck’s constant) and, so, they also carry momentum. In fact, since their speed (in vacuum) is always c, the magnitude of their momentum, using the above results, is always p = E/c = h f/c = h/wavelength.

> Why can't anything go beyond the speed of light? (Cliché but I never really understood why despite of many videos floating on YouTube)

Please take a read at this post I wrote here some time ago, where I address that question. Please ignore the first two paragraphs as those were part of a rant.

> How does a magnetic field originate?

A magnetic field is created by electric charges in motion. Since, however, motion is relative (you’re not moving with respect to your chair but you are moving with respect to, say, the Sun), so is a magnetic field. In a reference frame where an electric charge is at rest, you’ll only measure the electric field generated by the charge. In a reference frame where the charge is in motion, you’ll observe both an electric field and a magnetic field.

—

Excellent introductory books on special relativity, in my opinion, are (in increasing order of difficulty):

Special Relativity: For the Enthusiastic Beginner

https://www.amazon.co.uk/dp/1542323517/

Special Relativity (Mit Introductory Physics Series)

https://www.amazon.co.uk/dp/B079SB3MWS/

and

Spacetime Physics: Introduction to Special Relativity

https://www.amazon.co.uk/dp/0716723271/

Einstein’s own books are pretty great too, and are now in the public domain. Search the Gutenberg project for them.

This is a good introductory essay by Nick Bostrom from The Cambridge Handbook of Artificial Intelligence. And this is a relevant survey essay by Drew McDermott from The Cambridge Handbook of Consciousness.

If folks aren't taking well to the background reading, they might at least do alright jumping to Section 5 from the Descartes' Discourse (they can use this accessible translation). One little snippet:

>I worked especially hard to show that if any such machines had the organs and outward shape of a monkey or of some other animal that doesn’t have reason, we couldn’t tell that they didn’t possess entirely the same nature as these animals; whereas if any such machines bore a resemblance to our bodies and imitated as many of our actions as was practically possible, we would still have two very sure signs that they were nevertheless not real men. (1) The first is that they could never use words or other constructed signs, as we do to declare our thoughts to others. We can easily conceive of a machine so constructed that it utters words, and even utters words that correspond to bodily actions that will cause a change in its organs (touch it in one spot and it asks ‘What do you mean?’, touch it in another and it cries out ‘That hurts!’, and so on); but not that such a machine should produce different sequences of words so as to give an appropriately meaningful answer to whatever is said in its presence—which is something that the dullest of men can do. (2) Secondly, even though such machines might do some things as well as we do them, or perhaps even better, they would be bound to fail in others; and that would show us that they weren’t acting through understanding but only from the disposition of their organs. For whereas reason is a universal instrument that can be used in all kinds of situations, these organs need some particular disposition for each particular action; hence it is practically impossible for a machine to have enough different •organs to make •it act in all the contingencies of life in the way our •reason makes •us act. These two factors also tell us how men differ from beasts [= ‘non-human animals’].

That sets the stage for historically important essay from Turing of Turing-Test-fame. And that essay sets up nicely Searle's Chinese Room thought experiment. Scientific America has two accessible articles: Searle presents his argument here, and the Churchland's respond.

As always, the SEP and IEP are good resources for students, and they have entries with bibliographies on consciousness, the hard problem of consciousness, AI, computational theories of mind, and so on.

There are countless general introductions to philosophy of mind. Heil's Philosophy of Mind is good. Seager's introduction to theories of consciousness is also quite good, but maybe more challenging than some. Susan Blackmore's book Conversations on Consciousness was a very engaging read, and beginner friendly. She also has a more textbook-style Introduction that I have not read, but feel comfortable betting that it is also quite good.

Searle's, Dennett's and Chalmer's books on consciousness are all good and influential and somewhat partisan to their own approaches. And Kim's work is a personal favorite.

(sorry for the broad answer--it's a very broad question!)

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!

• OpenIntro is a free basic statistics book including R labs on their website (it may be too basic for you, idk).
  
• Norm Matloff has a free book on statistics here. Even though it's intended for computer scientists, it's contents are really universal and basic (and it uses R too).
  
• Statistical inference by Casella and Berger is considered a "classic". It's heavy on theory though.
  
• All of Statistics by Larry Wasserman is very concise but offers a very good overview (all theory).
  
• See this post or this one for a compilation of freely available textbooks on statistics.
  
  As you wish to get into applied statistics (i.e. actually analyzing data), you'll need software. I'd strongly recommend learning and using R because it's completely free and incredibly powerful.
  
  Here are some resources for learning statistics using R:
  
  
• Statistics: An Introduction Using R by Michael Crawley introduces basic statistical methodology and its application with R. An alternative would be Introductory Statistics with R by Peter Dalgaard.
  
• http://www.r-statistics.com/2009/10/free-statistics-e-books-for-download/
  
• http://blog.revolutionanalytics.com/2011/11/three-free-books-on-r-for-statistics.html
  
• http://www.r-project.org/doc/bib/R-books.html
  
  Then, these websites provide very valuable resources for doing statistics with R:
  
  
• http://zoonek2.free.fr/UNIX/48_R/all.html
  
• http://www.cookbook-r.com/
  
• http://www.statmethods.net/
  
  Hope that helps.
  

That's one of my favorite popular science books, so it's wonderful to hear you're getting so much out of it. It really is a fascinating topic, and it's sad that so many Christians close themselves off to it solely to protect their religious beliefs (though as you discovered, it's good for those religious beliefs that they do).

As a companion to the book you might enjoy the Stated Clearly series of videos, which break down evolution very simply (and they're made by an ex-Christian whose education about evolution was part of his reason for leaving the religion). You might also like Coyne's blog, though these days it's more about his personal views than it is about evolution (but some searching on the site will bring up interesting things he's written on a whole host of religious topics from Adam and Eve to "ground of being" theology). He does also have another book you might like (Faith Versus Fact: Why Science and Religion are Incompatible), though I only read part of it since I was familiar with much of it from his blog.

> If you guys have any other book recommendations along these lines, I'm all ears!

You should definitely read The Selfish Gene by Richard Dawkins, if only because it's a classic (and widely misrepresented/misunderstood). A little farther afield, one of my favorite popular science books of all time is The Language Instinct by Steven Pinker, which looks at human language as an evolved ability. Pinker's primary area of academic expertise is child language acquisition, so he's the most in his element in that book.

If you're interested in neuroscience and the brain you could read How the Mind Works (also by Pinker) or The Tell-Tale Brain by V. S. Ramachandran, both of which are wide-ranging and accessibly written. I'd also recommend Thinking, Fast and Slow by psychologist Daniel Kahneman. Evolution gets a lot of attention in ex-Christian circles, but books like these are highly underrated as antidotes to Christian indoctrination -- nothing cures magical thinking about the "soul", consciousness and so on as much as learning how the brain and the mind actually work.

If you're interested in more general/philosophical works that touch on similar themes, Douglas R. Hofstadter's Gödel, Escher, Bach made a huge impression on me (years ago). You might also like The Mind's I by Hofstadter and Daniel Dennett, which is a collection of philosophical essays along with commentaries. Books like these will get you thinking about the true mysteries of life, the universe and everything -- the kind of mysteries that have such sterile and unsatisfying "answers" within Christianity and other mythologies.

Don't worry about the past -- just be happy you're learning about all of this now. You've got plenty of life ahead of you to make up for any lost time. Have fun!

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!

Alan Watts is great - but he's no philosopher. He even claims this himself.
He is more aligned with religion than anything else - maybe best described as a spiritualist. He wasn't exactly going about his work with the same rigor, for example, as St. Aquinas and Anselm.

Though Albert Camus claimed not to be a philosopher as well - but that is the funny thing about continental philosophy - half the time you can't distinguish them from plain authors. :-)

As for recommendations - this is really tough.

Descartes' Meditations on First Philosophy would be a good one to read - but maybe not for general purposes.
For epistemology, you can't beat Gettier's Is Justified True Belief Knowledge?. It's more like a one page read, however.

Hume's An Enquiry Concerning Human Understanding is great for the section on the problems of induction.

For general purpose though (and I have to give credit to my SO, who has a PhD in philosophy and has taught it for ages), I think Simon Blackburn's Think might be one of the better surveys and general introductions to philosophy.

Hope this helps. :-)

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

I think the best route is to trick her into being interested in books. I think I just might have a trick for that.

Send her the wikipedia article for "trolley problem", and then send her the wiki article on judith thomson's violinist argument in favor of abortion. Then send her a link to parfit's transporter thought experiment. It's ideal if you can find versions of these online which are easy to read and presented in a cool manner. (blog entries are ideal for this. Here's a blog entry on parfit's teletransporter: http://twophilosoraptors.blogspot.com/2010/07/teletransporter.html)

Then buy her What If...collected thought experiments in philosophy off amazon or ebay. A used one will be cheap, or take it out from the library and renew it online while she uses it. If she got intrigued by the above thought experiments, and is intrigued by strange paradoxes about truth, like the liar paradox, or leibniz's law, then she will absolutely love this book. It's full of one-page, easily consumable versions of thought experiments, and then the page next to that one contains elaboration on the experiment and current work on it. One of my favorites in there is Max Black's two spheres, which seem to violate leibniz's law. A fun alternative to this, with bite sized philosophy things is "plato and a platypus walk into a bar".

If she continues to show interest in these, you can feed her new information about them via blogs like peasoup and thoughts, arguments, and rants, by googling the name of blogs like these next to a particular paradox or thought experiment, e.g. "thoughts arguments and rants moores paradox". This will lead you to new work by contemporary philosophers on the subjects, which may feed her interest into what it is that philosophers actually do. Eventually this may prompt her to want to read a full book on philosophy, to have a more mature understanding of how these paradoxes and TE's work, then you could get her the very interesting Think by simon blackburn, which is a general intro to philosophy, or the shorter very short introduction books. You can work up to more advanced, interesting work from there (like David Lewis' On the plurality of worlds, which opens the trippy possibility that all possibilities are realities).

Hope she enjoys her reading!

I haven't a clue there. I've just built stuff on Earth haha and know plywood and siding square footage adds up pretty quick for a structure which would be the similar case with a mold.

Personally I've always imagined something inflatable for living areas at first like Bigelow is testing on ISS. Once we had a good handle on excavating and manufacturing some sort of concrete or brick from local materials I'd imagine buried barrel vault type construction like Zubrin seems to like in some of his books, although I did some math on that once (in this sub I believe), I'll see if I saved it.


Edit: hmmm I can't seem to find it but here's a comment along the ideas

-------------
https://www.reddit.com/r/space/comments/4qg9i9/bill_nye_warns_about_problems_colonizing_mars/d4sv0r5/

> I never see the lack of a magentosphere getting brought up.

It's not an issue. You aren't going to be living/temporarily living in clear nylon inflated bubbles. Yes, you'll absolutely pick up more rads if you are living in an unshielded habitat but shielding it is going to be quite easy if you have even modest mechanical means of moving regolith.

Worst case for a non permanent mission, the areas of the habitat you spend most of your time in have the water stored in the walls and ceiling.

Quick shielding for more permanent living you take a strong, but light, material like Nylon 6 with you ultra-light metal poles. You place the poles around the habitat you then weave the material between them (think 'under over') and then spend your first few days using modestly powered Martian wheelbarrow to scoop and move regolith between the material and the habitat with the exception of shielded doors. Again, have some of the water stored in the top of the modules for the hours the sun is overhead. OR make a simple machine that fills sandbags, the sandbags would require more material (fabric/plastic) but would likely be quicker than carting regolith around.

More long term shielding, your habitats are largely underground OR you use regolith as a component for making bricks and stack bricks around the hab modules.


For a short term mission I'd do something like what I laid out here with LEGO with the modules being inflatables then I'd come in with poles, sheeting and loose regolith to get in-hab rad exposure similar to what you'd get on Earth. For fun I have about 18.5 m2 of PV panels displayed in the model which would provide about 1415w at high noon and the tanks are actually landed ahead of time largely empty containing ISRU units to generate/capture usable things from the atmosphere. Probably WAVAR for one of the ISRU units which upon landing could quickly be used for starting soil washing experiments and/or hydroponics, if near the northern polar region you could take your time harvesting water ice for melting, you could also have some of the water from the WAVAR going to a second ISRU purely to make oxygen and hydrogen, you could also have one making monopropellant hydrogen peroxide for the return mission and/or return samples.


As far as atmospheric depletion, exactly what /u/Pimozv said

----------------------


Edit 2: another relevant comment of mine

----
https://www.reddit.com/r/Colonizemars/comments/551o13/as_much_as_everyone_hates_burning_man_man_he_had/d88fg39/

> and sending builders?

Companies might. A lot of the habitats are likely going to be inflatable in nature at first. If you can assemble a tent you'll likely be able to assemble a habitat. Later you can relatively easy make bricks from local materials (almost entirely from the regolith) and build vaults/bunkers under ground and then cover with regolith, pressurize them and they'll eventually seal themselves off thanks to the temperature... moisture from exhalation and what not will seep through any cracks and ultimately freeze You could also go in and paint some sort of sealant. Above ground you'd use a sealant or put an inflatable inside the brick structure. I suggest reading Zubrin's books The Case for Mars and Mars Direct: Space Exploration, the Red Planet, and the Human Future and his fiction, but scientifically accurate book, How to Live on Mars which is a guide written in the future for those that are on their way to Mars. His fiction book First Landing is also worth reading, it came out before The Martian and involves an entire crew trying to scrape by on Mars.

u/LeeHyori provides a great outline of the main aspects of logical positivism, e.g. the verification principle, so I won't bother addressing the 'what is logical positivism' question in detail. (The only things I would add are things like a general tendency towards: reductionism, formalism, a Wittgensteinian metaphilosophy, support of the sciences and unifying them, etc). What I want to bring up is about the objections to LP and positivists today, like Dennett.

>From my understanding, it was because their main idea seemed contradictory ("only verifiable things can be true" is itself not verifiable).

Aside from the self-refuting nature of the verification principle that you point out here, there were other problems as well, such as the theory-ladenness of observation, consequent problems with logical positivism's reductionism and empiricism (e.g., observation/protocol statements are not purely empirical), the holistic nature of confirmation, the [difficulties defining what an analytic statement is/the circular nature of the concept] (http://www.ditext.com/quine/quine.html), and the apparent irreducibility of the sciences. So you're right that LP suffered tremendously by relying on a self-undermining theory of meaning, but there were other serious problems, which gave rise to a ton of awesome new literature on the subject.

>However, has there been any prominent philosophy that has grown out of logical positivism that is in itself a stronger version of the positivist's philosophy?

I don't think anyone that famous became more positivist, in the sense of embracing a more extreme verification principle, but Dennett has said publicly he is kind of a closet verificationist - examples of which are in [Consciousness Explained] (http://www.amazon.ca/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661). He talks for instance about how his analysis of the inverted qualia argument supports "the shockingly "verifications" or "positivist" view that the very idea of inverted qualia is nonsense--and hence that the very idea of qualia is nonsense" (p.390 in my edition). He also mentioned we're all verificationists in some sense, using the example of impossible-to-detect gremlins in the engine of your car - but here he seems to be more saying the obvious claim that we need evidence to verify hypotheses, not that unverifiable = nonsense.

In any case, Dennett's definitely one of the biggest philosophers still writing today who inherited the positivist tradition, and if we can still use the term I'd say he's one of the most positivist philosophers alive.

No. A survey of the world's oceanic life is already underway; mapping the ocean floor is not terribly useful or important, and most mapping techniques aren't precise enough to detect small artifacts of the sort that ancient tribes would have had.

NASA, on the other hand, is trying to develop technologies which will make it easier for us to explore and later colonize other planets.

It is almost inevitable that humans will colonize Mars at some point in the next few hundred years (to make a very conservative estimate- it would actually be possible to send a manned mission to mars using a combination of Apollo technology and 1800s industrial chemical reactions to make rocket fuel from the atmosphere of mars).

Space is the final frontier- a frontier with almost limitless potential for expansion. History shows us that nations which are expanding along a frontier show far more innovation and far less stagnation; an example is the American frontier, which gave America a huge boost of innovation and corresponding world power for centuries. Once humanity takes the leap to exploring and colonizing space, it's quite likely that the challenges of that task will unlock a huge wave of technological progress for our entire species.

At the moment, the problem with NASA is that everything in its budget is subject to review by Congress, even though most Congressmen know nothing about what NASA does. This has created a small project centered culture at NASA; groups of scientists lobby for NASA to change its overarching goals in order to justify their individual projects, instead of NASA creating a long term strategy on the lines of the Apollo program which individuals would then adjust their projects to support. Because of this, very little useful gets done, and NASA wastes massive amounts of time and money sitting in the space station doing this test and that test without actually going anywhere.

If you really want to make NASA useful, it should have a set budget (higher than it is now) and a long term plan of action which is controlled by the NASA director, not one which changes every time a new president is elected.

If any of that interested you, The Case for Mars by Robert Zubrin is a great read on the subject of NASA and what we should be doing with our space program.

Here are some cool videos for you(not really informative about the makeup of cells but nonetheless might interest you enough to read the amazing books that I've listed below! The microcosmos really is a whole 'nother world!):

Kinesin Walking Narrated Version:

http://youtu.be/YAva4g3Pk6k


This is a better model. Notice how the 'legs' shake around violently until it snaps into place. Sometimes the random motion of the jiggling atoms(these aren't shown. Imagine the Kinesin molecules shown in a sea of water molecules, all jiggling about ferociously. The 'invisible' water molecules are bumping up against the Kinesin, and it's evolved to work with the random motions) makes it step backwards! But the ATP/ADP process makes it more likely to step forward than backwards(an evolved process). This is explained well in the book Life's Ratchet below.

Molecular Motor Kinesin Walks Like a Drunk Man:

http://youtu.be/JckOUrl3aes

Here are some amazing book to read. Seriously read all of these, preferably in the order listed to get the best understanding. They will blow your mind many times over. Many, if not all, may be at your local library.


QED: The Strange Theory of Light and Matter:

http://www.amazon.com/gp/aw/d/0691125759


Quarks: The Stuff of Matter

http://www.amazon.com/gp/aw/d/0465067816


Thermodynamics:A Very Short Introduction

http://www.amazon.com/gp/aw/d/0199572194


Life's Ratchet:

http://www.amazon.com/gp/aw/d/0465022537/


The Greatest Show on Earth: The Evidence for Evolution

http://www.amazon.com/gp/aw/d/1416594795


The Drunkard's Walk: How Randomness Rules Our Lives

http://www.amazon.com/gp/aw/d/0307275175p

I would also recommend taking a biology and maybe a chemistry class at your local community college, if possible. My biology class started with the smallest stuff, atoms(technically not the smallest, but whatever), and worked its way up through the chain of sizes up to the biosphere. It was very informative and there were a few people in their 40s(a guess) that really enjoyed the class. So you can do it, too!

Already been mentioned but:

Neuromancer - genre defining, gritty, required reading. ;)

Snow Crash - Excellent, hugely enjoyable characters, good sci fi



Also good and haven't been mentioned:

Headcrash by Bruce Bethke - bizarre, silly, fun cyberpunk (for instance, full sensoral cyberspace connection is done through a rectally inserted probe..)

The Mind's I by Douglas Hofstadter - Excellent collection of short stories about cognitive machines

Wyrm by Mark Fabi - "Interweaving mythology, virtual reality, role-playing games, chess strategy, and artificial intelligence with a theory of a Group Overmind Daemon susceptible to religious symbolism, first-timer Fabi pits a group of computer programmers and hackers against a formidable opponent who may fulfill end-of-the-world prophesies as the millennium approaches."

(I know I'm late, but would like to add my 2 cents anyway.)

I'd say the series stays about the same. (But I also loved it to begin with.) I only remember disliking some of the developments with the Deltans storyline (though I did like it again at the end) and perhaps the romance being a bit of a mixed bag for me.

>... the narrative left behind a lot of what I found most intriguing about the story (Cartesian dilemma of soul and body) ...

Do you mean dualism? When exactly was this brought up?

As I understood it, Bob 1 was pondering whether or not he (a computer program) could be considered conscious -- Something living, something of moral significance. I thought this was settled adequately by his extended monologue. He was wondering whether he was a philosophical zombie (i.e. acting as if conscious without actually being conscious.) He was not wondering how his soul interacted with his replicant hardware (or software.)

And I'd say he's revealed himself as a sort a functionalist: "Handsome is as handsome does." Or rather "Bob is as Bob does."

On that subject, one of my favorite philosophy books is Consciousness Explained by Daniel Dennett. It's heavy reading but I still recommend it. Here's a review. Also this preface by Tadeusz Zawidzki about Dennett's corpus :D


Edit: phrasing

Your best bet is to contact the instructor(s) for any classes you're interested in to see if there will be lectures covering material you are uncomfortable with; it would be helpful to be specific (for example, if you're okay with diagrams of organs and tissues but aren't comfortable with images of the actual thing).

That being said, in my experience (4th year graduate student in molecular biology) few classes have been especially graphic. Off the top of my head, the only ones to be careful of are anatomy/physiology (duh :) ) and general bio as there is usually at least one dissection in the lab section (which you might be able to opt out of).

Another option is to explore your interest in biology and evolution outside of coursework. There are quite a few great books out there that discuss the field without being gory. I personally recommend “The Beak of the Finch”, which discusses the decades-long research project tracking finch evolution in the Galapagos. http://www.amazon.com/The-Beak-Finch-Story-Evolution/dp/067973337X

Good luck!

You're English is great.

I'd like to reemphasize /u/Plaetean's great suggestion of learning the math. That's so important and will make your later career much easier. Khan Academy seems to go all through differential equations. All of the more advanced topics they have differential and integral calculus of the single variable, multivariable calculus, ordinary differential equations, and linear algebra are very useful in physics.

As to textbooks that cover that material I've heard Div, Grad, Curl for multivariable/vector calculus is good, as is Strang for linear algebra. Purcell an introductory E&M text also has an excellent discussion of the curl.

As for introductory physics I love Purcell's E&M. I'd recommend the third edition to you as although it uses SI units, which personally I dislike, it has far more problems than the second, and crucially has many solutions to them included, which makes it much better for self study. As for Mechanics there are a million possible textbooks, and online sources. I'll let someone else recommend that.

I have not taken the class yet (I'm taking 161 and 225 in January), but I looked at the syllabi already and here's the textbook for the class:

http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073383090/ref=sr_1_1?ie=UTF8&qid=1417826968&sr=8-1&keywords=Rosen+Discrete+Math

You may want to go ahead and pick this up and start looking through it prior to January. I already grabbed a copy; I finish Calculus II tomorrow at my community college and I am going to be starting Rosen very soon.

This book is also commonly recommended:

http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0495391328/ref=sr_1_1?ie=UTF8&qid=1417827137&sr=8-1&keywords=Epp

I'm not sure what your math background is, but one of the most important success factors (in my experience) in math classes is a lot of practice. If you start working through either of those books now, you'll probably be in a good place once class starts in January.

We could also probably get a study group going on in here; I'm pretty comfortable with math, so I am happy to help out anyone else who needs help.

Take lots of classes and keep learning. When I was in high school, things like ecology and wildlife biology were appealing to me because I understood what plants, animals, and ecosystems were, but I had no idea what a ribosome or a micro-RNA really were. I found that the more I learned about molecular and cell biology, the more fascinated I became by these tiny little machines that power every living thing. I started taking neuroscience classes because brains are cool; I ended up getting a PhD in neuroscience with a very cellular/molecular focus to my research (my whole dissertation was on one gene/protein that can cause a rare human genetic disorder).

Get some experience working in a lab. Until you've spent time in that environment it's hard to know whether you'll like it. And as others have mentioned, population biology and evolutionary genetics can combine some aspects of field work and molecular lab work, so those might be areas to investigate.

Want some books? Try The Beak of the Finch and Time, Love, Memory. The first is focused on experimental validation of evolutionary theory (involving lots of field work), the second is about the history of behavioral genetics in fruit flies. Both were assigned or suggested reading in my college biology classes.

Good luck, and stay curious!

The better question to ask is why do you need this in the first place? If you were playing good and running good your mental game would be fine. The only thing that affecting poker player results are playing bad or running bad. Playing bad can be fixed by analyzing hands, reading good poker books and training. The effects of running bad can be lessened by understanding probability and randomness better. Running bad shouldn't really be an issue if you are bank rolled properly because if it is, then you are playing bad.

Most poker players that I know that are always frustrated or constantly tilting are almost always playing at stakes their bankroll doesn't support.
If you are using the 100 times big blind and 25 buyins recommendation, you shouldn't really have a mental game issue because you should be able to absorb the variance.

Mental Game Books

• The Mental Game of Poker
  
  
• The Poker Mindset
  
  More understanding about probability, randomness and focusing on the present can be helpful. If you understand those more it should help your mental game. I would recommend these books and at least understand their central points:
  
  
• The Power of Now - relates to poker because the hand you are playing now is the only hand you should worry about. There is no last hand. Each hand is a clean slate. Focus on the present hand.
  
  
• The Drunkard's Walk - relates to poker because whether you double up and lost two buy-ins could just be randomness.
  
  
• The 80 / 20 Principle - relates to poker because 80% of your wins or losses will most likely come from 20% of hands played. Thus making hand selection important.
  
  
• The Black Swan - one "black swan" situation could triple you up or make you lose your whole stack. Typically this means knowing when to fold big hands like AA or KK.
  
  
• Fooled By Randomness - relates to poker because you could win the main event and millions of dollars and still not be a good poker player. The poker gods and luck could have just wanted to hang out with you for a week.
  
  
  
  
  

Like justrasputin says, there usually is quite a lot of work to be done before you start to really see the beauty everyone refers to. I'd like to suggest a few book about mathematics, written by mathematicians that explicitly try to capture the beauty -

By Marcus Du Sautoy (A group theorist at oxford)

1. Symmetry
   
2. The Music of the Primes
   
   By G.H. Hardy,
   
3. A Mathematician's Apology
   
   Also, a good collection of seminal works -
   God Created the Integers
   
   And a nice starter -
   What is Mathematics
   
   Good luck and don't give up!

I am a Strange Loop is about the theorem

Another book I recommend is David Foster-Wallace's Everything and More. It's a creative book all about infinity, which is a very important philosophical concept and relates to mind and machines, and even God. Infinity exists within all integers and within all points in space. Another thing the human mind can't empirically experience but yet bears axiomatic, essential reality. How does the big bang give rise to such ordered structure? Is math invented or discovered? Well, if math doesn't change across time and culture, then it has essential existence in reality itself, and thus is discovered, and is not a construct of the human mind. Again, how does logic come out of the big bang? How does such order and beauty emerge in a system of pure flux and chaos? In my view, logic itself presupposes the existence of God. A metaphysical analysis of reality seems to require that base reality is mind, and our ability to perceive and understand the world requires that base reality be the omniscient, omnipresent mind of God.

Anyway these books are both accessible. Maybe at some point you'd want to dive into Godel himself. It's best to listen to talks or read books about deep philosophical concepts first. Jay Dyer does a great job on that

https://www.youtube.com/watch?v=c-L9EOTsb1c&t=11s

The only previous knowledge I really used when I took intro to proofs were some factoring methods that were helpful with proofs by induction, although they weren't necessary. That said, reviewing exponent/log laws, and certain methods of factoring couldn't hurt.

An intro to proofs course should be fairly self contained, meaning any necessary axioms and definitions should be covered in the course. Those examples that you gave are exactly the type of things that should be proven and not knowing them beforehand should be fine. The important thing is being able to understand and reproduce the proofs on your own, and with a bit of experience you will be able to intuitively reason whether a statement is true or false. This intuitive reasoning will also become much more important than memorizing later in the course when you come across statements you've never seen before that aren't immediately obvious.

I would recommend getting very comfortable with logic and basic set theory. I also highly recommend this book if you want some extra reading material (pdf). It's still one of my favorite math books. Hope that helps.

If you are looking for something very calculus-based, this is the book I am familiar with that is most grounded in that. Though, you will need some serious probability knowledge, as well.

If you are looking for something somewhat less theoretical but still mathematical, I have to suggest my favorite. Statistics by William L. Hays is great. Look at the top couple of reviews on Amazon; they characterize it well. (And yes, the price is heavy for both books.... I think that is the cost of admission for such things. However, considering the comparable cost of much more vapid texts, it might be worth springing for it.)

Beginner Resources: These are fantastic places to start for true beginners.

Introduction to Probability is an oldie but a goodie. This is a basic book about probability that is suited for the absolute beginner. Its written in an older style of english, but other than that it is a great place to start.

Bayes Rule is a really simple, really basic book that shows only the most basic ideas of bayesian stats. If you are completely unfamiliar with stats but have a basic understanding of probability, this book is pretty good.

A Modern Approach to Regression with R is a great first resource for someone who understands a little about probability but wants to learn more about the details of data analysis.

​

Advanced resources: These are comprehensive, quality, and what I used for a stats MS.

Statistical Inference by Casella and Berger (2nd ed) is a classic text on maximum likelihood, probability, sufficiency, large sample properties, etc. Its what I used for all of my graduate probability and inference classes. Its not really beginner friendly and sometimes goes into too much detail, but its a really high quality resource.

Bayesian Data Analysis (3rd ed) is a really nice resource/reference for bayesian analysis. It isn't a "cuddle up by a fire" type of book since it is really detailed, but almost any topic in bayesian analysis will be there. Although its not needed, a good grasp on topics in the first book will greatly enhance the reading experience.

We're delighted to announce that r/SpaceX will be hosting an AMA with Dr. Robert Zubrin! The event will take place in its own dedicated thread this Saturday, November 23rd at 12:00 Pacific Time, which is 20:00UTC. As you may already know, Dr. Z's book The Case for Mars was a significant early influence on SpaceX's Mars colonization plans. His recent IAC2019 Mars Direct 2.0 presentation generated some good discussion here.

This is happening for real! We've been in contact with representatives of the Mars Society and Dr. Zubrin himself. We are very thankful to everyone involved for giving us their time and attention.

We'll collect the top few questions from this thread and repost them in the dedicated AMA thread on Saturday. Everyone will of course be welcome to ask their own questions in the AMA thread as well. Dr. Z will probably stick around answering questions for a few days.

Just to reiterate, this is NOT the actual AMA thread! That will be created a few hours before the AMA begins on Saturday.

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.

Are you open to doing some reading?

​

"Behave" by Robert Sapolsky

​

This book is an amalgamation of scientific research, referencing study after study that demonstrates how different aspects of our biology play key roles in our demeanor, our emotions and how we think and behave. Our gut flora, for instance, plays key roles in mood and perhaps even our social interactions [1] [2] [3]. That's just one example of the many dozens of lines of evidence that the book describes.

​

Now, it does look as though you've done some research into the philosophy of human subjective experiences, specifically qualia. I'm sure you're aware, but there are other philosophers who explain that qualia doesn't exist at all. Even one of the larger proponents of qualia, John Searle, doesn't ascribe it to a soul, or substance dualism, but to property dualism. Interestingly, Searle and Dan Dennett (a denier of qualia) had a published exchange on this very topic some 20 years ago. I'm not versed enough on the topic to actively engage in a debate on it, but it seems that, at second glance, qualia isn't necessarily all it's cracked up to be. Time will tell, of course.

​

With that said, there are vast amounts of data that thoroughly link our emotions, feelings, behaviors, etc. specifically to certain function of our biology. There is certainly more to be discovered in this field, but "Behave" spells out all of the nitty gritty details and compiles years and years worth of research. If you're actually interested in reading a thorough hypothesis coupled with the multiple lines of evidence to support it, I have a pdf copy of this book I'd be willing to share. Simply PM me your email address.

There's a lot of orders you could study mathematics in, and it's hard to say you should definitely pick one over the others.

One thing I can say pretty assuredly, though, is you should get a good background in algebra before you do much else. It's really the backbone of everything else. You can pick a bunch of different subjects after that, but study algebra first.

There are good online resources. Khan Academy is pretty good, as is Alcumus and Purple Math. Khan Academy has tests, and Alcumus is basically a big test.

Personally, though, I've learned way more from good books like this one than I tend to learn from websites.

Well, if you want a concentrated course of study you might consider looking for secondary sources that focus on particular areas of research in philosophy rather than trying to read very few (5-10) authors in real depth. I see Kant has been suggested, for example, and while I would never doubt his importance as a philosopher, if you set out with the intention of reading the bulk of his works as you say you might you would have to tackle a great deal of dry, technical material which I think would prove to be a lot more work than you could expect. Same could be said for Aristotle, Plato, Hegel, Descartes, nearly anyone you really might care to list. I don't know if you've read much philosophy, but you might instead look at something like an introduction to philosophy, an intro to ethics, or an intro to the philosophy of mind. These are only some examples, there are books like this for pretty much any area of study that attracts your interest. I'm sure others could provide suggestions as well.

This may not exactly be an answer to your question but I would recommend buying this book: https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192

It's not quite a textbook nor it is a pop-sci book for the layperson. The blurb on the front says " "A lucid representation of the fundamental concepts and methods of the whole field of mathematics." - Albert Einstein"

In and of itself it is not a complete curriculum. It doesn't have anything about linear algebra for example but you could learn a lot of mathematics from it. It would be accessible to a reasonably intelligent and interested high-schooler, it touches on a variety of topics you may see in an undergraduate mathematics degree and it is a great introduction to thinking about mathematics in a slightly more creative and rigorous way. In fact I would say this book changed my life and I don't think I'm the only one. I'm not sure if i would be pursuing a degree in math if I had never encountered it. Also it's pretty cheap.

If you're still getting a handle on how to manipulate fractions and stuff like that you might not be ready for it but you will be soon enough.

Start here.

Then go here.

When you're ready for the real thing, start reading this.

If you want to become an expert, go here.

Edit: Between steps 2 and 3, get a physics degree. You need to understand basically all of physics before you can understand anything properly in General Relativity. Sorry...

Edit 2: If you really want a full list of topics to understand before tackling general relativity, the bare minimum is special relativity (the easier bit) and tensor calculus on pseudo-Riemannian manifolds (extremely difficult). I'd strongly advise a deep understanding of differential equations in general, and continuum mechanics in particular. Some knowledge of statistical mechanics and the covariant formulation of electromagnetism would be pretty helpful too. It is also essential to realize that general relativity is still poorly understood by professionals, and almost certainly breaks down at large energy densities. I strongly advise just taking a look at the first two links I posted, since that will give you an excellent and non-dumbed-down flavour of general relativity.

First, please make sure everyone understands they are capable of teaching the entire subject without a textbook. "What am I to teach?" is answered by the Common Core standards. I think it's best to free teachers from the tyranny of textbooks and the entire educational system from the tyranny of textbook publishers. If teachers never address this, it'll likely never change.

Here are a few I think are capable to being used but are not part of a larger series to adopt beyond one course:
Most any book by Serge Lang, books written by mathematicians and without a host of co-writers and editors are more interesting, cover the same topics, more in depth, less bells, whistles, fluff, and unneeded pictures and other distracting things, and most of all, tell a coherent story and argument:

Geometry and solutions

Basic Mathematics is a precalculus book, but might work with some supplementary work for other classes.

A First Course in Calculus

For advanced students, and possibly just a good teacher with all students, the Art of Problem Solving series are very good books:
Middle & high school:
and elementary linked from their main page. I have seen the latter myself.

Some more very good books that should be used more, by Gelfand:

The Method of Coordinates

Functions and Graphs

Algebra

Trigonometry

Lines and Curves: A Practical Geometry Handbook

Have you read The Case For Mars ?

It completely lays out an affordable, technologically feasible (not even any "moonshot"-level technological development required) plan to visit mars. A series of missions which would each cost less than the yearly NASA budget.

Why isn't NASA doing this already? I won't spoil it too much (you should read the book! PM me your email and I'll happily send you a kindle copy), but, Zubrin attributes most of the problem to NASA administrators being too entrenched and too set in their ways. NASA money is thrown around as the biggest pork-barrel by the congress because many congressmen see NASA as being worthless besides providing their districts with jobs. Very similar things happen with military spending where bases are kept open and projects (planes/tanks/etc) continue to be ordered after their useful lifetime and after it makes sense to do so, simply because congressmen fear the economic impact. Trump understands this waste and sees privatization as a path to correcting this issue. Helping the economic recovery will avoid this too, there's no reason to keep that NASA or military factory open making things we don't need anymore if the people can just go across the street and get jobs at the new Carrier AC factory, right :).

That leads well into my next point, keep in mind also, the only way we have money for expanded spending on things like mars missions is if we fix our economy. That said, any good leader understand the value of inspiration. I have no evidence to support this, and I'm not suggesting that I do, but I wouldn't rule out a moonshot-style proclamation from Trump. Its the type of grand vision that he has and its something amazing he could do that could actually HAPPEN (as-in, humans walking on Mars) before the end of his 2nd term.

I'm listening to the JFK speech now in the background and just chills. I (way) missed out on the moon shot race. I really do hope I get to see us (humanity) land on Mars and I would really love for America to have that kind of leadership again and be the one to do it.

What level E&M? If it is intro physics 2 then look for AP physics B/C stuff in addition to what you would normally look for since that's the same level.

If it is an upper division E&M class then I will recommend a book you can probably find in most of your professors offices somewhere: Div, Grad, Curl, and All That. Older editions are much cheaper even and archive.org has a PDf of the 3rd edition. I have no idea what the differences are, but I have the 4th and it is just great.

I have yet to find an E&M textbook I like. Griffiths is alright and when paired with Div, Grad, Curl and maybe a Schaum's outline on E&M it forms what I think should just be one textbook.

As for online resources I think The Mechanical Universe about Maxwell does a great job at covering Maxwell's laws, especially the bit starting around 15 minutes in

I've never used this site but it looks like it has a bunch of solved problems as well.

This is a good start

and so is this!

This is, possibly surprisingly, good too.

If you're looking to jump right into a text and think you have a grip on the language, try Foucault's Madness and Civilization It's great and pretty easy to read.

Another good introduction (or at least, MY introduction to philosophy is Slavoj Zizek. He's pretty easy to read and understand, but makes ties to Lacan, Nietzsche, Heidegger, etc in a cohesive manner that makes you want to learn more. Of his work, I'd check out The Sublime Object of Ideology, The Parallax View or watch his movie! (Which is extraordinarily entertaining for how dense it is. He's also kind of amazing in a philosophical rock star kind of way.)

Hope that gets you started!

John Gribbin is a favorite science author of mine. In Search of Schrödinger's Cat is a cornerstone for understanding quantum physics as a layman and the follow-up Schrodinger's Kittens and the Search for Reality is also very good.

Michio Kaku is another good one. Rudy Rucker's nonfiction is definitely worth a look.

Dealers of Lightning: Xerox PARC and the Dawn of the Computer Age is a pretty awesome account of the lab that pretty much single-handedly invented the modern computer age.

And lastly (offhand) there's nothing better than The Structure of Scientific Revolutions for a view on how our notions of what the Big Ideas are in science change.

What do you want to do, though? Is your goal to read math textbooks and later, maybe, math papers or is it for science/engineering? If it's the former, I'd simply ditch all that calc business and get started with "actual" math. There are about a million books designed to get you in the game. For one, try Book of Proof by Richard Hammack. It's free and designed to get your feet wet. Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand/Polimeni/Zhang is my favorite when it comes to books of this kind. You'll also pick up a lot of math from Discrete Math by Susanna Epp. These books assume no math background and will give you the coveted "math maturity".

There is also absolutely no shortage of subject books that will nurse you into maturity. For example, check out [The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs by Grinberg](https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Princeton/dp/0691172935/ref=sr_1_1?ie=UTF8&qid=1486754571&sr=8-1&keywords=real+analysis+lifesaver() and Book of Abstract Algebra by Pinter. There's also Linear Algebra by Singh. It's roughly at the level of more famous LADR by Axler, but doesn't require you have done time with lower level LA book first. The reason I recommend this book is because every theorem/lemma/proposition is illustrated with a concrete example. Sort of uncommon in a proof based math book. Its only drawback is its solution manual. Some of its proofs are sloppy, messy. But there's mathstackexchange for that. In short, every subject of math has dozens and dozens of intro books designed to be as gentle as possible. Heck, these days even grad level subjects are ungrad-ized: The Lebesgue Integral for Undergraduates by Johnson. I am sure there are such books even on subjects like differential geometry and algebraic geometry. Basically, you have choice. Good Luck!

> that random stock algos can beat pros. That just doesn't seem right.

It makes sense if you look at investing as a game of chance rather than a game of skill. It's not like darts, it's like roulette. There's just too much randomness involved in the game to win when betting on single numbers/stocks.

Maybe you keep track of the table operators and realize that Joe lands mostly on low, even numbers, and hey! -- Jane has hit 21 red three times in the last quarter. And if she set up the wheel in the exact same position and launched the ball in the exact same way as those last three times you'd be a winner for betting on 21 red. But she won't, because she can't, even if she tries to. Someone sneezed nearby, there was an earthquake, her fingers are a little oily. There's just too much interference in the real world.

However, there is a winning strategy. Turns out betting (variable amounts) on all options wins you enough to keep playing. A little more, a little less, but the longer you play the better your prospects.

For another interesting book about a walk, see The Drunkard's Walk by Leonard Mlodinow.

I think Oxford's Very Short Introduction series is a pretty good place to start as far as books go. You can pick a part of philosophy you are interested in and find the introduction to that, or just read the general Philosophy intro. My personal favourite is the VSI to Philosophy of Science by Samir Okasha.

Another good introductory book is Think by Simon Blackburn.

I have found these good introductions, they are written by experts, and directed to the general reader, but without dumbing it down.

As far as the classics of philosophy go, someone else suggested Plato's dialogues and I would add Descartes' Meditations to that. It is short and a pretty good example of how modern philosophy operates. In it Descartes tries to find out what we can know for sure. It is reasonably easy to read too.

Of course, books can be quite expensive (if you torrent you can usually find downloads of many VSIs, and Meditations is out of copyright), and you shouldn't feel you have to have read any of these if you can find cheap copies.

No, I haven't read that, but just checked a summary on wikipedia.

The impression I got that is that it is quite populistic. He doesn't say anything new apart from something I seems to have published about the same time on my blog, this part about accelerated returns. I did my PhD in computational neuroscience and have so far, not heard anyone but my self speculate about this about accelerated returns being of importance to the computational efficiency of the brain[1], so this is interesting. Otherwise (only gave it a quick look through, will likely get the book and read) it seems as he is just repeating things which e.g. Douglas Hofstadter, Gerald Edelman, Daniel Dennet and me (thesis from 2003, chapter 7 speculative part) have written about.

> apparently to give him the resources to put into practice his hypothesis from that book.

Yes, this is my theory as well, to make it appear as he will put into practice the hypotheses from that book.

The employment of him can have many reasons:

1. to ride on the singularity "AI-hype"
   
2. to stop him from actually implement conscious AI.
   
3. naïve assumption that he could make it.
   
   No 1 would simply be a reasonable business image approach. No 2 would be a sensible beings action, as we do not really need any "conscious AI" (unless I am an AI, have A.I. in my middle names though...) to implement the singularity (which is my project). No 3 is also reasonable, as if the google engineers actually had as goal to implement conscious AI and knew how to do it, they wouldn't need Kurzweil.
   
   However, I suspect that google already know how to implement ethical conscious AI, as when I showed this algorithm from my thesis , he almost instantly refused talking to me more, and said that they can not help me.
   
   I showed that algorithm for 25 strong AI researchers at a symposium in Palo Alto 2004, and they said, yes, this is it.
   
   However, I have later refined it and concluded that the "rules" are not needed, these are built in due to the function of the neural system, all the time striving towards consistent solutions. I wrote a semi jokular (best way to hide something, learned from Douglas Adams) approach to almost rule free algorithm in 2011. The disadvantage with this algorithm is that it can trivially be turned evil. By switching the first condition you could implement e.g. Hitler, by switching the second condition you could implement the ordinary governmental politician...
   
   
4. OK, my PhD opponent prof Hava Siegelmann has proved that the neural networks are Super Turing, but not explicitly explained the reason for them being, that is, not in language of "accelerated returns". She is considerably smarter than me, I do not understand the details of the proof.

I graduated w/ degree in Math n' Physics but have been doing programming for startup for last 5+ years so many of my math skills got rusty.

While trying to get back into it went through several books and have found this to be the best if you're interested in more advanced mathematics: https://www.amazon.com/Mathematical-Proofs-Transition-Advanced-Mathematics/dp/0321797094. It's not only been an excellent review but has fleshed out some areas I was weak (in higher level courses like complex analysis, topology, group theory the methodology of proofs was assumed and often not taught).

The explanations are solid, varied, and they go through each proof they present (often w/ exhaustive step-by-step details).

From there pick a domain you're interested in and pickup the relevant undergraduate (and maybe some graduate) level books/textbooks and see if you can pick it up.

Although this sort of historical approach may work for some people, and it will definitely give you a very good background, it certainly didn't work for me. I wanted to get ideas that were articulated in easy to understand contemporary terms that I could grapple with right away without having to worry about interpreting them correctly first.

I started in early high school, after being recommended by a friend who was majoring in philosophy at the time with The Philosophy Gym by Stephen Law which gave a great and really readable introduction to a lot of philosophy problems. Depending on your previous knowledge of philosophy, it might be a bit basic, but even still it's a worthwhile read I think.

From then, I went on The Mind's I by Daniel Dennett and Douglass Hofstadter, which was a really good and fun introduction to philosophy of mind and related issues. After that I think you'll have enough exposure to dive into various subjects and authors that you come across.

I know people are bombarding you with sources, but if you ever get a chance I recommend reading the book The Beak of the Finch by Jonathan Weiner.

People often think of evolution as this drawn out process over millions and millions of years, but the truth is that evolution can occur quickly... in a matter of 1 year even!

This is evidenced in this book which tracks two researchers, Rosemary and Peter Grant, who measure every single finch on an island in the Galapagos every year for 20+ years now.

I had the fortune of listening to the Grants give a lecture at my college, I definitely recommend checking out this book if you want to learn more about evolution in action!

Interviews with mathematicians from MIT (haven't read it, but it is leisurely):
http://www.amazon.com/Recountings-Conversations-Mathematicians-Joel-Segel/dp/1568817134

Some good magazines from AMS:
http://www.amazon.com/Whats-Happening-Mathematical-Sciences-Mathermatical/dp/0821849999

If you want to learn some math in a leisurely way (although it does get pretty deep at times):
http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewart/dp/0486284247

A good book on the history of mathematics:
http://www.amazon.com/Mathematics-Nonmathematician-Dover-explaining-science/dp/0486248232

I'll definitely check out that Poincare book, it looks good!

Hi,

I'm a TA in my school's CS theory course (a mixture of discrete math, and the automata, languages and complexity topics most CS theory courses cover).

As others have said, "theory" is pretty broad, so there are an awful lot of resources you could look at. As far as textbooks go, we use two - Sipser's Introduction to the Theory of Computation (which others have recommended), and the freely available textbook Mathematics for Computer Science, by Lehman, Leighton and Meyer - which concentrates more on the "discrete math" side of things. Both seem fine to me. Another discrete-math–focused set of notes is by James Aspnes (PDF here) and seems to have some good introductions to these topics.

If you feel that you're "terrible at studying for these types of courses", it might be worth stepping back a bit and trying to find some sort of an intro to university-level math that resonates for you. A few books I've recommended to people who said they were "terrible at uni-level math", but now find it quite interesting, are:

• Keith Devlin, The Language of Mathematics: Making the Invisible Visible
  
• Ian Stewart, Concepts of Modern Mathematics
  
• Martin Liebeck, A Concise Introduction to Pure Mathematics (rather terser than the previous two, but still a lot gentler than some uni-level texts)
  
  These aren't specific to computer science, but might be of help. Good luck!
  
  
  

"Don't Sleep, there are snakes" by Dan Everett - it's a fascinating book about a linguist/missionary who went to work with a tribe of Piraha speakers in the Amazon. Loses his religion, and discovers a language that doesn't really fit into the orthodox view of linguistics and is causing a whole lot of debate.

The Drunkard's Walk - is a great book on how misconceptions of probability rule your life. It's a fun introduction to probability theory and has all sorts of WTF moments in it.

Edit: oh and possibly my favorite book I've read all year is David Attenborough's autobiography A life on air - it's full of all sorts of amazing, hilarious, and insightful anecdotes of Attenborough's 40-odd years of making nature documentaries, and contains lots of interesting info about the state-of-the art in TV making over time (e.g. "we could only run that type of camera for 20 seconds, or it would overheat and catch fire"). Great stuff.

awesome, I am currently reading The grand design and I love to go out, smoke a bowl, get to a [4] and then start reading. My mind just wanders about for ages thinking about stars and planets. It's awesome

Uptokes for you and your afternoon xD

The important part of this question is what do you know? By saying you're looking to learn "a little more about econometrics," does that imply you've already taken an undergraduate economics course? I'll take this as a given if you've found /r/econometrics. So this is a bit of a look into what a first year PhD section of econometrics looks like.

My 1st year PhD track has used
-Casella & Berger for probability theory, understanding data generating processes, basic MLE, etc.

-Greene and Hayashi for Cross Sectional analysis.

-Enders and Hamilton for Time Series analysis.

These offer a more mathematical treatment of topics taught in say, Stock & Watson, or Woodridge's Introductory Econometrics. C&B will focus more on probability theory without bogging you down in measure theory, which will give you a working knowledge of probability theory required for 99% of applied problems. Hayashi or Greene will mostly cover what you see in an undergraduate class (especially Greene, which is a go to reference). Hayashi focuses a bit more on general method of moments, but I find its exposition better than Greene. And I honestly haven't looked at Enders or Hamilton yet, but they will cover forecasting, auto-regressive moving average problems, and how to solve them with econometrics.

It might also be useful to download and practice with either R, a statistical programming language, or Python with the numpy library. Python is a very general programming language that's easy to work with, and numpy turns it into a powerful mathematical and statistical work horse similar to Matlab.

The analogous book for me was Townsend's Quantum Physics: A Fundamental Approach to Modern Physics. It spends a good deal of time on introducing you to quantum mechanics, as it should, but there are also discussions of solid state, nuclear, and particle physics, in addition to relativity.

Honestly, if you are looking for an in-depth treatment of special relativity it might be worth finding a book on that specifically, because it's generally not treated in a lot of depth in classes, since such depth isn't needed (it's relatively simple, if potentially unintuitive at first). Chapter 15 of Taylor, for example, has a good treatment of special relativity, and it's regarded as one of the canonical texts for classical mechanics (edit: at the introductory/intermediate level, that is).

Start with arithmetic. Make sure you are comfortable in adding, subtracting, multiplying, and dividing integers, negatives, fractions, and decimals. Old school books are great for this. This shouldn't take too long and for your sake DO NOT USE A CALCULATOR. You have no idea how the introduction of a calculator early on ruins kids, they become dependent on it. Train yourself to not need one.

Once you are comfortable with arithmetic, move on to algebra. I recommend reading both Lang's Basic Mathematics and the series of books by I.M. Gelfand for this. These are great books for their subjects and will introduce rigor into your math. The going will be a bit difficult at first but you will come out better than before. You want to focus on UNDERSTANDING math, not just doing it.

When you are done with algebra, you can move on to geometry and trigonometry. Both of the authors I mentioned cover these. for the most part, you want to understand basic things like area, volume, congruence theorems, and whatnot.

A bit of advice: practice is the secret to being successful. If you do enough practice problems, you will eventual reach a point where you will question how the hell you didn't know this stuff before. Also, feel free to find other books to supplement these, there is nothing wrong with getting multiple explanations so long as it all benefits you.

To answer your second question, KhanAcademy is always good for algebra/trig/basic calc stuff. Another good resource is Paul's online Math Notes, especially if you prefer reading to watching videos.

To answer your second question, here are some classic texts you could try (keep in mind that parts of them may not make all that much sense without knowing any calculus or abstract algebra):

Men of Mathematics by E.T. Bell

The History of Calculus by Carl Boyer

Some other well-received math history books:

An Intro to the History of Math by Howard Eves, Journey Through Genius by William Dunham, Morris Kline's monumental 3-part series (1, 2, 3) (best left until later), and another brilliant book by Dunham.

And the MacTutor History of Math site is a great resource.

Finally, some really great historical thrillers that deal with some really exciting stuff in number theory:

Fermat's Enigma by Simon Sigh

The Music of the Primes by Marcus DuSautoy

Also (I know this is a lot), this is a widely-renowned and cheap book for learning about modern/university-level math: Concepts of Modern Math by Ian Stewart.

There are some really good books that you can use to give yourself a solid foundation for further self-study in mathematics. I've used them myself. The great thing about this type of book is that you can just do the exercises from one side of the book to the other and then be confident in the knowledge that you understand the material. It's nice! Here are my recommendations:

First off, three books on the basics of algebra, trigonometry, and functions and graphs. They're all by a guy called Israel Gelfand, and they're good: Algebra, Trigonometry, and Functions and Graphs.

Next, one of two books (they occupy the same niche, material-wise) on general proof and problem-solving methods. These get you in the headspace of constructing proofs, which is really good. As someone with a bachelors in math, it's disheartening to see that proofs are misunderstood and often disliked by students. The whole point of learning and understanding proofs (and reproducing them yourself) is so that you gain an understanding of the why of the problem under consideration, not just the how... Anyways, I'm rambling! Here they are: How To Prove It: A Structured Approach and How To Solve It.

And finally a book which is a little bit more terse than the others, but which serves to reinforce the key concepts: Basic Mathematics.

After that you have the basics needed to take on any math textbook you like really - beginning from the foundational subjects and working your way upwards, of course. For example, if you wanted to improve your linear algebra skills (e.g. suppose you wanted to learn a bit of machine learning) you could just study a textbook like Linear Algebra Done Right.

The hard part about this method is that it takes a lot of practice to get used to learning from a book. But that's also the upside of it because whenever you're studying it, you're really studying it. It's a pretty straightforward process (bar the moments of frustration, of course).

If you have any other questions about learning math, shoot me a PM. :)

I'm not sure I understand your concern, but if you struggle with math, it may help to start with coding. It can make things a little more concrete. You might try code academy, a coding bootcamp, or MIT open courseware.

An Emory prof has a great intro stats course online: https://www.youtube.com/user/RenegadeThinking

Linear algebra is the foundation of the most widely used branch of stats. This book teaches it by coding example. It's full of interesting practical applications (there's a coursera course to go with it): https://www.amazon.com/Coding-Matrix-Algebra-Applications-Computer/dp/0615880991/ref=sr_1_1?ie=UTF8&qid=1469533241&sr=8-1&keywords=coding+the+matrix

Once you start to feel comfortable, this book offers a great (albeit dense) introduction to mathematics. It used to be used in freshman gen ed math courses, but sadly, American unis decided that actually doing math/logic isn't a priority anymore: https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192/ref=sr_1_1?ie=UTF8&qid=1469533516&sr=8-1&keywords=what+is+mathematics

Usual hierarchy of what comes after what is simply artificial. They like to teach Linear Algebra before Abstract Algebra, but it doesn't mean that it is all there's to Linear Algebra especially because Linear Algebra is a part of Abstract Algebra.

Example,

Linear Algebra for freshmen: some books that talk about manipulating matrices at length.

Linear Algebra for 2nd/3rd year undergrads: Linear Algebra Done Right by Axler

Linear Algebra for grad students(aka overkill): Advanced Linear Algebra by Roman

Basically, math is all interconnected and it doesn't matter where exactly you enter it.

Coming in cold might be a bit of a shocker, so studying up on foundational stuff before plunging into modern math is probably great.

Books you might like:

Discrete Mathematics with Applications by Susanna Epp

Learning to Reason: An Introduction to Logic, Sets, and Relations by Nancy Rodgers

Building Proofs: A Practical Guide by Oliveira/Stewart

Book Of Proof by Hammack

Mathematical Proofs: A Transition to Advanced Mathematics by Chartrand et al

How to Prove It: A Structured Approach by Velleman

The Nuts and Bolts of Proofs by Antonella Cupillary

How To Think About Analysis by Alcock

Principles and Techniques in Combinatorics by Khee-Meng Koh , Chuan Chong Chen

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!) by Carol Ash

Problems and Proofs in Numbers and Algebra by Millman et al

Theorems, Corollaries, Lemmas, and Methods of Proof by Rossi

Mathematical Concepts by Jost - can't wait to start reading this

Proof Patterns by Joshi

...and about a billion other books like that I can't remember right now.

Good Luck.

Gödel proved several theorems; I'm guessing you're referring to the incompleteness theorems, which are the most well-known. The key point is that Gödel's incompleteness theorems are precise mathematical statements about certain formal systems — not vague philosophical generalities about the nature of truth or anything like that.

In particular, the content of the first incompleteness theorem is essentially:

>In any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true (in the standard model of arithmetic), but not provable in the theory.

This statement, as with any other statement mathematicians call a "theorem", has been formally proven. Philosophical questions like whether mathematical objects are "real" in whatever sense are irrelevant to the question of whether something is a theorem or not.

By the way, if you want a good introduction to the details of what Gödel's incompleteness theorems say and how they can be proved, I highly recommend Gödel's Proof by Nagel and Newman.

It sounds like you now want an education in the whole process of science. The best way to get that is to read material directly on that topic. I suggest starting with Beak of the Finch but Jonathan Weiner. It is an account of a long term research project on Galapagos, but along the way Weiner does a very good job in showing the reader how science actually works. It is a Pulitzer Prize winner and very accessible. After than if you want something in depth, read, as I suggested, Science as a Process by David Hull. A deeper, much deeper, exploration into how science works and the philosophical underpinnings.

I don't see me as jumping the gun, I keep trying to get back to the topic.

Since you are still in college, why not take a statistics class? Perhaps it can count as an elective for your major. You might also want to consider a statistics minor if you really enjoy it. If these are not options, then how about asking the professor if you can sit in on the lectures?

It sounds like you will be able to grasp programming in R, may I suggest trying out SAS? This book by Ron Cody is a good introduction to statistics with SAS programming examples. It does not emphasize theory though. For theory, I would recommend Casella & Berger, many consider this book to be a foundation for statisticians and is usually taught at a grad level.

Good luck!

the new stephen hawking book the grand design is pretty fantastic. it's a very interesting, easily readable explanation of modern physics as well as the history of physics. this book is where hawking finally comes out of the atheist closet in a very non-political way, basically explaining that while people can believe in a god our knowledge of physics doesn't have a need for it.

• The Elements of Statistical Learning
  
  It's available free online, but I've def got a hard cover copy on my bookshelf. I can't really deal with digital versions of things, I need physical books.
  
  
• If you're looking for something less technical, try The Lady Tasting Tea
  
  
• You haven't mentioned how old your sister is. If she's on the younger side of the spectrum, she might enjoy Flatland.
  
  
• Also, you mention how much your sister loves proofs. Godel's Proof is a really incredible result (sort of brain melting) and the book I linked does a great job of making it accessible. I think I read this book in high school (probably would have understood more if I read it in college, but I got the gist of it).

It's truly a whole new world to explore. I read the book Think: A Compelling Introduction to Philosophy by Simon Blackburn last year as a starting point. Great stuff. I'd recommend it if you'd like to dip your toes into philosophy a bit more. It's pretty cheap on used book sites as well.

I dont know much about boot camp, but it sounds like having a physical book will be your best bet.

Personally, my favorite text book to use is Calculus: an Intutitive Approach by Morris Kline, but you might want something more advanced than that.

• The Canon by Natalie Angier.
  
  This is a fast-paced, beautifully written, introduction to the sciences- there's a chapter each devoted to scientific theory, probability, measurement, physics, chemistry, evolutionary and molecular biology, geology, and astronomy. It's written entirely for laymen in an engaging way, and from 2007, so the information is quite current.
  
  For instance, from the evolutionary bio chapter:
  > Evolution is neither organized nor farsighted, and you wouldn't want to put it in charge of planning your company's annual board meeting, or even your kid's birthday party at Chuck E. Cheese. As biologists like to point out, evolution is a tinkerer, an ad-hocker, and a jury-rigger. It works with what it has on hand, not with what it has in mind. Some of its inventions prove elegant, while in others you can see the seams and dried glue.
  
  
• I don't have The Drunkard's Walk by Leonard Mlodinow in front of me, but it's a good introduction to probability, with a bunch of real-world examples, and also good explanations of the theory. It changed the way I think about statistics.

If this is a troll then it is excellent; I'm falling for it hook line and sinker.

However, if you are open to reading about why the reaction has been so negative (with all the downvotes) and want to read something cool instead Zubrin has a book called ["The Case for Mars"][1].

The book is not perfect (there are a few sections that could do with more recent information or more research input) but largely it's a good book that makes the wider points clear.

Or just read the much more approachable blog by Wait but why. Many people on this subreddit are here from that one post.

I promise this is usually a fun sub and people don't often get downvoted so harshly. :)

[1]: http://www.amazon.com/The-Case-Mars-Settle-Planet/dp/145160811X

You won't get a hang of anything until and unless you practice. Since you are having Object Oriented Programming, go on and make a project. This will give you a sense of accomplishment and on the way you will learn a lot of things.

Talking about data structures, you will need the concepts of this course everywhere. I would suggest you to strengthen your basics by refering to CLRS or some other resource, that is totally your choice. But, implement the data structure you have learned. There are a lot of resources out there, I am listing some of my favorites:
>https://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P
>https://www.coursera.org/specializations/algorithms

I would also suggest you to read discrete mathematics. The book that I use is
>https://www.amazon.com/Discrete-Mathematics-Applications-Seventh-Higher/dp/0073383090/ref=sr_1_1?ie=UTF8&qid=1492831532&sr=8-1&keywords=discrete+mathematics+kenneth+rosen
You can also go through the discrete mathematics course from MIT OCW.
In case you need some help, PM me. I'll be more than happy to help :)

You might want to try "What is Mathematics?" by R.Courant and H.Robbins. The book is written for people new to the field of theoretical mathematics and is intended for those who wish to develop a solid foundation on the topic.

I had started college as an engineer, switched to English, and now work as an ESL instructor. However, my love of math never died (despite my university professors' best attempts). So, I picked up that book a little while ago. It's a good read (albeit a dense one), and it covers a little bit of what you have listed.

[Amazon link here] (http://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192)

Edit: some words

I'll take the time to write it up if you meant that sincerely (because I haven't tried explaining it to someone else before, which is usually pretty helpful for understanding).

But if you meant that facetiously, I expect you'll be surprised how much about the phenomenon of consciousness has been convincingly explained (or, rather, explained away) in the last 20 years. Watch some videos via Google, or try this 9 year old book with some mind-changing perspectives on the subject.

Happy exploring!

This is an older book that I read almost 25 years ago, so I'm not sure how it holds up, but I remember really enjoying In Search of Schrödinger's Cat: Quantum Physics and Reality. I'm by no means a science person, but I remember that I was really into the book, and if I concentrated on what I was reading in it, I felt like I really understood it. It's good writing.

Maybe someone else on here has read it and can chime in, otherwise you'll have to read the reviews on Amazon and make a judgement call. I will say that I enjoyed it far more than A Brief History of Time.

this book is quite short but perfect for an aspiring mathematician that is going to start hearing about Gödel's proof in casual conversation. This provides a concise easy treatment of it's importance and how the proof works. Also, see it's reviews on goodreads

Textbooks (calculus): Fundamentals of Physics: http://www.amazon.com/Fundamentals-Physics-Extended-David-Halliday/dp/0470469080/ref=sr_1_4?ie=UTF8&qid=1398087387&sr=8-4&keywords=fundamentals+of+physics ,

Textbooks (calculus): University Physics with Modern Physics; http://www.amazon.com/University-Physics-Modern-12th-Edition/dp/0321501217/ref=sr_1_2?ie=UTF8&qid=1398087411&sr=8-2&keywords=university+physics+with+modern+physics

Textbook (algebra): [This is a great one if you don't know anything and want a book to self study from, after you finish this you can begin a calculus physics book like those listed above]: http://www.amazon.com/Physics-Principles-Applications-7th-Edition/dp/0321625927/ref=sr_1_1?ie=UTF8&qid=1398087498&sr=8-1&keywords=physics+giancoli

If you want to be competitive at the international level, you definitely need calculus, at least the basics of it.
Here is a good book: http://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/ref=sr_1_1?ie=UTF8&qid=1398087834&sr=8-1&keywords=calculus+kline
It is quite cheap and easy to understand if you want to self teach yourself calculus.

Another option would be this book:http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?ie=UTF8&qid=1398087878&sr=8-1&keywords=spivak
If you can finish self teaching that to yourself, you will be ready for anything that could face you in mathematics in university or the IPhO. (However it is a difficult book)

Problem books: Irodov; http://www.amazon.com/Problems-General-Physics-I-E-Irodov/dp/8183552153/ref=sr_1_1?ie=UTF8&qid=1398087565&sr=8-1&keywords=irodov ,

Problem Books: Krotov; http://www.amazon.com/Science-Everyone-Aptitude-Problems-Physics/dp/8123904886/ref=sr_1_1?ie=UTF8&qid=1398087579&sr=8-1&keywords=krotov

You should look for problem sets online after you have finished your textbook, those are the best recourses. You can get past contests from the physics olympiad websites.

It was my favorite book in undergrad and from what I remember it's really well written. I recall that if I was confused about a topic in lecture I could go to the relevant chapter and end up with a clear understanding.

Admittedly it's been a while since I last read it but hopefully there may be some more helpful reviews here https://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X

Cheers!

I'm 2 years into a part time physics degree, I'm in my 40s, dropped out of schooling earlier in life.

As I'm doing this for fun whilst I also have a full time job, I thought I would list what I'm did to supplement my study preparation.

I started working through these videos - Essence of Calculus as a start over the summer study whilst I had some down time. https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

Ive bought the following books in preparation for my journey and to start working through some of these during the summer prior to start

Elements of Style - A nice small cheap reference to improve my writing skills
https://www.amazon.co.uk/gp/product/020530902X/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1

The Humongous Book of Trigonometry Problems https://www.amazon.co.uk/gp/product/1615641823/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1

Calculus: An Intuitive and Physical Approach
https://www.amazon.co.uk/gp/product/0486404536/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

Trigonometry Essentials Practice Workbook
https://www.amazon.co.uk/gp/product/1477497781/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1

Systems of Equations: Substitution, Simultaneous, Cramer's Rule
https://www.amazon.co.uk/gp/product/1941691048/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1

Feynman's Tips on Physics
https://www.amazon.co.uk/gp/product/0465027970/ref=oh_aui_detailpage_o07_s00?ie=UTF8&psc=1

Exercises for the Feynman Lectures on Physics
https://www.amazon.co.uk/gp/product/0465060714/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1

Calculus for the Practical Man
https://www.amazon.co.uk/gp/product/1406756725/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

The Feynman Lectures on Physics (all volumes)
https://www.amazon.co.uk/gp/product/0465024939/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

I found PatrickJMT helpful, more so than Khan academy, not saying is better, just that you have to find the person and resource that best suits the way your brain works.

Now I'm deep in calculus and quantum mechanics, I would say the important things are:

Algebra - practice practice practice, get good, make it smooth.

Trig - again, practice practice practice.

Try not to learn by rote, try understand the why, play with things, draw triangles and get to know the unit circle well.

Good luck, it's going to cause frustrating moments, times of doubt, long nights and early mornings, confusion, sweat and tears, but power through, keep on trucking, and you will start to see that calculus and trig are some of the most beautiful things in the world.

If you want things that "click" for quantum mechanics, the following three popular books were helpful to me (as a layperson):

• John Gribbin's two books In Search of Schrödinger's Cat: Quantum Physics and Reality (1984) and Schrodinger's Kittens: And The Search For Reality (1995). These cover several different interpretations of Quantum Mechanics, and many perspectives.
  
• Richard Feyman's QED (1985). This (while not being explicit about it) is rooted in the multiple worlds interpretation (which supposedly fits with Feynman's favorite formalism.)
  
  I know QED have been recommended to people that "know the math" but can't make it click.
  
  I'm sure there exists newer popular books that would also be helpful; I'm just not familiar with them.

Here's three very good books:

1. De Morgan, On the Study and Difficulty of Mathematics. This is a free book available on the internet. Read the parts you find interesting.
   
   
2. Gelfand, Algebra.
   
   
3. Chrystal, Algebra: An Elementary Text-Book. This is available online for free. A lot of the greatest mathematicians and physicists of the last century lauded this (erdos, feynman...)

A true classic that will make you a beast at calculus:

Calculus: An Intuitive and Physical Approach by Morris Kline

It's old-school but totally awesome. Gives you great explanations for why we use what we use in the mathematical world.

Made me the man I am today.

http://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536

I once took a first-year course in logic, starting with the propositional calculus. All these years later, I still regard it as the most important thing I ever did. Proof-writing became [almost] easy after that. It wasn't always easy to put the pieces together, but at least I had a blueprint. I knew that if I could clearly define a contrapositive, or understand how set identities like DeMorgan's Laws were constructed, I was on much firmer ground. I highly recommend Discrete Mathematics and Its Applications. It's such an enormous and comprehensive text, in so many subjects, that I found myself referring back to it, for something, in almost every class of my undergraduate.

:D
http://betterexplained.com/

http://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/ref=sr_1_1?ie=UTF8&qid=1422649729&sr=8-1&keywords=calculus+an+intuitive&pebp=1422649747330&peasin=486404536

The first site is fun, because it teaches you how to intuitively understand math. I love it. Second is a book that makes you think. Read the reviews for it. I really hope it helps because it's helped me, and I didn't even like math that much in the beginning, now I'm all excited for it :D

Barton Zwiebach's First Course in String Theory provides a good overview of quite a complex topic. Unfortunately, even though it is meant as an introductory textbook, it is likely to be entirely incomprehensible to the average reader.

 

To make it through this book, knowledge of quite a few preliminary topics is needed:

1. Previous knowledge of Quantum Mechanics is incredibly important. MIT OpenCourseware has some useful video lectures for the beginner, as well as textbook recommendations.
   
   
2. It is necessary to be fully comfortable with the principles of Special Relativity, as well as at least familiar with the mathematics of General Relativity. Unfortunately, since I learned relativity entirely from the homemade class notes of a professor at my university, I have no textbook recommendations.
   
   
3. Even though string theory is a theory of quantum gravity, some techniques and principles from classical physics are useful. In particular, ideas from the Lagrangian formulation of mechanics come up fairly often. John Taylor's book is useful here. Knowledge of Electricity and Magnetism is also useful; for that, I recommend Griffiths.
   
   
4. It doesn't come up quite as often in this particular book, but Group Theory and Lie Algebras are ubiquitous in string theory. I liked Gilmore's book on this subject.

i am reading these two books, http://www.amazon.com/In-Search-Schr%C3%B6dingers-Cat-Quantum/dp/0553342533 and http://www.amazon.com/Erwin-Schrodinger-Quantum-Revolution-Gribbin/dp/1118299264. i just ordered this book (http://www.amazon.com/gp/product/0983358931/ref=ox_sc_sfl_title_1?ie=UTF8&psc=1&smid=A1KIF2Y9A1PQYE) like 3 days ago and am gonna start reading it soon. also i started playing wow in early sept so i will skim the official mop strat guide just as some extra help once in a while. in school we just finished catcher in the rye and its pretty cool and mind altering.

I don't want to say that it's impossible for you to get through Spivak, but I think it will be frustrating. Spivak is, I think, most useful for someone who already knows a little bit about what calculus is about. You might be better suited going with a gentler introduction to calculus like Stewart (pdfs exist on torrent sites if you don't want to drop $200), or even a proofs book like Chartrand, Polimeni, Zhang.

Where did he claim atheists are (more) intelligent? Do you think he claimed it with this part?
>Atheists see religious people as idiots...


When a believer and an atheist come to different conclusions on a moral issue, both sides logic behind the argument should be scrutinized, however one side wins easily when the other side usually only come up with "because I said so" or "because someone said so".


When people in disputes (like theists and atheists) through different ways come to agree on some part of an issue that's called common ground, and that is generally sought after, but you don't seem to want that, or think one couldn't come to the same conclusions for different reasons.
>Oh please don’t claim religion.

Yet you claim atheists to be the hypocritical ones?


Still, I can also quote random people unnecessarily ;)
>It is impossible to begin to learn that which one thinks one already knows.

– Epictetus


>The old argument from design in nature, as given by Paley, which formerly seemed to me so conclusive, fails, now that the law of natural selection has been discovered. There seems to be no more design in the variability of organic beings and in the action of natural selection, than in the course which the wind blows.

– Charles Darwin


Actually, the fields of psychology and sociology do have things to say about evolution of consciousness, free will, behavioral analysis and morality. Although everything is not known yet, at least some are trying. Here's a few interesting articles/books on the subject:


The Evolution of Ethics by Francisco Ayala


The Moral Landscape by Sam Harris, on Google Books


Consciousness Explained by Daniel C. Dennett

Edit: formatting

I know this isn't what you requested, but as a high schooler, I enjoyed In Search of Schödinger's Cat.

The top level presentations on QM are very light on math, and anything below that brings out heavy linear algebra, differential equations, calculus, etc. So you've probably got that top level covered, and now you need to start solving problems. You could get credit for your efforts by picking one of the undergrad versions of QM from the Chemistry and/or the Physics depts.

I took the chemistry route, so we used Atkins, Cohen-Tanoudji, etc. For all the classes that I took and TA'd, the professor might recommend a book, but rarely reference it.

Sipser's Introduction to the Theory of Computation is the standard textbook. The book is fairly small and quite well written, though it can be pretty dense at times. (Sipser is Dean of Science at MIT.)

You may need an introduction to discrete math before you get started. In my udergrad, I used Rosen's Discrete Mathematics and Its Applications. That book is very comprehensive, but that also means it's quite big.

Rosen is a great reference, while Sipser is more focused.

Depending on how strong your math/stats background is you might consider Statistical Inference by Casella and Berger. It's what we use for our first year PhD Mathematical Statistics course.

That might be a little too difficult if you're not very comfortable with probability theory and basic statistics. If you look at the first few chapters on Amazon and it seems like too much I recommend Mathematical Statistics and Data Analysis by Rice which I guess I would consider a "prequel" to the Casella text. I worked through this in an advanced statistics undergrad course (along with Mostly Harmless Econometrics and the Goldberger's course in Econometrics).

Let's see, if you're interested in Stochastic Models (Random Walks, Markov Chains, Poisson Processes etc), I recommend Introduction to Stochastic Modeling by Taylor and Karlin. Also something I worked through as an undergrad.

I highly recommend reading about the research going on into evolution of finches in the Galapagos. They've been the subject of study since the 70's and it's fascinating stuff.

For a short read, check out this National Geographic article. There's also the Pulitzer prize winning book on the subject, The Beak of the Finch.

tl;dr - Significant evolutionary change can happen in the span of just a few months, rather then millennia. (E.g. researchers have seen the average size of finch beaks change by 15% in just 1-2 years).

What Is Mathematics?: An Elementary Approach to Ideas and Methods

"Succeeds brilliantly in conveying the intellectual excitement of mathematical inquiry and in communicating the essential ideas and methods." Journal of Philosophy

https://www.amazon.ca/What-Mathematics-Elementary-Approach-Methods/dp/0195105192

The Drunkard's Walk: How Randomness Rules Our Lives

I read this 5 or 6 years ago and really enjoyed it. Has a lot of math, but includes a lot of history and some psychology as well.

From the Amazon page:

"By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more informed decisions. From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire."

Read naturalist explanations of decision-making, the image of the self, how thoughts work, qualia, etc. You probably want to start with I am a Strange Loop, then Consciousness Explained, and work your way to Godel Escher Bach. There are also many essays online about the non-supernatural nature of the mind, this one being one that atheist Redditors link to often. Also see Wikipedia articles about the mind, free will, etc.

Even after I became an atheist, I could not shake the feeling that consciousness could not be just patterns of atoms. Even in a universe that follows rules and that was not deliberately created as part of a plan, I thought that maybe there's some kind of "soul stuff" that interacts with our brains and is responsible for consciousness. But then, if I can tell that I am conscious, then 1) the soul stuff impacts the natural world and is thus observable and not supernatural, and 2) I am no different from a computer that understands itself well enough to say it is conscious. (It helped me to think of AIs from fiction, like HAL and Data, and try to think of what it would be "like" to be them. Books like The Mind's I are full of such thought experiments). So after thinking about it for a while, I was able to shed that last and most persistent bit of supernaturalism and embrace the naturalistic view of the mind.

I have no experience with Young's books, but if you want to look into alternatives a very popular text book for physics is Physics for Scientists & Engineers by Giancoli, perfect for introductionary courses into classical mechanics. For a more advanced text book about classical mechanics you might want to look into Classical Mechanics by John R. Taylor.

A lot of it is probably confirmation bias, but yes, it does happen.

HP used to have expiry dates on their cartridges claiming they degraded printing after a certain time: http://www.hp.com/pageyield/articles/uk/en/InkExpiration.html

Another example from the software development world: Red Gate announced that one of their products (Reflector) would no longer be free starting from the next version and disabled all existing free copies, a move that upset many developers: http://www.infoq.com/news/2011/02/NET-Reflector-Not-Free

College textbooks are the most literal example of planned obsolescence; the new editions often contain very few new material and cost a lot while all older versions can be bought for almost nothing... and of course most classes require the new version.
For instance, Kenneth Rosen's "Discrete Mathematics and its Applications" currently sells for $125 if you want the [latest edition] (http://www.amazon.com/Discrete-Mathematics-Applications-Kenneth-Rosen/dp/0073383090/), $100 for the one before that and $16 for an older one even though the number of pages only increased by 100 each time. Thankfully, my teacher gave us the page numbers for both the latest and the second-latest editions...

This question gets asked all the time on this sub. I did a search for the term books and compiled this list from the dozens of previous answers:

How to Read the Solar System: A Guide to the Stars and Planets by Christ North and Paul Abel.


A Short History of Nearly Everything by Bill Bryson.


A Universe from Nothing: Why There is Something Rather than Nothing by Lawrence Krauss.


Cosmos by Carl Sagan.

Pale Blue Dot: A Vision of the Human Future in Space by Carl Sagan.


Foundations of Astrophysics by Barbara Ryden and Bradley Peterson.


Final Countdown: NASA and the End of the Space Shuttle Program by Pat Duggins.


An Astronaut's Guide to Life on Earth: What Going to Space Taught Me About Ingenuity, Determination, and Being Prepared for Anything by Chris Hadfield.


You Are Here: Around the World in 92 Minutes: Photographs from the International Space Station by Chris Hadfield.


Space Shuttle: The History of Developing the Space Transportation System by Dennis Jenkins.


Wings in Orbit: Scientific and Engineering Legacies of the Space Shuttle, 1971-2010 by Chapline, Hale, Lane, and Lula.


No Downlink: A Dramatic Narrative About the Challenger Accident and Our Time by Claus Jensen.


Voices from the Moon: Apollo Astronauts Describe Their Lunar Experiences by Andrew Chaikin.


A Man on the Moon: The Voyages of the Apollo Astronauts by Andrew Chaikin.


Breaking the Chains of Gravity: The Story of Spaceflight before NASA by Amy Teitel.


Moon Lander: How We Developed the Apollo Lunar Module by Thomas Kelly.


The Scientific Exploration of Venus by Fredric Taylor.


The Right Stuff by Tom Wolfe.


Into the Black: The Extraordinary Untold Story of the First Flight of the Space Shuttle Columbia and the Astronauts Who Flew Her by Rowland White and Richard Truly.


An Introduction to Modern Astrophysics by Bradley Carroll and Dale Ostlie.


Rockets, Missiles, and Men in Space by Willy Ley.


Ignition!: An Informal History of Liquid Rocket Propellants by John Clark.


A Brief History of Time by Stephen Hawking.


Russia in Space by Anatoly Zak.


Rain Of Iron And Ice: The Very Real Threat Of Comet And Asteroid Bombardment by John Lewis.


Mining the Sky: Untold Riches From The Asteroids, Comets, And Planets by John Lewis.


Asteroid Mining: Wealth for the New Space Economy by John Lewis.


Coming of Age in the Milky Way by Timothy Ferris.


The Whole Shebang: A State of the Universe Report by Timothy Ferris.


Death by Black Hole: And Other Cosmic Quandries by Neil deGrasse Tyson.


Origins: Fourteen Billion Years of Cosmic Evolution by Neil deGrasse Tyson.


Rocket Men: The Epic Story of the First Men on the Moon by Craig Nelson.


The Martian by Andy Weir.


Packing for Mars:The Curious Science of Life in the Void by Mary Roach.


The Overview Effect: Space Exploration and Human Evolution by Frank White.


Gravitation by Misner, Thorne, and Wheeler.


The Science of Interstellar by Kip Thorne.


Entering Space: An Astronaut’s Oddyssey by Joseph Allen.


International Reference Guide to Space Launch Systems by Hopkins, Hopkins, and Isakowitz.


The Fabric of the Cosmos: Space, Time, and the Texture of Reality by Brian Greene.


How the Universe Got Its Spots: Diary of a Finite Time in a Finite Space by Janna Levin.


This New Ocean: The Story of the First Space Age by William Burrows.


The Last Man on the Moon by Eugene Cernan.


Failure is Not an Option: Mission Control from Mercury to Apollo 13 and Beyond by Gene Kranz.


Apollo 13 by Jim Lovell and Jeffrey Kluger.


The end

PS - /u/DDE93 this list has all the links.

You should check out Stephen Hawking's "The Grand Design" . I'm not sure I agree with all of it and I'm really not sure about M-Theory, but he makes an interesting case for the big bang resulting from quantum effects and our universe resulting from Richard Feynman's theory of a sum of histories.

It's not a definitive work, but it's an interesting read and will introduce the lay reader to a series of fascinating concept in classical and quantum physics.

I reallt hopoe you have a decent background in and love of studying math. Live it and love it. If you have that and the curiosity to ask the questions above you are getting ready for one cool academic 'trip' when you advance beyone high school. That said go an buy 'In Search of Schrödinger's Cat: Quantum Physics and Reality" by John Gribbon it addresses almost exactly what you are asking. It is completely in layman's terms. I have been reading this over and over for at least 17 years and get a little closer, understand a little more each time. Link

Not sure if they qualify as "beautifully written", but I've got two that are such good reads that I love to go back to them from time to time:

• One Two Three . . . Infinity
  
• Div, Grad, Curl, and All That

Read The Drunkards Walk. Sounds like it might be up your alley. As I recall, although its been quite a while, it has some interesting analysis of how the way we perceive how and why things happen in business or other areas of our lives.

Like movie execs who would get brought in to revitalize the studio, they would green-light a bunch of projects that would get added to the production pipeline and then a year or two later they would be removed from their position because the situation of the studio hadn't changed. Only then a year later the movies they had put into production would get released, like Titanic, make a billion dollars and they would get no credit for being the ones who chose to make that movie as someone else already has their job.

Fascinating read.

Im currently in a mechanics physics course and this is the main text book we use

https://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X

I'd say it's pretty good and an easy read as well

We have also been using a math text book to complement some of the material

https://www.amazon.com/Mathematical-Methods-Physical-Sciences-Mary/dp/0471198269

Hope this helps

Mars is 37% of Earth's gravity according to wikipedia. It could be true that it may prove detrimental to those living on Mars long-term. I doubt it, but there's one good way to study those affects, and that's to go to Mars. A 3 year mission is unlikely to cause severe issues, especially if gravity is simulated en-route.

You can do that by spinning the craft, as you alluded to, but you can also do so by tethering the habitable portion to another object (such as the burnt out upper stage of the rocket that is sending you to Mars). In doing so you can decrease the size requirements of the habitable portion of the craft. This is discussed as part of Mars Direct. To be fair, this hasn't been tested (certainly not on a large scale - I think a small scale test is happening this year) but the principle is sound.

On that note, some sources on Mars Direct that I found very interesting and helpful:

https://www.youtube.com/watch?v=EKQSijn9FBs

http://www.amazon.com/Case-Mars-Plan-Settle-Planet/dp/145160811X/ref=sr_1_1?ie=UTF8&qid=1456935955&sr=8-1&keywords=a+case+for+mars

For probability I'd recommend Introduction to Probability Theory by Hoel, Port & Stone. It has the best explanations of any probability book I've seen, great examples, and answers to most of the problems are in the back (making it well-suited for self-study). I think it's still the best introductory book on the subject, despite its age. Amazon has used copies for cheap.

For statistics, you have to be more precise as to what you mean by an "average undergraduate statistics" course. There's a difference between the typical "elementary statistics" course and the typical "mathematical statistics" course. The former requires no calculus, but goes into more detail about various statistical procedures and tests for practical uses, while the latter requires calculus and deals more with theory than practice. Learning both wouldn't be a bad idea. For elementary stats there are lots of badly written books, but there is one jewel: Statistics by Freedman, Pisani & Purves. For mathematical statistics, Introduction to Mathematical Statistics by Hogg & Craig is decent, though a bit dry. I don't think that Statistical Inference by Casella & Berger is really any better. Those are the two most-used textbooks on the subject.

A good intro book on calculus I found helpful was Calculus: A Physical and Intuitive Approach by Morris Kline. Jumping right into Spivak, while doable, is not for the faint of heart. (But one should definitely approach it eventually!)

Edit: spelling

I really enjoyed Dennett's Consciousness Explained. Chalmers' The Conscious Mind presents another popular view which, if I recall correctly, opposes Dennett's views. I'm slowly getting into work's by Steven Pinker.

Probably a general Philosophy of Mind reader would also benefit you just to get a good idea of the different views and topics out there within the discipline. I cannot remember which one I read years ago, although if I read one today I'd pick Chalmers' Philosophy of Mind or Kim's Philosophy of Mind.

Here's an easy read that I liked: Concepts of Modern Mathematics by Ian Stewart. It gives a pretty broad overview. And you can't beat the price of those Dover paperbacks.

You may also be interested in a more thorough exploration of the history of the subject. Try History of Mathematics by Carl Boyer.

You received A's in your math classes at a major public university, so I think you're in pretty good shape. That being said, have you done proof-based math? That may help tremendously in giving intuition because with proofs, you are giving rigor to all the logic/theorems/ formulas, etc that you've seen in your previous math classes.

Statistics will become very important in machine learning. So, a proof-based statistics book, that has been frequently recommended by /r/math and /r/statistics is Statistical Inference by Casella & Berger: https://www.amazon.com/Statistical-Inference-George-Casella/dp/0534243126

I've never read it myself, but skimming through some of the beginning chapters, it seems pretty solid. That being said, you should have an intro to proof-course if you haven't had that. A good book for starting proofs is How to Prove It: https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/0521675995

I know I'm tardy to the party, but I found that it's best to start with general surveys of philosophy, so you're exposed to a wide range of thought, then narrowing down your interests.

Personally, I found the following to be the most helpful:

From Socrates to Sartre: The Philosophic Quest

Think

What Does It All Mean?

The Problems of Philosophy

I'd recommend you to read this book, it provides some answers to great questions like these. Also, this video :)

CS182 is a discrete mathematics course. It has a lot to do with logic and proofs, and less to do with algebra and calculus. Most have never really seen what you will be covering. If you can, I would get the book and work through some of the problems before the start of the semester.

CS240 is similar to CS180, but it is taught in C — a much lower-level language. Once again, I recommend getting the book (I assume it will be The C Programming Language) and doing some of the exercises. Java syntax comes from C/C++, so that part will be somewhat familiar. C is pretty barebones, though. There are no classes, only functions. There is no ArrayList, LinkedList, etc. You have to build it all yourself. And when you allocate memory using malloc() (similar to calling new), you have to remember to free it when you’re done using free(). There is no garage collection.

Good luck!

These are, in my opinion, some of the best books for learning high school level math:

• I.M Gelfand Algebra {[.pdf] (http://www.cimat.mx/ciencia_para_jovenes/bachillerato/libros/algebra_gelfand.pdf) | Amazon}
  
• I.M. Gelfand The Method of Coordinates {Amazon}
  
• I.M. Gelfand Functions and Graphs {.pdf | Amazon}
  
  These are all 1900's Russian math text books (probably the type that /u/oneorangehat was thinking of) edited by I.M. Galfand, who was something like the head of the Russian School for Correspondence. I basically lived off them during my first years of high school. They are pretty much exactly what you said you wanted; they have no pictures (except for graphs and diagrams), no useless information, and lots of great problems and explanations :) There is also I.M Gelfand Trigonometry {[.pdf] (http://users.auth.gr/~siskakis/GelfandSaul-Trigonometry.pdf) | Amazon} (which may be what you mean when you say precal, I'm not sure), but I do not own this myself and thus cannot say if it is as good as the others :)
  
  
  I should mention that these books start off with problems and ideas that are pretty easy, but quickly become increasingly complicated as you progress. There are also a lot of problems that require very little actual math knowledge, but a lot of ingenuity.
  
  Sorry for bad Englando, It is my native language but I haven't had time to learn it yet.

I would caution you about Dennett because, while he is a well-respected and important philosopher, he also write books for a popular audience that are less philosophical in nature.

So I would stay clear of his new atheism stuff, stay away from his beef with Sam Harris (who isn't a philosopher), and try to find lectures where he talks about consciousness (which is his main topic in philosophy).

So I would recommend starting with Daniel Dennett's TED talks, which are much easier and accessible. Here's a good introductory lecture:

https://www.youtube.com/watch?v=cYh0lAWCnpI

https://www.ted.com/speakers/dan_dennett


Next, I would try to watch this lecture and see if you can follow it (it's a bit more complicated, but it outlines the debates around consciousness in a similar way to what you might find on the SEP):

https://youtu.be/JoZsAsgOSes

Finally, his book Consciousness Explained outlines his basic approach to consciousness. While not for a general audience, he does clarify and explain his positions well, so it might be worth looking into:

https://www.amazon.com/Consciousness-Explained-Daniel-C-Dennett/dp/0316180661/ref=sr_1_1?ie=UTF8&qid=1518209721&sr=8-1&keywords=consciousness+explained

since you are a computer science student, you can start with proofs in Discrete Mathematics fo this you can look at Kenneth Rosen's book, it can help you with a lot of basic concepts, constructing proofs. Its a good book for those who want to go in algorithms or theoretical cs or a even want to work on pure maths problems. I had this same confusion I wanted to do maths but also cs with it. After this you can try "The art of computer programming"(this has 4 volumes) by Donald Knuth but CLRS is a must along with Rosen's if you want to take cs and maths side by side. If you want to explore further you can look at Design of Approximation Algorithms and Randomised Algorithms. These book can help you with concepts of probability, number theory, geometry, linear algebra etc. But then if you want pure math problems then search for them, go though different journals, SIAM and Combinatorica are really good ones, search them pick a problem you like, then find text relevant to problem and try to give better solutions.

While it's a bit out of date, "Consciousness Explained" by Daniel C. Dennett can give a good introduction to what we know about how the brain really functions, and the vast difference between directly perceiving the world and the actual action of the brain to filter out most of the world, and translate what's left into an internalized model our consciousness is made aware of. It's a philosophy book, but leans heavily on medical understanding of brain biology, real-world behavior testing, and AI development progress (as of the 1990's).

The biggest aspect of it being out of date has to do with the sections on AI; our neural network architectures in use today are significantly more advanced and more similar to biological systems than what was available in the 1990's. That said, the insights from the state of development at the time (and its failures) are even more prescient in light of the last 10 years of AI development and progress.

1984. I can't remember how old I was, but I must have been a young teenager. I'd say of any book I've read, it's the one that comes to mind most often.

Also Think by Simon Blackburn. A basic introduction to western philosophy, it really sparked my interest at a young age and formed the basis for a love of philosophy, metaphysics, and just taking the time to deeply examine concepts and ideas.

Quantum Mechanics is not really a subject that can be summed up in a reddit comment. The best way to learn about something is to read about it. Go to your local book shop or library and look for some books on the subject. I've read dozens of books on the subatomic and I still don't understand it fully. If you're aspiring to be a physicist, you should become reeeeeally familiar with reading.

Uncertainty is a good one that I've read. And another great one is In Search of Schrodinger's Cat

Gelfand's Algebra is interesting, encourages mathematical thinking, and has the additional advantage of being much more approachable than the books you've listed.

This is probably a much better place to start for someone who's interested in "starting from the basics."

I have this sometimes (I also don't remember events but remember facts). Like something will happen and I feel like I dreamt it years before. But I kind of assume that I must just think that I had dreamt it years earlier. But now that I think about it, I guess it's possible I really did remember something that didn't happen yet in a dream, given what I read in The Grand Design.

Something weird is that I specifically remember getting out of a pool and walking towards a house -- and having deja vu about it -- thinking it had happened months before. And then, it happening again and remembering both deja vu times before. But the "3rd time", it was the first time I had ever been to that house.

I thought of some books suggestions. If you're going all in, go to the library and find a book on vector calculus. You're going to need it if you don't already know spherical coordinates, divergence, gradient, and curl. Try this one if your library has it. Lots of good books on this though. Just look for vector calculus.

Griffiths has a good intro to E&M. I'm sure you can find an old copy on a bookshelf. Doesn't need to be the new one.

Shankar has a quantum book written for an upper level undergrad. The first chapter does an excellent job explaining the basic math behind quantum mechanics .

> It has always been about flags and footprints

He literally went against all of NASA by saying 30 days missions were a huge waste of resources and that the only way to properly do Mars Missions was to do opposition class mission, with a year and half stay... That's all in the book.

What's also in the book is that after 5 or 6 cycles (MAV lands at window n, crew lands at window n+1, leaves at window n+2), the covered surface by the frequently spaced landing sites (and by the methane powered rovers) would be sufficient to decide on the best landing site to start a more permanent base.

It's called The Case for Mars (which incidentally will totally be the name of my suitcase if I ever get a seat on one of these MCT), and while it smells like the 90s (built on STS assets, expandable rockets), it definitely is geared toward creating a permanent civilization on Mars. Watch this and tell me again that he is an Apollo kind of guy.

For multivariable calculus I cannot recommend Div, Grad, Curl and All That enough. It’s got wonderful physically motivated examples and great problems. If you work through all the problems you’ll have s nice grasp on some central topics of vector calculus. It’s also rather thin, making it feel approachable for self learning (and easy to travel with).

Many thanks for the suggestions!

For the interested, I bought this book for GT:

http://www.amazon.com/Introductory-Graph-Theory-Gary-Chartrand/dp/0486247759

I also was tempted by the following book:

http://www.amazon.com/Concepts-Modern-Mathematics-Ian-Stewart/dp/0486284247



I think buying a book feels better than sex. (I can compare.)

Maybe try applied math programs. Some of them seem to have astrophysics faculty https://www.princeton.edu/gradschool/about/catalog/fields/applied_mathematics/. You'll probably have an easier time getting in with your background and can take the math GREs. In a physics BS you would at least have the knowledge of these books:

http://www.amazon.com/Classical-Mechanics-John-R-Taylor/dp/189138922X,

http://www.amazon.com/Introduction-Electrodynamics-4th-David-Griffiths/dp/0321856562/ref=sr_1_1?s=books&ie=UTF8&qid=1396384599&sr=1-1&keywords=griffiths,

http://www.amazon.com/Introduction-Quantum-Mechanics-David-Griffiths/dp/0131118927/ref=sr_1_2?s=books&ie=UTF8&qid=1396384599&sr=1-2&keywords=griffiths,

http://www.amazon.com/Introduction-Thermal-Physics-Daniel-Schroeder/dp/0201380277/ref=sr_1_1?s=books&ie=UTF8&qid=1396384625&sr=1-1&keywords=schroeder+statistical+physics.

The more you know from those books, the better. Although an applied math program, probably wouldn't expect you to have read all of them. Also try x-posting to /r/askacademia. I'm sure someone there could be more helpful.

As with most things you gotta know the basics. Start with classical mechanics. The best book is Landau's Mechanics, but it's quite advanced. The undergraduate text I used at university was Thornton and Marion. If that's still too much I've heard Taylor's book is even gentler.

Also, make sure you know your calculus.

From the first 40 pages, it looks like a discussion on free will, determinism, religion, morality, etc. It's interesting, and the pages are really short. Reminds me of one of the stories of The Mind's I.
Edit: reading a bit further, it has a nice twist halfway.. I daren't predict what the rest is about.

If you want a more general introduction into philosophy there's a Think: A Compelling Introduction to Philosophy by Simon Blackburn and the older What Does It All Mean?: A Very Short Introduction to Philosophy by Thomas Nagel. A more academic introduction (the last two books are more aimed at a general audience) is Fundamentals of Philosophy edited by John Shand. If you're willing to sit through it there also Russel's classic A History of Western Philosophy, which is a sort of introduction to philosophy through the history of the field (the audiobook is on youtube btw), and there also his Problems of Philosophy

I'm not that familiar with eastern philosophy, but a classic introduction to Existentialism is Walter Kaufmann's Existentialism from Dostoyevsky to Sartre and it should go nicely with Existentialism is a Humanism.

Hope this helps :)

I really enjoyed Godel's Proof by Nagel + Newman. It's a layman's guide to Godel incompleteness theorem. It avoids some of the more finnicky details, while still giving the overall impression.

https://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/0814758371/

If you like that, it's edited by Hofstadter, who wrote Godel-Escher-Bach, a famous book about recurrence.

Finally, I would recommend Nonzero: The Logic of Human Destiny by Robert Wright. It's a life-changing book that dives into the relevance of game theory, evolutionary biology and information technology. (Warning that the first 80 pages are very dry.)

https://www.amazon.com/Nonzero-Logic-Destiny-Robert-Wright/dp/0679758941/

These are different fields (programming vs math etc) however I will ask you, do you like math or programming ? If not maybe you need to get to know these quite interesting fields better. For math I would recommend one of the Dover introduction books, such as Ian Stewarts' concepts of modern math.

I learned from Wackerly which is decent, though I think Devore's presentation is better, but not as deep. Both have plenty of exercises to work with.

Casella and Berger is the modern classic, which is pretty much standard in most graduate stats programs, and I've heard good things about Stat Labs, which uses hands-on projects to illuminate the topics.

There's a great book on Amazon called Gravitation that explains it pretty well.

If you multiply the probability of winning times the payoff, you find that each entry, assuming you wouldn't have to share it and you get the full $400 million, is worth $1.74. Since it costs $2 to play and there are other things that reduce the winning amount, it is not a good bet.

Source: page 77 of this book.

In 1992 the Virginia Lottery had a game in which the value of the ticket was a little over $3, but they charged $1 per ticket. So investors got together and bought a lot of tickets, and won doing it.

Any decent introduction to special relativity should cover it. I don't know how technical you are, though. If you're mathematically inclined, Taylor and Wheeler's Spacetime Physics is an awesome book. A lot cheaper and pretty accessible would be Relativity: A Very Short Introduction

How To Build Your Own Spaceship is a fantastic introduction to rocket appliances and commercial space flight. It's pretty short, too. I highly recommend.

And obviously The Case for Mars.

I know this is not exactly what you had in mind, but one of the most significant proofs of the 20th century has an entire book written about it:

http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814758371

The proof they cover is long and complicated, but the book is nonetheless intended for the educated layperson. It is very, very well written and goes to great lengths to avoid unnecessary mathematical abstraction. Maybe check it out.

> The concept "Spacetime" makes no sense at all

Why do you say that?

> If you can define it in causal/physical terms that would be very interesting.

I'll leave that to the pros. Here is a list of good books that cover the subject. I strongly recommend Gravitation by Misner, Wheeler and Thorne, a classic textbook on GR that covers such concepts exhaustively. It's not an easy read (and definitely not for laypersons) but in my opinion it counts as among the greatest books ever written

1. Vector Calculus isn't just a required math course, and the often-suggested supplementary textbook Div, Grad, Curl, and All That has a terribly misleading title - VC's not just a temporary annoyance, you'll actually need this stuff later.
   
   
2. Same for probability. If you skate thru probability hoping you can forget it right away, you're gonna have a bad time in your Signals classes and your Communications classes later. Stochastic Processes will strangle you and urinate on your corpse.
   
   
3. During your internship(s), do your best to befriend the engineers you work around & with. They have much to teach you and can give you excellent advice after your internship is over. Plus they can write letters of reference that are a lot more influential than your Logic Design professor can write.
   
   
4. No matter how much you enjoyed your Chemistry classes, and no matter how well you did in them, it turns out that Chemistry is 99% irrelevant to EE. Sorry.
   
   
5. Programming and software are a fact of EE life. Become a good coder and don't let your skills atrophy. Learn Linux or at least UNIX or at least the UNIX underpinnings of MAC OSX. Learn command line tools.
   
   
6. Often the best EEs are the ones with the most bravery, the least afraid of the unknown. "I've never done that before" is a reason to jump in and try something, NOT an excuse to back away.
   
   
7. Analysis Paralysis really does exist. Avoid it.

I looked at the free pages on Amazon and it does seem a bit wordier than the physics books I remember. It could just be the chapter. Maybe it reads like a book; maybe it's incredibly boring :/

If money isn't an issue (or if you're resourceful and internet savvy ;) you can try the book by Serway & Jewett. It's fairly common.

http://www.amazon.com/Physics-Scientists-Engineers-Raymond-Serway/dp/1133947271

As for DE, this book really resonated with me for whatever reason. Your results may vary.

http://www.amazon.com/Course-Differential-Equations-Modeling-Applications/dp/1111827052/ref=sr_1_2?s=books&ie=UTF8&qid=1372632638&sr=1-2&keywords=differential+equations+gill

If your issue is with the technical nature of textbooks in general, then you'll either have to deal with it or look for some books that simplify/summarize the material in some way. The only example I can come up with is:

http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161/ref=sr_1_1?s=books&ie=UTF8&qid=1372632816&sr=1-1&keywords=div+grad+curl

Although Div, Grad, Curl, and all That is intended for students in an Electromagnetics course (not Physics 2), it might be helpful. It's an informal overview of Calculus 3 integrals and techniques. The book uses electromagnetism in its examples. I don't think it covers electric circuits, which are a mess of their own. However, there are tons of resources on the internet for circuits. I hope all this was helpful :)

Try to find entry points that interest you personally, and from there the next steps will be natural. Most books that get into the nitty-gritty assume you're in school for it and not directly motivated, at least up to early university level, so this is harder than it should be. But a few suggestions aimed at the self-motivated: Lockhart Measurement, Gelfand Algebra, 3blue1brown's videos, Calculus Made Easy, Courant & Robbins What Is Mathematics?. (I guess the last one's a bit tougher to get into.)

For physics, Thinking Physics seems great, based on the first quarter or so (as far as I've read).

I recommend this book: http://www.amazon.ca/Spacetime-Physics-Taylor-Archibald-Wheeler/dp/0716723271

We covered it as part of a 3rd year physics course. It's actually very accessible, and prefers to provide good explanations (and help you to learn how to resolve apparent paradoxes) instead of lots of mathematical exercises.

If you're interested in consciousness, The Mind's I is a great collection of essays and dialogues from different authors, most of which are very accessible. They cover the topic from a lot of different angles and do a good job of prompting the kind of conceptual groundwork you need in order to delve deeper into the subject.

How about selected chapters from Stewart's Concepts of Modern Mathematics? It has a pretty wide range of jumping off points and is a relatively affordable Dover book. You could go into more or lesser detail on these topics based on the students' backgrounds.

Another idea would be to focus on foundations like set theory, logic, construction/progression of number systems from ℕ -> ℤ -> ℚ -> ℝ -> ℂ , and then maybe move into some philosophy of math. There could be some fun and accessible class discussion, such as having them argue for or against Platonism. [Edit: You could throw in some Smullyan puzzle book stuff for the logic portion of this for further entertainment value.]

I recommend going through some of the lessons on Brilliant, and here is Brilliant's quick exposition on the set of complex numbers.

I don't know what a softer explanation would entail exactly, but I would offer you the alternative perspective that the representation of complex numbers as two real numbers a+ib for the real numbers a and b is extremely useful because of the interpretation of the extension of the one dimensional real number line into the two dimensional complex plane.

Also, I recommend reading on a simple exposition of complex numbers from Richard Courant's "What is Mathematics".

For a more realistic concept of Martian colonization,
The Case For Mars by Robert Zubrin is an excellent read. Zubrin focuses on a smaller scale, less expensive method of colonizing Mars which involves three Ares class launches, one for a MAV (Mars Ascent Vehicle), an ERV (Earth Return Vehicle), and habituation module. The MAV will use in-situ, or on planet resources to produce methane rocket propellant and fuel the crew’s method of leaving the planet once their stay ends. They will dock with the ERV in LMO (Low Martian Oribit), where the ERV will perform a transfer burn to get back home. This plan is known as Mars Semi-Direct (the original, known as Mars Direct, combined the MAV and ERV, but NASA necessitated the modifications that created Semi-Direct) and has been a vision of Zubrin since he originally proposed it to NASA in the 1990s. It should be noted, however, that one needs at least a small scientific background to understand Zubrin’s book. (Concepts such as ISP, deltaV, orbital mechanics ex. Hohmann Transfer, and chemistry involving synthesis of propellants as well as catalyst reactions. Most of it is explained but a minimal background in rocket science is helpful)

EDIT: this plan comprises NASA’s most recent Mars plan, which was actually designed around Zubrin’s suggestions and collaboration with NASA as part of the SEI. This plan can be found in more detail
here

If I recall correctly it's pretty good. The basic concepts behind relativity (and quantum mechanics) haven't really changed over the past, say, 50 years. Even the Standard Model, developed in the 1970s, is the best description of elementary particles we currently have.

The most important novelties would be the very "flat" Cosmic Background Radiation, nevertheless having small seemingly random fluctuation; and inflation, which is one attempt to explain those phenomena.

I would argue that many modern books are actually straying from accuracy in favour of speculating about solutions to open questions with for instance string theory and multiverses, for which there is no evidence. Hawking himself is guilty of that too:
http://www.amazon.com/Grand-Design-Stephen-Hawking/dp/0553805371

A physics-guru friend of mine recommends this three-pronged punch: In Search of Schrödinger's Cat, The Tao of Physics, and Autobiography of a Yogi. Haven't gotten to the third one yet myself, but the first two were quite excellent.