(Part 2) Reddit mentions: The best science & math books

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

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

>This is fascinating stuff!

I'm glad you like it!

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

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

Nifty, isn't it?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

I hope I am not too late.

You can post this to /r/suicidewatch.

Here is my half-baked attempt at providing you with some answers.

First of all let's see, what is the problem? Money and women. This sounds rather stereotypical but it became a stereotype because a lot of people had this kind of problems. So if you are bad at money and at women, join the club, everybody sucks at this.

Now, there are a few strategies of coping with this. I can tell you what worked for me and perhaps that will help you too.

I guess if there is only one thing that I would change in your attitude that would improve anything is learning the fact that "there is more where that came from". This is really important in girl problems and in money problems.

When you are speaking with a girl, I noticed that early on, men tend to start being very submissive and immature in a way. They start to offer her all the decision power because they are afraid not to lose her. This is a somehow normal response but it affects the relationship negatively. She sees you as lacking power and confidence and she shall grow cold. So here lies the strange balance between good and bad: you have to be powerful but also warm and magnanimous. You can only do this by experimenting without fearing the results of your actions. Even if the worst comes to happen, and she breaks up with you .... you'll always get a better option. There are 3.5 billion ladies on the planet. The statistics are skewed in your favor.

Now for the money issue. Again, there is more where that came from. The money, are a relatively recent invention. Our society is built upon them but we survived for 3 million years without them. The thing you need to learn is that your survival isn't directly related to money. You can always get food, shelter and a lot of other stuff for free. You won't live the good life, but you won't die. So why the anxiety then?

Question: It seems to me you are talking out of your ass. How do I put into practice this in order to get a girlfriend?

Answer: Talk to people. Male and female. Make the following your goals:
Talk to 1 girl each day for one month.
Meet a few friends each 3 days.
Make a new friend each two weeks.
Post your romantic encounters in /r/seduction.
This activities will add up after some time and you will have enough social skill to attract a female. You will understand what your female friend is thinking. Don't feel too bad if it doesn't work out.

Question: The above doesn't give a lot of practical advice on getting money. I want more of that. How do I get it?

Answer: To give you money people need to care about you. People only care about you when you care about them. This is why you need to do the following:
Start solving hard problems.
Start helping people.
Problems aren't only school problems. They refer to anything: start learning a new difficult subject (for example start learning physics or start playing an instrument or start writing a novel). Take up a really difficult project that is just above the verge of what you think you are able to do. Helping people is something more difficult and personal. You can work for charity, help your family members around the house and other similar.

Question: I don't understand. I have problems and you are asking me to work for charity, donate money? How can giving money solve anything?

Answer: If you don't give, how can you receive? Helping others is instilling a sense of purpose in a very strange way. You become superior to others by helping them in a dispassionate way.

Question: I feel like I am going to cry, you are making fun of me!
Answer: Not entirely untrue. But this is not the problem. The problem is that you are taking yourself too serious. We all are, and I have similar problems. The true mark of a person of genius is to laugh at himself. Cultivate your sense of humor in any manner you can.

Question: What does it matter then if I choose to kill myself?

Answer: There is this really good anecdote about Thales of Miletus (search wiki). He was preaching that there is no difference between life and death. His friends asked him: If there is no difference, why don't you kill yourself. At this, he instantly answered: I don't kill myself because there is no difference.

Question: Even if I would like to change and do the things you want me to do, human nature is faulty. It is certain that I would have relapses. How do I snap out of it?

Answer: There are five habits that you should instill that will keep bad emotions away. Either of this habits has its own benefits and drawbacks:

1. Mental contemplation. This has various forms, but two are the best well know: prayer and meditation. At the beginning stage they are quite different, but later they begin to be the same. You will become aware that there are things greater than you are. This will take some of the pressure off of your shoulders.
   
2. Physical exercise. Build up your physical strength and you will build up your mental strength.
   
3. Meet with friends. If you don't have friends, find them.
   
4. Work. This wil give you a sense of purpose. Help somebody else. This is what I am doing here. We are all together on this journey. Even though we can't be nice with everyone, we need to at least do our best in this direction.
   
5. Entertainment. Read a book. Play a game. Watch a movie. Sometimes our brain needs a break. If not, it will take a break anyway and it will not be a pretty one. Without regular breaks, procrastination will occur.
   
   Question: Your post seems somewhat interesting but more in an intriguing kind of way. I would like to know more.
   
   Answer: There are a few good books on these subjects. I don't expect you to read all of them, but consider them at least.
   
   For general mental change over I recommend this:
   http://www.amazon.com/Learned-Optimism-Change-Your-Mind/dp/1400078393/ref=sr_1_1?ie=UTF8&qid=1324795853&sr=8-1
   
   http://www.amazon.com/Generous-Man-Helping-Others-Sexiest/dp/1560257288
   
   For girl issues I recommend the following book. This will open up a whole bag of worms and you will have an entire literature to pick from. This is not going to be easy. Remember though, difficult is good for you.
   http://www.amazon.com/GAME-UNDERCOVER-SOCIETY-PICK-UP-ARTISTS/dp/1841957518/ref=sr_1_1?ie=UTF8&qid=1324795664&sr=8-1 (lately it is popular to dish this book for a number of reasons. Read it and decide for yourself. There is a lot of truth in it)
   
   Regarding money problem, the first thing is to learn to solve problems. The following is the best in my opinion
   http://www.amazon.com/How-Solve-Mathematical-Princeton-Science/dp/069111966X
   The second thing about money is to understand why our culture seems wrong and you don't seem to have enough. This will make you a bit more comfortable when you don't have money.
   http://www.amazon.com/Story-B-Daniel-Quinn/dp/0553379011/ref=sr_1_3?ie=UTF8&qid=1324795746&sr=8-3 (this one has a prequel called Ishmael. which people usually like better. This one is more to my liking.)
   
   For mental contemplation there are two recommendations:
   http://www.urbandharma.org/udharma4/mpe.html . This one is for meditation purposes.
   http://www.amazon.com/Way-Pilgrim-Continues-His/dp/0060630175 . This one is if you want to learn how to pray. I am an orthodox Christian and this is what worked for me. I cannot recommend things I didn't try.
   
   For exercising I found bodyweight exercising to be one of the best for me. I will recommend only from this area. Of course, you can take up weights or whatever.
   http://www.amazon.com/Convict-Conditioning-Weakness-Survival-Strength/dp/0938045768/ref=sr_1_1?ie=UTF8&qid=1324795875&sr=8-1 (this is what I use and I am rather happy with it. A lot of people recommend this one instead: http://www.rosstraining.com/nevergymless.html )
   
   Regarding friends, the following is the best bang for your bucks:
   http://www.amazon.com/How-Win-Friends-Influence-People/dp/1439167346/ref=sr_1_1?ie=UTF8&qid=1324796461&sr=8-1 (again, lots of criticism, but lots of praise too)
   
   The rest of the points are addressed in the above books. I haven't given any book on financial advices. Once you know how to solve problems and use google and try to help people money will start coming, don't worry.
   
   I hope this post helps you, even though it is a bit long and cynical.
   
   Merry Christmas!

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.

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.

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.

Here's a list of books I've read that have had a big impact on my journey.

First and foremost tho, you should learn to meditate. That's the most instrumental part of any spiritual path.

 Ram Dass – “Be Here Now” - https://www.amazon.com/Be-Here-Now-Ram-Dass/dp/0517543052 - Possibly the most important book in the list – was the biggest impact in my life.  Fuses Western and Eastern religions/ideas. Kinda whacky to read, but definitely #1

Ram Dass - “Journey Of Awakening” - https://www.amazon.com/dp/B006L7R2EI - Another Ram Dass book - once I got more into Transcendental Meditation and wanted to learn other ways/types of meditation, this helped out.

 Clifford Pickover – “Sex, Drugs, Einstein & Elves…” - https://www.amazon.com/Sex-Drugs-Einstein-Elves-Transcendence/dp/1890572179/ - Somewhat random, frantic book – explores lots of ideas – planted a lot of seeds in my head that I followed up on in most of the books below

 Daniel Pinchbeck – “Breaking Open the Head” - https://www.amazon.com/Breaking-Open-Head-Psychedelic-Contemporary/dp/0767907434 - First book I read to explore impact of psychedelics on our brains

 Jeremy Narby – “Cosmic Serpent” - https://www.amazon.com/Cosmic-Serpent-DNA-Origins-Knowledge/dp/0874779642/ - Got into this book from the above, explores Ayahuasca deeper and relevancy of serpent symbolism in our society and DNA

 Robert Forte – “Entheogens and the Future of Religion” - https://www.amazon.com/Entheogens-Future-Religion-Robert-Forte/dp/1594774382 - Collection of essays and speeches from scientists, religious leaders, etc., about the use of psychedelics (referred to as Entheogens) as the catalyst for religion/spirituality

 Clark Strand – “Waking up to the Dark” - https://www.amazon.com/Waking-Up-Dark-Ancient-Sleepless/dp/0812997727 - Explores human’s addiction to artificial light, also gets into femininity of religion as balance to masculine ideas in our society

 Lee Bolman – “Leading with Soul” - https://www.amazon.com/Leading-Soul-Uncommon-Journey-Spirit/dp/0470619007 - Discusses using spirituality to foster a better, more supportive and creative workplace – pivotal in my honesty/openness approach when chatting about life with coworkers

 Eben Alexander – “Proof of Heaven” - https://www.amazon.com/Proof-Heaven-Neurosurgeons-Journey-Afterlife/dp/1451695195 - A neurophysicist discusses his near death experience and his transformation from non-believer to believer (title is a little click-baity, but very insightful book.  His descriptions of his experience align very similarly to deep meditations I’ve had)

 Indries Shah – “Thinkers of the East” - https://www.amazon.com/Thinkers-East-Idries-Shah/dp/178479063X/ - A collection of parables and stories from Islamic scholars.  Got turned onto Islamic writings after my trip through Pakistan, this book is great for structure around our whole spiritual “journey”

 Whitley Strieber – “The Key: A True Encounter” - https://www.amazon.com/Key-True-Encounter-Whitley-Strieber/dp/1585428698 - A man’s recollection of a conversation with a spiritual creature visiting him in a hotel room.  Sort of out there, easy to dismiss, but the topics are pretty solid

 Mary Scott – “Kundalini in the Physical World” - https://www.amazon.com/Kundalini-Physical-World-Mary-Scott/dp/0710094175/ - Very dense, very difficult scientific book exploring Hinduism and metaphysics (wouldn’t recommend this for light reading, definitely something you’d want to save for later in your “journey”)

 Hermann Hesse – “Siddartha” - https://www.barnesandnoble.com/w/siddhartha-hermann-hesse/1116718450? – Short novel about a spiritual journey, coming of age type book.  Beautifully written, very enjoyable.

Reza Aslan - “Zealot” - https://www.amazon.com/ZEALOT-Life-Times-Jesus-Nazareth/dp/140006922X - Talks about the historical Jesus - helped me reconnect with Christianity in a way I didn’t have before

Reza Aslan - “No god but God” - https://www.amazon.com/god-but-God-Updated-Evolution/dp/0812982444 - Same as above, but in terms of Mohammad and Islam.  I’m starting to try to integrate the “truths” of our religions to try and form my own understanding

Thich Nhat Hanh - “Silence” - https://www.amazon.com/Silence-Power-Quiet-World-Noise-ebook/dp/B00MEIMCVG - Hanh’s a Vietnamese Buddhist monk - in this book he writes a lot about finding the beauty in silence, turning off the voice in our heads and lives, and living in peace.

Paulo Coelho - “The Alchemist” - https://www.amazon.com/Alchemist-Paulo-Coelho/dp/0062315005/ - Sort of a modern day exploration of “the path” similar to “Siddhartha.”  Very easy and a joy to read, good concepts of what it means to be on a “path”

Carlos Castaneda - "The Teachings of Don Juan" - The Teachings of Don Juan: A Yaqui Way of Knowledge https://www.amazon.com/dp/0671600419 - Started exploring more into shamanism and indigenous spiritual work; this book was a great intro and written in an entertaining and accessible way. 

Jean-Yves Leloup - “The Gospel of Mary” - https://www.amazon.com/Gospel-Mary-Magdalene-Jean-Yves-Leloup/dp/0892819111/ - The book that finally opened my eyes to the potentiality of the teachings of Christ.  This book, combined with the one below, have been truly transformative in my belief system and accepting humanity and the power of love beyond what I’ve found so far in my journey.

Jean-Yves Leloup - “The Gospel of Philip” - https://www.amazon.com/Gospel-Philip-Magdalene-Gnosis-Sacred/dp/1594770220 - Really begins to dissect and dive into the metaphysical teachings of Christ, exploring the concept of marriage, human union and sexuality, and the power contained within.  This book, combined with the one above, have radically changed my perception of The Church as dissimilar and antithetical to what Christ actually taught.

Ram Dass - “Be Love Now” - https://www.amazon.com/Be-Love-Now-Path-Heart/dp/0061961388 - A follow-up to “Be Here Now” - gets more into the esoteric side of things, his relationship with his Guru, enlightenment, enlightened beings, etc.

Riane Eisler - “The Chalice and the Blade” - https://www.amazon.com/Chalice-Blade-Our-History-Future/dp/0062502891 - An anthropoligical book analyzing the dominative vs cooperative models in the history and pre-history of society and how our roots have been co-opted and rewritten by the dominative model to entrap society into accepting a false truth of violence and dominance as “the way it is”

> I've come to the conclusion that my minimum requirements are to see the Rings of Saturn and the bands on Jupiter.

Go big.

I've a 50 mm finderscope (an auxiliary "rifle sights" scope that sits on top of a much larger scope) that can "resolve" the rings of Saturn if I put a strong eyepiece in it, but it looks like a little dot crossed out by a very thin thread. And this is a high-quality Stellarvue achromat refractor.

Get the biggest aperture your money can buy. That basically means a dobsonian reflector. Someone suggested a refurbished 6" dob. If that's all you can afford, go for it. You may have to get an extra eyepiece for it, something like a 12 mm or even 8 mm.

The smallest dob that is not a compromise in any way is the Zhumell Z8 - the archetypal 8" dob. If you can afford it, it could be a "forever scope". If you can't afford it, just get the biggest dob you can - it's the architecture that provides the most aperture per dollar. Smart 8 year olds can handle a 6" ... 8" dob; they may need a small stool to step on when the 8" dob is vertical, but that will cease being a problem in a year or so, when the kid gets taller. :)

You can sort-of cheat with a small-ish aperture for the rings of Saturn, but you'll see them small. Jupiter's bands, OTOH, are low-contrast features. You could see them on a sub-100mm scope, but they are not very impressive; you can tell they are there, but that's it. There is no substitute for large aperture in that case. Go BIG.

Aperture is king.

BTW, Saturn goes in hiding for the next several months. But Jupiter is on the rise in the East; very bright and pretty, go outside tonight and look east.

> Everyone is familiar with refractor telescopes.

It's easy to make small-aperture refractors, that's why they are popular. But as soon as aperture goes beyond a certain limit, things get flipped over and reflectors rule the game.

A good 4" (100 mm) refractor is a thousand bucks. A good 4" dob is 1/4 of that price.

> Do you think we would be disappointed with the 80mm refractor when trying to view Saturn & Jupiter?

Yes. Anything is disappointing after looking at big colorful space telescope images. Well, almost anything, except over-24" dobs under dark skies with great seeing. :) If your goal is to blow the kid's mind, go big. Forget anything else, features, bells, whistles - hunt for aperture instead.

Make sure you have at least two eyepieces; one at, let's say, 30x ... 50x magnification (for wide images - large but faint objects like nebulae), another at 120x ... 180x or so (for higher magnification - small objects like planets or double stars). Good dobs usually come with two glasses like that included. You'll figure out later when/if you need a more diverse collection of glass. This assumes you get a reasonable aperture; a tiny 80mm scope will fall apart at 180x.

Magnification is like a car's speed. You don't drive your car all the time at 200 km/h; sometimes you drive slow, when you go to the grocery store; other times you go fast, such as on the freeway. Each situation requires a certain speed. Same with scopes and magnification. Don't fall into the beginner's trap and believe that "more is better" for magnification. It is not. However, more is always better when it comes to aperture.

Get Turn Left At Orion - it's a wonderful book that will teach you where and how to find all sorts of amazing objects on the sky. It's perfect for the kid too - not too complicated, lots of pictures.

Install Stellarium on a laptop or iPhone. It's like a map, but for the sky. You could also get the Pocket Sky Atlas after a few months - it's a bit more technical but it's a real sky map like the ones "real" astronomers use.

Keep your scope collimated for best performance. link1 link2

Not knowing what your budget is, I'll start small and work up :)

• Turn Left At Orion is the bible of star hopping and familiarization with the sky. Since he's already demonstrated enjoyment of pointing out this star or that, it's right up his alley.
  
  
• Maybe a nice pair of binoculars. I know he has a scope, but good binocs can offer really stunning views in their own right, and are much more portable and easy to "grab and go" on a hike, or a neighborhood walk, or whatever. Doesn't have to be the pair I linked, that's simply one fairly well regarded brand/model.
  
• Maybe something as simple as a gift certificate to his favorite astronomy store?
  
• Is he a tinkerer or DIYer? If so, then introduce him to Stellafane and maybe take a trip there for one of their ATM workshops, or maybe buy him a starter mirror grinding kit. I've had great success with the folks at First Hand Discovery but there are plenty of other top notch companies that can hook you up as well. :)
  
• Not sure where you live, but a trip to dark skies could be amazing. /u/KaneHau has already provided you with lots of info about a trip to the islands, but if CONUS is more in your budget, then there are LOTS of great trips to the SW USA for dark skies. My personal favorite are the fine folks at Marathon Sky Park in Marathon, TX. They are an amazing group of people, service is first rate, facilities are amazing, and the skies are gorgeous. :)
  
  
  

Edit at the top for the OP - Don't buy a telescope until you're committed to the hobby. If you live in the US go to a local star party whenever you have the chance. People will be more than happy to let you take a quick peek through their scopes and explain what you're looking at. Before you buy a scope, get acquainted with the hobby by getting a simple star chart, you can pick those up for $10 online. And then buy these binoculars Those are the gold standard for people just starting out. They're only $50 and they're great. On the off chance that they are mis-collimated just call their customer service line and they'll walk you through how to fix it. It's not the big deal some people make it out to be. They have a nice wide field and they're great for learning the sky. The seven sisters are amazing through them as is the moon, and they're just powerful enough to see Albireo clearly. On a dark night you can also see the Orion Nebula (although small) and see the full disc of Andromeda as well as all the Galilean moons around Jupiter.

Books:

The Backyard Astronomers guide

Turn Left at Orion

Websites:

• Astronomy Cast - Start at episode one and just work your way up. Probably the best astronomy podcast in existence.
  
  
• Universe Today Run by Fraser Cain of Astronomy cast
  
  
• Star Stryder - Dr. Pamela Gay's blog
  
  
• APOD Gorgeous photos and explanations to go with them.
  
  
• Centauri Dreams - For when you want to dream big... but not necessarily realistic.
  
  
• EarthSky - Science news with an Astronomy slant
  
  
• SpaceWeather - Shit about the sun
  
  
• Zooniverse - Participate in real science
  
  
• Space.com - All space all the time.
  
  
• Planetary Society - More awesome space stuff
  
  
• Citizen Sky - Little more advanced but another way to contribute.
  
  
• AAVSO - Learn about variable stars and contribute to the cause.
  
  Phone apps: (If you have an android phone)
  
  
• Google Sky - Augmented reality app that shows you exactly what you're looking at.
  
• Satellite AR - Will show all satellite passes above you in real time. Also augmented reality.
  
• SkEye - Similar to google sky but with much more detail
  
• Heavens Above - Find satellite passes, Iridium flares, ISS passes, all sortable by date, time, location, and luminosity.
  
• Where is IO - A great Jupiter map for figuring out which moons you're looking at when observing Jupiter
  
• Star Odyssey - A great tool to find data on stars. Like a mini encyclopedia about star targets.
  
• Telescope Calculator Lite - When you get a scope, you can input all variables and get specs for your scope and eyepieces. Great tool for the field.
  
  Must have programs for your computer:
  
  
• Celestia - Can do anything but the learning curve can be discouraging. Amazing program once you learn the basics.
  
  
• Stellarium - The most essential amazing amateur program ever created. Look up any star, constellation, asterism, messier object, etc etc etc, then see what it will look like through your exact telescope at any time of night. INCREDIBLE and essential program.
  
  
• Virtual Moon Atlas - Unreal program for lunar observing. Love it. Love it. Love it.
  
  That should keep you busy for awhile.
  
  Edit: Can't believe I forgot Cloudy Nights Pretty much the most comprehensive Astronomy forum on the web.
  

Imagine you have a dataset without labels, but you want to solve a supervised problem with it, so you're going to try to collect labels. Let's say they are pictures of dogs and cats and you want to create labels to classify them.

One thing you could do is the following process:

1. Get a picture from your dataset.
   
2. Show it to a human and ask if it's a cat or a dog.
   
3. If the person says it's a cat or dog, mark it as a cat or dog.
   
4. Repeat.
   
   (I'm ignoring problems like pictures that are difficult to classify or lazy or adversarial humans giving you noisy labels)
   
   That's one way to do it, but is it the most efficient way? Imagine all your pictures are from only 10 cats and 10 dogs. Suppose they are sorted by individual. When you label the first picture, you get some information about the problem of classifying cats and dogs. When you label another picture of the same cat, you gain less information. When you label the 1238th picture from the same cat you probably get almost no information at all. So, to optimize your time, you should probably label pictures from other individuals before you get to the 1238th picture.
   
   How do you learn to do that in a principled way?
   
   Active Learning is a task where instead of first labeling the data and then learning a model, you do both simultaneously, and at each step you have a way to ask the model which next example should you manually classify for it to learn the most. You can than stop when you're already satisfied with the results.
   
   You could think of it as a reinforcement learning task where the reward is how much you'll learn for each label you acquire.
   
   The reason why, as a Bayesian, I like active learning, is the fact that there's a very old literature in Bayesian inference about what they call Experiment Design.
   
   Experiment Design is the following problem: suppose I have a physical model about some physical system, and I want to do some measurements to obtain information about the models parameters. Those measurements typically have control variables that I must set, right? What are the settings for those controls that, if I take measurements on that settings, will give the most information about the parameters?
   
   As an example: suppose I have an electric motor, and I know that its angular speed depends only on the electric tension applied on the terminals. And I happen to have a good model for it: it grows linearly up to a given value, and then it becomes constant. This model has two parameters: the slope of the linear growth and the point where it becomes constant. The first looks easy to determine, the second is a lot more difficult. I'm going to measure the angular speed at a bunch of different voltages to determine those two parameters. The set of voltages I'm going to measure at is my control variable. So, Experiment Design is a set of techniques to tell me what voltages I should measure at to learn the most about the value of the parameters.
   
   I could do Bayesian Iterated Experiment Design. I have an initial prior distribution over the parameters, and use it to find the best voltage to measure at. I then use the measured angular velocity to update my distribution over the parameters, and use this new distribution to determine the next voltage to measure at, and so on.
   
   How do I determine the next voltage to measure at? I have to have a loss function somehow. One possible loss function is the expected value of how much the accuracy of my physical model will increase if I measure the angular velocity at a voltage V, and use it as a new point to adjust the model. Another possible loss function is how much I expect the entropy of my distribution over parameters to decrease after measuring at V (the conditional mutual information between the parameters and the measurement at V).
   
   Active Learning is just iterated experiment design for building datasets. The control variable is which example to label next and the loss function is the negative expected increase in the performance of the model.
   
   So, now your procedure could be:
   
   
5. Start with:
   
   • a model to predict if the picture is a cat or a dog. It's probably a shit model.
     
   • a dataset of unlabeled pictures
     
   • a function that takes your model and a new unlabeled example and spits an expected reward if you label this example
     
6. Do:
   
   1. For each example in your current unlabeled set, calculate the reward
      
   2. Choose the example that have the biggest reward and label it.
      
   3. Continue until you're happy with the performance.
      
7. ????
   
8. Profit
   
   Or you could be a lot more clever than that and use proper reinforcement learning algorithms. Or you could be even more clever and use "model-independent" (not really...) rewards like the mutual information, so that you don't over-optimize the resulting data set for a single choice of model.
   
   I bet you have a lot of concerns about how to do this properly, how to avoid overfitting, how to have a proper train-validation-holdout sets for cross validation, etc, etc, and those are all valid concerns for which there are answers. But this is the gist of the procedure.
   
   You could do Active Learning and iterated experiment design without ever hearing about bayesian inference. It's just that those problems are natural to frame if you use bayesian inference and information theory.
   
   About the jargon, there's no way to understand it without studying bayesian inference and machine learning in this bayesian perspective. I suggest a few books:
   
   

• Information Theory, Inference, and Learning Algorithms, David Mackay - for which you can get a pdf or epub for free at this link.
  
  Is a pretty good introduction to Information Theory and bayesian inference, and how it relates to machine learning. The Machine Learning part might be too introductory if already know and use ML.
  
  
• Bayesian Reasoning and Machine Learning by David Barber - for which you can also get a free pdf here
  
  Some people don't like this book, and I can see why, but if you want to learn how bayesians think about ML, it is the most comprehensive book I think.
  
  
• Probability Theory, the Logic of Science by E. T. Jaynes. Free pdf of the first few chapters here.
  
  More of a philosophical book. This is a good book to understand what bayesians find so awesome about bayesian inference, and how they think about problems. It's not a book to take too seriously though. Jaynes was a very idiosyncratic thinker and the tone of some of the later chapters is very argumentative and defensive. Some would even say borderline crackpot. Read the chapter about plausible reasoning, and if that doesn't make you say "Oh, that's kind of interesting...", than nevermind. You'll never be convinced of this bayesian crap.
  
  

Hello :-)

This one, right? http://www.celestron.com/browse-shop/astronomy/telescopes/cometron-114az (not the 114 on EQ mount)


Resources

consider getting "turn left at orion" http://www.amazon.com/Turn-Left-Orion-Hundred-Telescope/dp/0521781906

and download http://stellarium.org.


What you can see

Stellarium uses photographs of objects, this will not represent the visual view, for that, check out

• http://stargazerslounge.com/topic/196278-what-can-i-expect-to-see/
  
  
• and http://www.deepskywatch.com/Articles/what-can-i-see-through-telescope.html
  
  Especially if you are interested in deep-sky (galaxies, nebulae...) and you can see the milky way from your location (else light pollution might be too high) the book is a very good resource (along with a dim red light to preserve night vision).
  
  Saturn, Jupiter, Mars, Venus will appear as very bright "stars", so if you check the general direction in Stellarium you should be able to find them easily.
  
  Set up
  
  Align the finder scope of your telescope during the day on a very far object. Never look into the sun with your telescope without a GOOD front filter, else you can damage or loose your eye sight instantly.
  
  Practice focusing during the day.
  
  Eyepieces
  
  Do you have the original eyepieces?
  
  
  The magnification is easily calculated. The telescope has a 450mm focal length and comes with 10mm and 20mm eyepieces.
  
  
  450 : 10 = 45x magnification, 450 : 20 = 22.5x magnification.
  
  That is great for the Andromeda Galaxy, the Orion nebula, h&chi Persei and many others, enough to see Jupiter's moons and that Saturn is not round, but to really enjoy any surface details a bit more magnification is in order.
  
  Please note that Magnification is not the main quality of a telescope, as many objects look great in 20-60x magnification and the higher you magnify, the dimmer the image gets. The manufacturer states 269x magnification and that will be pretty much useless on such a telescope. They state that it is a parabolic mirror, but at f/4 (short focal length to aperture diameter ratio) and in this price range I would stay way under that. Especially seeing (Atmospheric turbulences) limit magnification on most days anyway.
  
  Accessories
  
  Do you have any additional equipment?
  
  I would not spend too much on this telescope. Use it as-is for now. If you do want to try more magnification: Be aware that cheap eyepieces that will give you more magnification under 10-6mm have a verrrrry short eye relief, making it almost impossible to view through.
  
  A achromatic barlow (Will add chromatic abberration/lower the contrast) increasing the magnification, typically by the factor 2: http://www.ebay.com/itm/Achromatische-Barlow-Linse-BA2-2x-fur-Teleskope-31-7mm-/200607942106?pt=DE_Foto_Camcorder_Okulare&hash=item2eb52a45da (Cheapest achromatic I could find on ebay USA, actually I own this one, the shop is in germany though so it will take a while)
  
  and/or
  
  A nice wide angle eyepiece such as this 6mm http://corvus-optics.com/product/ultrawide-eyepieces/ (used to sell on ebay for $30 shipped, the shop increased the price; On Aliexpress you can get it for $24 sometimes, but from Hong Kong).
  
  The HR Planetary and BST Explorer eyepieces are another "cheap" ($40-60) choice for eyepieces under 6mm. For 10mm and up you can buy $20-$30 Plössl eyepieces or the $30 "gold-line" I mentioned, but I would use the kit eyepieces for now.
  
  
  Upgrade warning
  
  You would be amazed what is visible with the kit accessories under a truly dark site. Even a mile or two out of town to avoid some of the light pollution helps a great deal.
  
  Before spending too much consider an upgrade to a larger telescope. The short 4.5" telescope will have it's limits, and some people tend to spend more on accessories then what a upgrade would cost :-)
  
  Have fun with your telescope and this amazing hobby :-)
  
  
  
  ___
  
  Here a few links regarding light pollution
  
  
• http://www.perezmedia.net/beltofvenus/archives/images/2011/img201101AN_M42PosLG.jpg
  
  
• http://astrobob.areavoices.com/2010/12/06/how-dark-is-your-sky/
  
  
• http://www.rocketmime.com/astronomy/Telescope/sky.html
  
  
• http://academo.org/demos/bortle-scale/
  
  

I started from scratch on the formal CS side, with an emphasis on program analysis, and taught myself the following starting from 2007. If you're in the United States, I recommend BookFinder to save money buying these things used.

On the CS side:

• Basic automata/formal languages/Turing machines; Sipser is recommended here.
  
• Basic programming language theory; I used University of Washington CSE P505 online video lectures and materials and can recommend it.
  
• Formal semantics; Semantics with Applications is good.
  
• Compilers. You'll need several resources for this; my personal favorites for an introductory text are Appel's ML book or Programming Language Pragmatics, and Muchnick is mandatory for an advanced understanding. All of the graph theory that you need for this type of work should be covered in books such as these.
  
• Algorithms. I used several books; for a beginner's treatment I recommend Dasgupta, Papadimitriou, and Vazirani; for an intermediate treatment I recommend MIT's 6.046J on Open CourseWare; for an advanced treatment, I liked Algorithmics for Hard Problems.
  
  On the math side, I was advantaged in that I did my undergraduate degree in the subject. Here's what I can recommend, given five years' worth of hindsight studying program analysis:
  
  
• You run into abstract algebra a lot in program analysis as well as in cryptography, so it's best to begin with a solid foundation along those lines. There's a lot of debate as to what the best text is. If you're never touched the subject before, Gallian is very approachable, if not as deep and rigorous as something like Dummit and Foote.
  
• Order theory is everywhere in program analysis. Introduction to Lattices and Order is the standard (read at least the first two chapters; the more you read, the better), but I recently picked up Lattices and Ordered Algebraic Structures and am enjoying it.
  
• Complexity theory. Arora and Barak is recommended.
  
• Formal logic is also everywhere. For this, I recommend the first few chapters in The Calculus of Computation (this is an excellent book; read the whole thing).
  
• Computability, undecidability, etc. Not entirely separate from previous entries, but read something that treats e.g. Goedel's theorems, for instance The Undecidable.
  
• Decision procedures. Read Decision Procedures.
  
• Program analysis, the "accessible" variety. Read the BitBlaze publications starting from the beginning, followed by the BAP publications. Start with these two: TaintCheck and All You Ever Wanted to Know About Dynamic Taint Analysis and Forward Symbolic Execution. (BitBlaze and BAP are available in source code form, too -- in OCaml though, so you'll want to learn that as well.) David Brumley's Ph.D. thesis is an excellent read, as is David Molnar's and Sean Heelan's. This paper is a nice introduction to software model checking. After that, look through the archives of the RE reddit for papers on the "more applied" side of things.
  
• Program analysis, the "serious" variety. Principles of Program Analysis is an excellent book, but you'll find it very difficult even if you understand all of the above. Similarly, Cousot's MIT lecture course is great but largely unapproachable to the beginner. I highly recommend Value-Range Analysis of C Programs, which is a rare and thorough glimpse into the development of an extremely sophisticated static analyzer. Although this book is heavily mathematical, it's substantially less insane than Principles of Program Analysis. I also found Gogul Balakrishnan's Ph.D. thesis, Johannes Kinder's Ph.D. thesis, Mila Dalla Preda's Ph.D. thesis, Antoine Mine's Ph.D. thesis, and Davidson Rodrigo Boccardo's Ph.D. thesis useful.
  
• If you've gotten to this point, you'll probably begin to develop a very selective taste for program analysis literature: in particular, if it does not have a lot of mathematics (actual math, not just simple concepts formalized), you might decide that it is unlikely to contain a lasting and valuable contribution. At this point, read papers from CAV, SAS, and VMCAI. Some of my favorite researchers are the Z3 team, Mila Dalla Preda, Joerg Brauer, Andy King, Axel Simon, Roberto Giacobazzi, and Patrick Cousot. Although I've tried to lay out a reasonable course of study hereinbefore regarding the mathematics you need to understand this kind of material, around this point in the course you'll find that the creature we're dealing with here is an octopus whose tentacles spread in every direction. In particular, you can expect to encounter topology, category theory, tropical geometry, numerical mathematics, and many other disciplines. Program analysis is multi-disciplinary and has a hard time keeping itself shoehorned in one or two corners of mathematics.
  
• After several years of wading through program analysis, you start to understand that there must be some connection between theorem-prover based methods and abstract interpretation, since after all, they both can be applied statically and can potentially produce similar information. But what is the connection? Recent publications by Vijay D'Silva et al (1, 2, 3, 4, 5) and a few others (1 2 3 4) have begun to plough this territory.
  
• I'm not an expert at cryptography, so my advice is basically worthless on the subject. However, I've been enjoying the Stanford online cryptography class, and I liked Understanding Cryptography too. Handbook of Applied Cryptography is often recommended by people who are smarter than I am, and I recently picked up Introduction to Modern Cryptography but haven't yet read it.
  
  Final bit of advice: you'll notice that I heavily stuck to textbooks and Ph.D. theses in the above list. I find that jumping straight into the research literature without a foundational grounding is perhaps the most ill-advised mistake one can make intellectually. To whatever extent that what you're interested in is systematized -- that is, covered in a textbook or thesis already, you should read it before digging into the research literature. Otherwise, you'll be the proverbial blind man with the elephant, groping around in the dark, getting bits and pieces of the picture without understanding how it all forms a cohesive whole. I made that mistake and it cost me a lot of time; don't do the same.

The Physics AS/A Levels are a funny lot of modules; I believe they're designed to be doable without any A Level-equivalent Maths knowledge, so they're riddled with weird explanations that really try to avoid maths - which often just makes everything harder in the long run. (I did AQA Physics A, but all were pretty similar as far as I gathered.)

With that in mind, if you're looking to study Physics further on, I'd recommend supplementing your mathematics. If you're doing Further Maths, you probably needn't bother, as the first year of any university course will bore you to death repeating everything you learnt about calculus etc.; if you're doing single Maths, I'd recommend getting confident with C1-4, and maybe purchasing the Edexcel (Keith Pledger) FP1/FP2 books to get slightly ahead before uni. They're great books, so might be useful to have for Y1 of uni and reference thereafter regardless. I was quite put off by the attitude towards Y1 maths of the Further Maths people (about half the cohort), who kept moaning about having done it all already, so found focusing in lectures a tad harder; I wish I'd bothered to read just a little ahead.

The second thing I'd recommend would be reading fairly broadly in physics to understand what aspect in particular you enjoy the most. In my experience, the students who have even a rough idea of what they want to do in the future perform better, as they have motivation behind certain modules and know how to prioritise for a particular goal, e.g. summer placement at a company which will look for good laboratory work, or even as far as field of research.

To that end (and beginning to answer the post!), books that aren't overly pop-science, like Feynman's Six Easy Pieces/Six Not-so-Easy Pieces are good (being a selection of lectures from The Feynman Lectures). Marcus Chown does a similarly good job of not dumbing things down too much in Quantum Theory Cannot Hurt You and We Need to Talk About Kelvin, and he talks about a good variety of physical phenomena, which you can look up online if they interest you. I could recommend more, but it really depends how you want to expand your physics knowledge!

E - darn, just read you're not in the UK. Oops. Mostly still applies.

Computer scientist here... I'm not a "real" mathematician but I do have a good bit of education and practical experience with some specific fields of like probability, information theory, statistics, logic, combinatorics, and set theory. The vast majority of mathematics, though, I'm only interested in as a hobby. I've never gone much beyond calculus in the standard track of math education, so I to enjoy reading "layman's terms" material about math. Here's some stuff I've enjoyed.

Fermat's Enigma This book covers the history of a famous problem that looks very simple, yet it took several hundred years to resolve. In so doing it gives layman's terms overviews of many mathematical concepts in a manner very similar to jfredett here. It's very readable, and for me at least, it also made the study of mathematics feel even more like an exciting search for beautiful, profound truth.

Logicomix: An Epic Search for Truth I've been told this book contains some inaccuracies, but I'm including it because I think it's such a cool idea. It's a graphic novelization (seriously, a graphic novel about a logician) of the life of Bertrand Russell, who was deeply involved in some of the last great ideas before Godel's Incompleteness Theorem came along and changed everything. This isn't as much about the math as it is about the people, but I still found it enjoyable when I read it a few years ago, and it helped spark my own interest in mathematics.

Lots of people also love Godel Escher Bach. I haven't read it yet so I can't really comment on it, but it seems to be a common element of everybody's favorite books about math.

>"Hawking says in his book "The Grand Design" that, given the existence of gravity, "the universe can and will create itself from nothing...It is not necessary to invoke God to light the blue touch paper [fuse] and set the universe going." he writes.

Reference: Stephen Hawking: God didn't create universe

Or perhaps the cyclic model applies as envisioned in the Rig Veda. In Hindu cosmology, the universe is created by Brahma and then, much later, destroyed by Shiva to be followed by a new universe, which matches the cyclic model for the universe.

Perhaps we are living in Brahma's dream.

>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.

~ Carl Sagan in Cosmos

Also see The Conscious Universe

You say "my respects to the one who made it." But is that Allah, Brahma, Hunab Ku, or another creator deity?

Is it Enki from whom the Old Testament god, Yahweh, was likely derived?

>Joseph Campbell believed that the serpent in the Eden story was lifted directly from either the Sumerian God Enki, God of Water and Wisdom, or his son Ningizzida. Both of them were identified as Serpent Gods, among other things. Enki was possessed of the food and water of life as well as the tablets of wisdom. Ningizzida was Lord of the Tree of Truth. These gods may have been carried into Canaan with the Israelites after they left the Sumerian/Babylonian city of Ur, or absorbed from their eastern neighbors at a later time. (Much of the Hebrew Bible was compiled, edited and rewritten after the Hebrews were conquered and exiled in Babylon in the 6th century BC.) Virtually all of the first 11 chapters of Genesis are rewritten from the much older Sumerian tales. In them, Enki rather than Yahweh creates humans from mud, and saves the prototype of Noah from the flood by teaching him to build an ark.

Source: Asherah, Part II: The serpent’s bride

Mankind has many creation myths and has long created gods as an explanation for what we don't understand. And usually those gods, which are credited with creating mankind, are made in man's image.

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

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

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

Start with talkorigins.org.

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

See the extensive FAQs index

Here are their questions for creationsists - see both links there

and then read the index to creationist claims

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

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

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

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

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

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

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

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

The Dictionary of Christianity and Science by Paul Copan, Tremper Longman III, Christopher L. Reese, and Michael G. Strauss. In one volume, you get reliable summaries and critical analyses of over 450 relevant concepts, theories, terms, movements, individuals, and debates on how Christian theology relates to scientific inquiry. It goes over the competing philosophies of science, and asks if they “work” with a Christian faith based on the Bible. Featuring the work of over 140 international contributors, the Dictionary of Christianity and Science is a deeply-researched, peer-reviewed, fair-minded work that illuminates the intersection of science and Christian belief.

Author Gerald L. Schroeder (widely known for converting atheist Anthony Flew to a Deist), Number 5 here was what convinced Flew. It's worth pointing out though that he conforms his theories to the current scientific paradigm of the age of the universe and strives for compatability when it comes to other areas like Pre-Adamite cave men. He is strongly against evolution and lays out why very thoroughly in his books. He is also Jewish.

The Structure of Scientific Revolutions by Thomas S. Kuhn. Kuhn makes a well-reasoned argument that science is not an objective search for "truth," as many people believe. Instead, "normal science" is a problem solving endeavor, solving known problems by known methods. Science only changes the rules by which it operates (its "paradigm" - that over-used and often misused term in contemporary language) only when the current paradigm causes more problems than it solves. This is the real answer to any from any field who say, "The science is settled. There is no room for discussion." Those who make that statement need to re-read Kuhn and come to grips with the reality that all knowledge is inevitably socially constructed.

https://answersingenesis.org/answers/ An excellent resource that looks seriously at natural phenomenon in light of Scriptural revelation. They attempt to meet the skeptics own burden of proof by using established scientific methods. An important claim of theirs is that evidence always has to be interpreted. In the evolution vs. creationism debate for instance, there is no such thing as evidence with big bright letters stating that "this is a transitional fossil". There are not creationist fossils and evolutionist fossils, but there are creationist and evolutionist interpretations of the fossils. Charles Darwin himself made this point. In the introduction to The Origin of Species, he stated, “I am well aware that scarcely a single point is discussed in this volume on which facts cannot be adduced, often apparently leading to conclusions directly opposite to those at which I arrived.” Darwin was willing to admit that interpretation was key to choosing a belief. One scientist might view a particular fact as supportive of naturalism; another scientist might view that same fact as supporting creationism. I'd also point out the difficulty in in defending the young earth stance as it requires you to lay out all the arguments exhaustedly (which answersingenesis has done). Not only do you have to call into question the current scientific viewpoints but you also have to put forward the alternative theories. You have to do all this while your debate opponent can just sit back and appeal to authority and the current scientific consensus.

When Skeptics Ask by Norman Geisler and Ronald Brooks. Contains a good general overview of science and Christianity along with some other great chapters that answer quite a few questions that have been brought up by biblical skeptics.

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

Because Reddit leans liberal, and most Christians have not done a deep dive into the philosophy of science, they accept evolution without much thought. That's why you see them promoting people like Christian Francis Collins who created Biologos.com and attempts to reconcile Biblical narrative with evolution. Never mind that the attempts of Dr. Collins are thwarted by Scripture contradicting the evolutionary timeline.

It's important for people to realize that science is based on axiomatic assumptions that requires faith. These assumptions turn into glaring flaws when trying to develop truths about the past like macroevolution and should significantly reduce the certainty one has regarding it.

It's also important to remember that the Bible is not written as a scientific document using the standards of our own recent methodology (the scientific method). Over history what we have seen are Christian's assumptions of the world that we live in by taking (often times vague) verses from Scripture and interpreting them. A good rundown of this is here. http://www.ligonier.org/blog/what-rc-sprouls-position-creation/

For a more exhaustive (but not complete) overview of books related to intelligent design, see this page. It's worth noting though that like Natural Theology, some intelligent design authors get you only half way there (i.e.. Theism). The rest would have to be done by studying comparative religion.

Math

• Multivariable Calculus
  
  
• Differential Equations
  
  
• Linear Algebra
  
  You have to know those three pretty well to start. You pick up some more math along the way as needed, but that's the bulk of it.
  
  Physics
  
  
• Classical Mechanics (basic, Newtonian)
  
  
• Electrostatics
  
  
• Electrodynamics
  
  
• Basic Quantum maybe. It's not necessiry for Lagrangians/Hamitonians but it's very cool stuff and you get to see Lagrangians/Hamiltonians in more action (oops, I made a pun...).
  
  
• Special Relativity
  
  More Math
  
  
• "Old school" differential geometry and Reimannian geometry. They both show up a lot, but Reimannian is more common in more advanced stuff. And notation starts to become more important
  
  
• Tensors (which comes with Reimannian geometry, but they're worth mentioning by themselves cuz they're important)
  
  
• Calculus of Variations
  
  
• Misc: Taylor Series, Taylor Series, Taylor Series. Basic Fourier Analysis and complex numbers.
  More physics
  
  
• Analytic Mechanics ("advanced" class mech/Lagrangian & Hamiltonian dynamics)
  
  
• General Relativity
  
  Some books
  
  
• Class Mech: Kleppner/Kolenkow for Newtonian stuff, Marian&Thornten for more basics and a pretty good intro to calculus of variations and Lagrangians/Hamiltonians. Both these have chapters on Special Relativity too.
  
  
• Griffiths E&M for E&M (first half of book is statics, second half is dynamics)
  
  
• Quantum: J.S. Townsend's A Modern Approach to QM
  
  
• General Relativity: I used Hartle's Gravity. It's good, but I had two or three major beefs with it. I've also heard Sean Carrol's book is good.
  
  
• This series. Fair warning though, those are very advanced and are more of a reference for professors than an actual book to learn by.
  
  
• This Math Methods in physics book is very nice.
  
  I come from a physics background so I'm familiar with a lot of this stuff. I'll let people better in the know suggest the relevant math books.
  
  It's a long road but well worth it in my opinion. Good luck.

Hey! This comment ended up being a lot longer than I anticipated, oops.

My all-time favs of these kinds of books definitely has to be Prime Obsession and Unknown Quantity by John Derbyshire - Prime Obsession covers the history behind one of the most famous unsolved problems in all of math - the Riemann hypothesis, and does it while actually diving into some of the actual theory behind it. Unknown Quantity is quite similar to Prime Obsession, except it's a more general overview of the history of algebra. They're also filled with lots of interesting footnotes. (Ignore his other, more questionable political books.)

In a similar vein, Fermat's Enigma by Simon Singh also does this really well with Fermat's last theorem, an infamously hard problem that remained unsolved until 1995. The rest of his books are also excellent.

All of Ian Stewart's books are great too - my favs from him are Cabinet, Hoard, and Casebook which are each filled with lots of fun mathematical vignettes, stories, and problems, which you can pick or choose at your leisure.

When it comes to fiction, Edwin Abbott's Flatland is a classic parody of Victorian England and a visualization of what a 4th dimension would look like. (This one's in the public domain, too.) Strictly speaking, this doesn't have any equations in it, but you should definitely still read it for a good mental workout!

Lastly, the Math Girls series is a Japanese YA series all about interesting topics like Taylor series, recursive relations, Fermat's last theorem, and Godel's incompleteness theorems. (Yes, really!) Although the 3rd book actually has a pretty decent plot, they're not really that story or character driven. As an interesting and unique mathematical resource though, they're unmatched!

I'm sure there are lots of other great books I've missed, but as a high school student myself, I can say that these were the books that really introduced me to how crazy and interesting upper-level math could be, without getting too over my head. They're all highly recommended.

Good luck in your mathematical adventures, and have fun!

Overviews of the evidence:

The greatest show on earth

Why evolution is true

Books on advanced evolution:

The selfish gene

The extended phenotype

Climbing mount improbable

The ancestors tale

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

I will hit one point though.

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

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

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

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

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

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

I would guess that career prospects are a little worse than CS for undergrad degrees, but since my main concern is where a phd in math will take me, you should get a second opinion on that.

Something to keep in mind is that "higher" math (the kind most students start to see around junior level) is in many ways very different from the stuff before. I hated calculus and doing calculations in general, and was pursuing a math minor because I thought it might help with job prospects, but when I got to the more abstract stuff, I loved it. It's easily possible that you'll enjoy both, I'm just pointing out that enjoying one doesn't necessarily imply enjoying the other. It's also worth noting that making the transition is not easy for most of us, and that if you struggle a lot when you first have to focus a lot of time on proving things, it shouldn't be taken as a signal to give up if you enjoy the material.

This wouldn't be necessary, but if you like, here are some books on abstract math topics that are aimed towards beginners you could look into to get a basic idea of what more abstract math is like:

• theoretical computer science (essentially a math text)
  
  
• set theory
  
  
• linear algebra
  
  
• algebra
  
  
• predicate calculus
  
  Different mathematicians gravitate towards different subjects, so it's not easy to predict which you would enjoy more. I'm recommending these five because they were personally helpful to me a few years ago and I've read them in full, not because I don't think anyone can suggest better. And of course, you could just jump right into coursework like how most of us start. Best of luck!
  
  (edit: can't count and thought five was four)

Indeed; you may feel that you are at a disadvantage compared to your peers, and that the amount of work you need to pull off is insurmountable.

However, you have an edge. You realize you need help, and you want to catch up. Motivation and incentive is a powerful thing.

Indeed, being passionate about something makes you much more likely to remember it. Interestingly, the passion does not need to be a loving one.

A common pitfall when learning math is thinking it is like learning history, philosophy, or languages, where it doesn't matter if you miss out a bit; you will still understand everything later, and the missing bits will fall into place eventually. Math is nothing like that. Math is like building a house. A first step for you should therefore be to identify how much of the foundation of math you have, to know where to start from.

Khan Academy is a good resource for this, as it has a good overview of math, and how the different topics in math relate (what requires understanding of what). Khan Academy also has good exercises to solve, and ways to get help. There are also many great books on mathematics, and going through a book cover-to-cover is a satisfying experience. I have heard people speak highly of Serge Lang's "Basic Mathematics".

Finding sparetime activities to train your analytic and critical thinking skills will also help you immeasurably. Here I recommend puzzle books, puzzle games (I recommend Portal, Lolo, Lemmings, and The Incredible Machine), board/card games (try Eclipse, MtG, and Go), and programming (Scheme or Haskell).

It takes effort. But I think you will find your journey through maths to be a truly rewarding experience.

Thank you for your response and for the citation of the text.

As I argued above from multiple texts across the Old Testament, slaves were to be treated as human beings. To take Leviticus 25:44 which belongs to the same body of work as contradictory to the other texts above (where I also noted that slaves were allowed to be taken in war), due to vesting a modern notion of “being property” into the text is to interpret anachronistically. To point it out from the 10 commandments as you ask:

> “but the seventh day is the Sabbath of the LORD your God. On that day you must not do any work, you, your son, your daughter, your male slave, your female slave, your ox, your donkey, any other animal, or the foreigner who lives with you, so that your male and female slaves, ‘like yourself’, may have rest. Recall that you were slaves in the land of Egypt and that the LORD your God brought you out of there by strength and power. That is why the LORD your God has commanded you to observe the Sabbath day.”
(Deut 5:14–15 NET)

Consider this as well: Israel has the law and knows the true God. If you are a slave there are many harsh places in the world that you could go, but if you go to Israel you have legal protections, and become acquainted with God.

Regarding applying moral notions to God, I wrote above. God doesn’t reserve rights for himself so much as dispense any rights anyone else has. That’s the Creator/Creature distinction.

Regarding DNA and paleontology, draw what conclusions fit with what is authoritative for you according to your worldview. Read Structure of Scientific Revolutions by Thomas Kuhn. For myself, science is great as natural revelation filling in special revelation, but something subject to paradigm shifts is shaky foundation for a philosophical basis.

Regarding Adam & Noah, forgive my simplicity but Jesus believed them (Matt 19:4-5; Matt 24:37-39), and I trust him more than any man’s guesses since he’s God and he made them. I am still in r/Christianity right? This is the right place to post this? If you rather believe that you are assessing science’s assessment of the data correctly (layered as that is from the original data), that’s your decision.

As I said in another comment on this post, once we get off the Christian concept of God what is even the point of considering the OP’s question? I mean if Jesus isn’t God, Adam & Noah aren’t real, the Bible isn’t an accurate account of God, then what does it even matter if God can deceive or not, seeing as such a being likely doesn’t exist anyway?

The question only matters within the context of Scripture: does Scripture present a God who is indistinguishable from the devil? The answer is no. If we are going to be picky about what Scripture we are allowed to inform that interpretation by invoking science, why not just invoke science to disallow the concept of God and be done? If you want to debate the Bible’s reliability there are places for that, but that wasn’t the original question.

Thanks for reading. Let me know if I can clarify

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

Sagan

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

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


Dawkins

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


Hofstadter

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


Feynman

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

Burke

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

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

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

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

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

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

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

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

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

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

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

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

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

Happy reading!

edit: Also, check out the Reasonable Doubts podcast.

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.

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

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

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

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

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

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

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'm not a professional in the field, but my favorite free-time science books are usually focused on evolutionary biology, so here goes. One of the best discussions on this particular topic I've read is in The Ancestor's Tale by Dawkins. It's an excellent 3-page discussion you can read in full by accessing the "Look Inside!" preview of the book on Amazon (link to book page) and scrolling to the bottom of page 430. Do this by searching for "Maynard Smith" and clicking on the result on page 430. You'll need to sign in in order to search.

Anyways, I'll try to summarize the discussion here (although I'm a huge fan of Dawkins' eloquence in this book so I'm afraid I won't do it much justice). At a fairly naive level, sex is an evolutionary paradox. Modern Darwinism says that every organism strives to pass on as many of its genes as possible to its offspring. If this is true, however, why does sex, which is basically throwing away half of your own genes and mixing them with half of those of some other stranger, make any sense? An asexual organism can pass on 100% of its genes to its offspring. A sexual organism can only pass on 50%.

And yet, sexual reproduction is pretty much the norm for multi-cellular organisms. This suggests that the "twofold" cost of sex is somehow "cancelled out" by some other advantage of having two parents. One possibility is if the male commits to the child (instead of just running off to have sex with some other female), the couple can, as a group, produce at least twice as many offspring as the asexual alternative. While it is true that the male puts as much effort into child-rearing as the female in a few species, (emperor penguins, for instance), it is by no means the norm. So there must be something else going on.

Genetic recombination Dawkins hesitates to say that it alone is sufficient to counteract the massive twofold cost of sex, but it is definitely a factor.

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

After this Dawkins makes some points that are very interesting but not totally relevant to your question, so I'll just summarize it very quickly. High school biology teaches us that genetic recombination introduces diversity and variety to the gene pool. Dawkins makes the point that sexual reproduction simultaneously has the opposing effect as well because it introduces the very concept of a gene pool. Think about it: an asexual organism shares none of its genes with its brethren. The very idea of a gene pool is nonsensical. In fact, you could say every new creature is a separate species because from that moment on, it's evolutionary path is completely different from that of its brother or sister. Yes, sexual reproduction, through the process of genetic recombination potentially allows for greater diversity and variety. But sexual reproduction introduces a gene pool that tends to diffuse the effects of genetic recombination. Gene pools have a massive "inertia" that a single wayward member cannot easily change. Dawkins forwards this not necessarily as a benefit of sex, but rather a consequence of it.

You should start with using your finder scope, so make sure it's aiming correctly, this is very important and will save you time later! I would also highly recommend a book like Turn Left at Orion. Its a great book to teach you how to find things, plus its a great guide on the best things to find year round.

For finding things you can't see, you use finder stars, starting with a star you can see and using the finder scope to jump from star to star on a path to your target.

However, you mentioned wanted to view planets, most of those will be visible to the naked eye during different parts of the year, Jupiter in particular is lovely and bright right now. Stellarium is an excellent tool to find out whats visible in your area at any time.

Of course, things are more difficult if you live in an urban area with loads of light pollution, this link might help you more with that.

If you have more questions, /r/telescopes or /r/Astronomy might be able to help you out more than I can.

Good Luck and dark skies!

Perhaps a lot will be clearer if you get the quantum nature of the measurement of light's polarization. Classically, light is a transverse electromagnetic wave. When one measures a photon's polarization it assumes a definite value, i.e. some orientation. To say that light is unpolarized means that all electric field directions of every photon in a beam will have equal probability to be measured. If the light is polarized then it can be measured in one of only two states. "Circular polarization" means each possible state is described by a plane waves of equal amplitude but differing in phase by 90°. If the light is "elliptically polarized" then it's unmeasured state is described by two simultaneous plane waves of differing amplitude related in phase by 90°. It can also be called elliptically polarized if the amplitudes of the two states are equal but the relative phase is other than 90°. So an unpolarized beam of photons say, or a single photon with a polarization at some angle relative to your measuring polarizer say, is not split into two when sent through a polarizer, rather each photon takes one path or another according to probability.



Concerning your next group of questions about how light propagates through dielectric solids like glass... There is only free propagation, absorption, and scattering. Scattering can be either elastic or inelastic. Scattering theory is a rich subject because materials are so diverse in composition. The most common form of scattering in isotropic media like the atmosphere and dielectric solids composed of small molecules is an elastic form of scattering called Rayleigh scattering. Rayleigh scattering occurs when a photon penetrates into a medium composed of particles whose sizes are much smaller than the wavelength of the incident photon. In this scattering process, the energy (and therefore the wavelength) of the incident photon is conserved and only its direction is changed. Rayleigh scattering has a simple classical origin: the electrons in the atoms, molecules or small particles radiate like dipole antennas when they are forced to oscillate by an applied electromagnetic field. This is not an absorption and re-emission. If the scattering sources are stationary, then this secondary radiation is phase locked to the driving electromagnetic field. So perhaps this is what you mean by "coherent transmission". But even for a truly coherent source of photons, from a laser say, the coherence length is shorted by the presence of the dielectric.



Lastly, your bonus question... You need to read Richard Feynman's, QED: The Strange Theory of Light and Matter. Light propagates as a wave, even single photons. It therefore takes all possible paths, not just the path of least time! It's just that only those paths which arrive at the detector in phase will result in a non-zero amplitude. And for a single ray of light passing from one isotropic medium to another of different index of refraction, there is only one path that satisfies that condition, the path of least time. Anyway, you will love the book and will come away understanding light much better.

Hey! I am a math major at Harvey Mudd College (who went to high school in the Pacific NW!). I'll answer from what I've seen.

1. There seems to be tons. At least I keep being told there are tons! My school has a lot of recruiters come by who are interested in math people!
   
   
2. I can definitely recommend HMC, but I would also consider MIT, Caltech, Carnegie Melon, etc. I've heard UW is good, too!
   
   
3. Most all of linear algebra is important later on. I will say that many texts treat linear algebra the same as "matrix algebra", which it is not. Linear algebra is much more general, and deals with things called vector spaces. Matrix algebra is a specific case of linear algebra. If you want a good linear algebra text (though it might be a bit difficult), check out http://www.amazon.com/Linear-Algebra-Right-Sheldon-Axler/dp/0387982582
   
   End: Also, if you wanna learn something cool, I'd check out Discrete math. It's usually required for both a math or CS major, and it's some of the coolest undergraduate math out there. Oh, and, unlike some other math, it's not terrible to self-teach. :)
   
   Good luck! Math is awesome!

The evidence is all around us. Start with the fact that, by helping to focus the process of natural selection, we generated broccoli, cabbage, cauliflower and kale from a wild mustard plant known as Brassica oleracea. Similarly, all dog breeds are descendents of a small population of wolves. In the end, though, to get a handle on the specificity, power, scope and sheer quantity of evidence you (and she) will need to dig a little deeper into the subject.

That being said, if you're interested in a (relatively) quick explanation of what Evolutionary Theory actually is (and a little of the evidence for it) I'd suggest Evolution in Cartoon Form by Darryl Cunningham. It's long for a cartoon, but amazingly short for the number and depth of ideas about evolution it conveys.

Why Evolution is True by Jerry Coyne is an excellent book, written for general audiences with an interest in science, which lays out the evidence clearly and concisely. I'd suggest it as a good place to start. Dawkins' Greatest Show On Earth is also great and I personally prefer his writing style.

But if you're going to go with Dawkins, I can't help but also suggest The Blind Watchmaker. It's purpose isn't so much to provide all the evidence for evolution, but more to explore the underlying philosophy, implications and further insights which stem from the fact of evolution.

Becoming educated about evolution is a great ride, but its full impact might not be available in a quick, easy format.

Hope this helps. Have a blast.

Edit: I'd also like to second Loki5654's suggestion of Talk Origins.

I second the reading idea! Ask your history or science teachers for suggestions of accessible books. I'm going to list some that I found interesting or want to read, and add more as I think of them.

A short history of nearly everything by Bill Bryson. Title explains it all. It is very beginner friendly, and has some very entertaining stories. Bryson is very heavy on the history and it's rather long but you should definitely make every effort to finish it.

Lies my teacher told me

The greatest stories never told (This is a whole series, there are books on Presidents, science, and war as well).

There's a series by Edward Rutherfurd that tells history stories that are loosely based on fact. There are books on London and ancient England, Ireland, Russia, and one on New York

I read this book a while ago and loved it- Autobiography of a Tibetan Monk It's about a monk who was imprisoned for 30 years by the Chinese.

The Grapes of Wrath.

Les Misérables. I linked to the unabridged one on purpose. It's SO WORTH IT. One of my favorite books of all time, and there's a lot of French history in it. It's also the first book that made me bawl at the end.

You'll also want the Adventures of Tom Sawyer, To Kill a Mockingbird, The Great Gatsby, The Federalist Papers.

I'm not sure what you have covered in history, but you'll definitely want to find stuff on all the major wars, slavery, the Bubonic Plague, the French Revolution, & ancient Greek and Roman history.

As for science, find these two if you have any interest in how the brain works (and they're pretty approachable).
Phantoms in the brain
The man who mistook his wife for a hat

Alex and Me The story of a scientist and the incredibly intelligent parrot she studied.

For a background in evolution, you could go with The ancestor's tale

A biography of Marie Curie

The Wild Trees by Richard Preston is a quick and easy read, and very heavy on the adventure. You'll also want to read his other book The Hot Zone about Ebola. Absolutely fascinating, I couldn't put this one down.

The Devil's Teeth About sharks and the scientists who study them. What's not to like?

Not exactly concrete, but several years ago I read a book called The Cosmic Serpent: DNA and the Origins of Knowledge.

The name of this thread reminded me of it, and I came here to share the recommendation with anyone interested.

Long story short (please read the book if you're interested) an anthropologist goes into South America, connects with a disconnected remote tribe, begins to study their... well, everything.

For instance, Ayahuasca has an extremely complex preparation procedure, involving a root from one and bark of another plant, combinations of drying and heating, etc. and if the process is not properly completed, you can end up with a toxic brew instead of your hallucino-spirit drug.

When our author would ask how they came to such a complex and seemingly random process, the shaman told him "The plants told us."

He starts to take such answers at face value, and draws some very interesting and awesome theories. The book is a great read, especially for a skeptic.

Relevant: The paintings and art of the shaman this particular anthropologist was involved with were very, very clearly (in some instances) depictions of micro-biological constructs. Here a mitochondria, there a cell wall, here some proteins, etc.

The ultimate "theory" posed by the book involves the idea that DNA is a language commonly "spoke" by all living organisms, and that there are ways to tap into that level of language to communicate on a more literal level.

Not... concrete, but still very interesting, and scientific in nature. :)

When I was his age, I read a lot of books on the history of mathematics and biographies of great mathematicians. I remember reading Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem.

Any book by Martin Gardner would be great. No man has done as much to popularize mathematics as Martin Gardner.

The games 24 and Set are pretty mathematical but not cheesy. He might also like a book on game theory.

It's great that you're encouraging his love of math from an early age. Thanks to people like you, I now have my math degree.

Maybe a bit off topic, but I think that if you have a "math phobia" as you say, then maybe you need to find a way to become interested in the math for math's sake. I don't think you'll be motivated to study unless you can find it exciting.

For me, The Universal History of Numbers was a great book to get me interested in math. It's a vast history book that recounts the development of numbers and number systems all over the world. Maybe by studying numbers in their cultural context you'll find more motivation to study, say, the real number system (leading to analysis and so on). That's just an example and there are other popular math books you could try for motivation (Fermat's Enigma is good).

Edit: Also, there are numerous basic math books that are aimed at educated adults. Understanding Mathematics is one which I have read at one point and wasn't bad as far as I can remember. I am sure there are more modern, and actually for sale on Amazon, books on this topic though.

I wanted to listen to part 2 before commenting.

I always love these dialogues. My particular fixation is with the collection of data, so this feeds my particular flavor of existence quite well.

As for content, this was my introduction to the term "pansychism" - even if I've previously been aware of the idea. So, thanks for that. I'm curious if you've read "The Cosmic Serpent" (https://www.amazon.com/Cosmic-Serpent-DNA-Origins-Knowledge/dp/0874779642)? It's an interesting panpsychic exploration of DNA instigated by an anthropologist's shamanic/psychedelic experience. Worth a read.

I'm also still digesting "neo-nihilism". Interesting idea, initially. Your conversation with Peter is a great example of why I've completely fallen in love with "psychedelic philosophy". Nothing is off limits, everything should be explored.

Thank you for bringing more of the exploratory spirit to us. Looking forward to more from you.

Edit: I LOVE your logo as well! Such a clean way to bring the yin/yang, forbidden fruit, and ouroboros out.

1. I found this article trying to answer the same question. I was looking at the stars the other night, and wondering if I was seeing photons directly from the star, or if I was really seeing photons emitted from the atoms in the air directly above my eyes. Maybe they pass between the atoms in the air, because atoms in gasses are distant compared to massless photons, I thought.
   
   I have been googling for the past hour and I think they are absorbed, but they are emitted with more-or-less the same wavelength, resulting in more-or-less the same image.
   
   Photons travel at c between the atoms, but the absorption and emission causes an average slower speed, and thus a bend in its path. From the linked article:
   
   > By "absorption" I mean that the energy of the photon causes an electron of
   the atom to be kicked to a higher energy level, and the photon ceases to
   exist. Then, after a very small time delay, the electron goes back to its
   original (usually ground state) energy and "emits" a photon of the same
   energy (and thus same frequency and thus same wavelength) as the original
   "absorbed" photon.
   
   So to answer your question, yes, refraction is absorption->emission. The article in OP sorta glosses over this, ("This is not due to gravity, but refraction as the lens of our air slants its path before its final plummet to the nighttime country-side below.") perhaps to keep the theme of following one photon on its journey. From what I've read online, a good resource for more info on this is QED: The Strange Theory of Light and Matter by Richard Feynman.
   
   I think my original question is more of philosophical identity (is it really the "same" photon?) than of physics.
   
   
2. The author used "burn" in the less literal definition: use (a type of fuel) as a source of heat or energy.
   
   
3. The video in this article shows what an observer might see while traveling at near the speed of light. So basically, nothing--your whole field of view collapses into a single point. Also, this game made with/by MIT shows how you might experience the world as you artificially lower c. And it's actually pretty fun. This doesn't answer the frozen in time bit, however...
   
   
4. This r/askscience post's answers generally seem to say that no time passes for a photon. However, they also stress that a "photon's reference frame" isn't a valid concept. I wanted to know why and I think the answer is in this wikipedia article about time dilation. It shows the formula for calculating the time elapsed for an observer moving at very high speed relative to a "stationary" observer. Basically, you divide the stationary time by the square root of 1-(velocity^2 / speedoflight^2 ).However if v=c, then v^2 / c^2 = 1, 1-1=0, the square root of 0=0, and you're now dividing by 0... which is probably why it's said that photons have no reference frame.
   
   Thanks for asking these questions, because I learned a lot in researching the answers lol. All this info made the original article seem even less science-based, but I still think it illustrates the awesome forces at work in this stellar hobby.

Thanks! :) That's a really good idea to wait until you are ready as mindset and intention matter quite a bit.

General Information:

/r/Ayahuasca

-http://forums.ayahuasca.com/

-good forum with general knowledge

-https://www.dmt-nexus.me/forum/
while it's mostly dmt centered, this is probably the best entheogen community online. Has some good writeups on Ayahuasca and DMT visuals are often pretty similar to Ayahuasca since it's the same chemical in most brews(n,n dmt). Breakthrough visuals are much more common on DMT but healing is rarer in my experience.

https://ayaadvisors.org/

Great review site for retreat centers. There are more in the US, especially if you look around.

Books:

The Cosmic Serpent

The Ayahuasca Test Pilot's Handbook

As for posts, this one from dmt nexus is a good primer:

https://www.dmt-nexus.me/forum/default.aspx?g=posts&t=8972


Hopefully that's enough to at least get the ball rolling. Feel free to reach out if you have any questions!

2 good books to get you set:

1. 'Nightwatch' by Terence Dickinson :
   This will get you oriented with everything astronomy.
   
   http://www.amazon.com/NightWatch-Practical-Guide-Viewing-Universe/dp/1552093026
   
   
2. 'Turn Left at Orion' :
   This book will show you how to actually find nebulae, double stars, and galaxies in the night sky. It will also show you what each looks like through the eyepiece of an amateur telescope.
   
   http://www.amazon.com/Turn-Left-Orion-Hundred-Telescope/dp/0521781906
   
   *You can probably find the e-book version of each of these online if you look. But then again, having a physical book in front of you is 10x better.
   
   
   
   
3. Software
   
   Stellarium :
   Pretty much a software planetarium thats free. All you have to do is type in your location and it'll show you exactly whats in your sky at the moment. Three useful keyboard buttons: 'pg up' = zoom in, 'pg down' = zoom out, 'n' = shows deep sky object locations.
   
   http://www.stellarium.org/
   
   Last but not least:
   Try to get yourself a used dobsonian telescope (8 inch or 6 inch). You can definitely get one for $200 used. Its a good investment b/c its something that lasts a lifetime and it retains its value extremely well. Remember astronomy is about actually seeing and experiencing the sky, and not just learning about it from a book.
   
   Hope you get hooked on astronomy like I did last year.

Yes. From "The High Frontier", a book on making space colonies, you could deflect meteors - even nonmetallic - from a colony with an electric field. It required a charge of about two gigavolts to be maintained across the whole of it.

This is costly. And any visiting craft would have to be neutralized relative to whatever charge the colony holds.

Just coating a colony in slag is pretty good; sure, spin up will be harder, but... well, reasons previously listed.

I'm reminded of a conversation a friend had with me; a force field is basically something that would repel an object from contact with the field, right? And you'd need some sort of stabilizing element, right? Something spread across the whole field, probable uniformly?

Something like atoms?

What with the nucleus holding it together and the electrons around it providing the desired electric field?

Yeah. A sheet of strong plastic is essentially a force field.

BUT, that's not nearly as cool.

So you could make an electric field strong enough to repel something moving like a meteor, but... well, here's food for thought. Cathode ray TV's and monitors operate at 35Kv or lower. And they are designed to fail if they over voltage, because they shoot beams of electrons through/at a metal screen, and would deliver X-rays to the viewer if they didn't have such circuits.

Why did you think they were made of lead/strontium glass? Rhetorical question, it's to not irradiate the user.

So, having metal buttons on your person may well enough end up giving you cancer. Not so bad if it's your only choice, or you have a short time to live anyway.

Now, maybe if you could entrap differently charged ions in two fields layered over each other, you'd just need like, a mesh to generate and hold the fields, and then when an object passes through the fields, it'd explosively short it. Sorta like ablative armor but... This may still end badly for the user. Layer it, perhaps?

We do have a very good understanding of electricity on the atomic level; Quantum Electro Dynamics. Feynman wrote a really great introduction to it - he was a great teacher, and was one of the inventors of the theory. It's called "QED: The Strange Theory of Light and Matter".

Gravity is also pretty solid; Laplace fixed our understanding of orbital mechanics in the Napoleonic age. Whooole lot of differential equations there.

I've heard people recommend Kiselev's Geometry, on a physics forum. Warning, though; Kiselev's Geometry series(in English) is translated from Russian.

Here's the link to where I got all these resources(I also copy-pasted what's in the link down below; although, I did omit a few entries, as it would be too long for this reddit comment; click the link to see more resources):

https://www.physicsforums.com/insights/self-study-basic-high-school-mathematics/

__

Note: Alternatively, you can order Kiselev's geometry series from http://www.sumizdat.org/

Geometry I and II by Kiselev

http://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202

http://www.amazon.com/Kiselevs-Geometry-Book-II-Stereometry/dp/0977985210

> If you do not remember much of your geometry classes (or never had such class), then you can hardly do better than Kiselev’s geometry books. This two-volume work covers a lot of synthetic (= little algebra is used) geometry. The first volume is all about plane geometry, the second volume is all about spatial geometry. The book even has a brief introduction to vectors and non-Euclidean geometry.

The first book covers:

• Straight lines
  
  
• Circles
  
  
• Similarity
  
  
• Regular polygons and circumference
  
  
• Areas
  
  The second book covers:
  
  
• Lines and Planes
  
• Polyhedra
  
• Round Solids
  
• Vectors and Foundations
  
  > This book should be good for people who have never had a geometry class, or people who wish to revisit it. This book does not cover analytic geometry (such as equations of lines and circles).
  
  ____
  
  

  Geometry by Lang, Murrow
  

  
  http://www.amazon.com/Geometry-School-Course-Serge-Lang/dp/0387966544
  
  > Lang is another very famous mathematician, and this shows in his book. The book covers a lot of what Kiselev covers, but with another point of view: namely the point of view of coordinates and algebra. While you can read this book when you’re new to geometry, I do not recommend it. If you’re already familiar with some Euclidean geometry (and algebra and trigonometry), then this book should be very nice.
  
  The book covers:
  
  

• Distance and angles
  
  
• Coordinates
  
  
• Area and the Pythagoras Theorem
  
  
• The distance formula
  
  
• Polygons
  
  
• Congruent triangles
  
  
• Dilations and similarities
  
  
• Volumes
  
  
• Vectors and dot product
  
  
• Transformations
  
  
• Isometries
  
  > This book should be good for people new to analytic geometry or those who need a refresher.
  
  > Finally, there are some topics that were not covered in this book but which are worth knowing nevertheless. Additionally, you might want to cover the topics again but this time somewhat more structured.
  
  > For this reason, I end this list of books by the following excellent book:
  
  

  Basic Mathematics by Lang
  

  
  http://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877
  
  > This book covers everything that you need to know of high school mathematics. As such, I highly advise people to read this book before starting on their journey to more advanced mathematics such as calculus. I do not however recommend it as a first exposure to algebra, geometry or trigonometry. But if you already know the basics, then this book should be ideal.
  
  

• The book covers:
  
  
• Integers, rational numbers, real numbers, complex numbers
  
  
• Linear equations
  
  
• Logic and mathematical expressions
  
  
• Distance and angles
  
  
• Isometries
  
  
• Areas
  
  
• Coordinates and geometry
  
  
• Operations on points
  
  
• Segments, rays and lines
  
  
• Trigonometry
  
  
• Analytic geometry
  
  
• Functions and mappings
  
  
• Induction and summations
  
  
• Determinants
  
  > I recommend this book to everybody who wants to solidify their basic knowledge, or who remembers relatively much of their high school education but wants to revisit the details nevertheless.
  
  _____
  
  More links:
  
  https://math.stackexchange.com/questions/34442/book-recommendation-on-plane-euclidean-geometry
  
  Note: oftentimes, you can find geometry book recommendations( as well as other math book recommendations) in stackexchange; just use the search bar.
  
  __
  
  https://www.physicsforums.com/threads/geometry-book.727765/
  
  https://www.physicsforums.com/threads/decent-books-for-high-school-algebra-and-geometry.701905/
  
  https://www.physicsforums.com/threads/micromass-insights-on-how-to-self-study-mathematics.868968/

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

To illustrate my point:

Linear Algebra:

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

Initially I'd avoid books on areas of science that might challenge her (religious) beliefs. You friend is open to considering a new view point. Which is awesome but can be very difficult. So don't push it. Start slowly with less controversial topics. To be clear, I'm saying avoid books that touch on evolution! Other controversial topics might include vaccinations, dinosaurs, the big bang, climate change, etc. Picking a neutral topic will help her acclimate to science. Pick a book related to something that she is interested in.

I'd also start with a book that the tells a story centred around a science, instead of simply trying to explain that science. In telling the story their authors usually explain the science. (Biographies about interesting scientist are a good choice too). The idea is that if she enjoys reading the book, then chances are she will be more likely to accept the science behind it.

Here are some recommendations:
The Wave by Susan Casey: http://www.amazon.com/The-Wave-Pursuit-Rogues-Freaks/dp/0767928857

Fermat's Enigma by Simon Singh: http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622

The Man who Loved Only Numbers by Paul Hoffman: http://www.amazon.com/Man-Who-Loved-Only-Numbers/dp/0786884061/ref=sr_1_1?s=books&ie=UTF8&qid=1405720480&sr=1-1&keywords=paul+erdos

I also recommend going to a book store with her, and peruse the science section. Pick out a book together. Get a copy for yourself and make it a small book club. Give her someone to discusses the book with.

After a few books, if she's still interested then you can try pushing her boundaries with something more controversial or something more technical.

Eh, first you have to read up on quantum mechanics and get a decent understanding of quantum mechanical spin and quantum numbers in general. Something like Shankar - Principles of Quantum Mechanics, though there are tons of textbooks on it. You won't really get into particle physics, but should read at least to the point of understanding addition of angular momentum and spin (typically in context of hydrogen atom).

Then a text on particle physics like Griffiths' Intro To Elementary Particle Physics. (You could also start Griffiths' Intro to QM).

You could also consult free resources like the particle data group, but their reviews will be largely gibberish if you don't understand the basics of QM / particle physics / group theory. (Articles like Quark Model, or Naming Scheme for Hadrons).

If you are looking at hobby-level interest without getting into any math/textbooks, the best I can suggest is Feynman's QED but it won't talk about isospin or hadrons or particle naming conventions but is a great layman introduction to quantum electrodynamics.

a. Stanford. But a lot of people who work with me did not go to big-name schools. UC Irvine, Iowa State, Oregon state, etc. Where I work, there's lots of UW. Where I used to work before that; lots of RPI and USC.

b. I got great grades in high school, but slipped a little bit in college. (This made my life difficult later. A good GPA makes it easier to be hired, and is practically necessary if you want a Masters, something that many many many engineers have today). Classes: I'm sure I'm not the first one to tell you this, but take all the math and physics you can. And try to learn some of this stuff outside of school (it can be more fun that way), pick up some books, try to get through the Feynman Lectures on Physics (or just Six Easy Pieces and QED to start off), some Martin Gardner, books like Euler's Gem, learn HTML, try your hand at programming, build LEGO robots... all that kind of stuff will make it easier to learn the stuff you need to learn to become an engineer.

Stop second-guessing your choice of major. Keep your eyes on what you actually want, and remember that the steps along the way will all build there eventually. Check in on your plans when you're picking classes each semester, to make sure you're still on course and still want that ultimate goal. The REU and some lab time will all help.

Try reading some science-related books, not actual science but stuff about scientists themselves or stories about specific scientific discoveries. Like The Immortal Life of Henrietta Lacks, Double Helix, Eighth Day of Creation, The Disappearing Spoon, and Surely You're Joking Mr. Feynman. Your school should have copies of most of them, and they aren't textbook-heavy (though not quite as light as fiction novels).

Don't forget to stay at least a little rounded. Someone on just about every recruitment weekend for grad school will ask about your hobbies. I'm pretty sure they're required to do so :) Or you'll discover you and your interviewer both do ceramics and can chat about that, leaving a stronger impression than if you were yet another person talking about science. It's good to be done with the requirements, but make sure you keep up something outside your major, even if it's just ultimate frisbee.

I've always heard good things about Edgar Rice Burrough's The Land that Time Forgot though I've sadly never read it myself. And, hey, it's free!

As far as science non-fiction, I consider A Short History of Nearly Everything to be absolutely essential since it covers so very much in a tremendously entertaining way. Also, if you are interested in physics but don't have any background in it I recommend any of Michio Kaku's books such as his latest Physics of the Future. He writes in an accessible manner that distills all the things that make the ongoing developments in physics exciting. I credit reading his books many years ago with getting me started in the sciences. Lastly, for learning about the universe, you can never go far wrong with Carl Sagan's Cosmos. It is easy to see from reading it why he is considered one of the greatest of the science popularizers.

Hi there,

For all intents and purposes, for someone your level the following will be enough material to stick your teeth into for a while.

Mathematics: Its Content, Methods and Meaning https://www.amazon.com/Mathematics-Content-Methods-Meaning-Volumes/dp/0486409163

This is a monster book written by Kolmogorov, a famous probabilist and educator in maths. It will take you from very basic maths all the way to Topology, Analysis and Group Theory. It is however intended as an overview rather than an exhaustive textbook on all of the theorems, proofs and definitions you need to get to higher math.

For relearning foundations so that they're super strong I can only recommend:

Engineering Mathematics
https://www.amazon.co.uk/Engineering-Mathematics-K-Stroud/dp/1403942463

Engineering Mathematics is full of problems and each one is explained in detail. For getting your foundational, mechanical tools perfect, I'd recommend doing every problem in this book.

For low level problem solving I'd recommend going through the ENTIRE Art of Problem Solving curriculum (starting from Prealgebra).
https://www.artofproblemsolving.com/store/list/aops-curriculum

You might learn a thing or two about thinking about mathematical objects in new ways (as an example. When Prealgebra teaches you to think about inverses it forces you to consider 1/x as an object in its own right rather than 1 divided by x and to prove things. Same thing with -x. This was eye opening for me when I was making the transition from mechanical to more proof based maths.)


If you just want to know about what's going on in higher math then you can make do with:
The Princeton Companion to Mathematics
https://www.amazon.co.uk/Princeton-Companion-Mathematics-Timothy-Gowers/dp/0691118809

I've never read it but as far as I understand it's a wonderful book that cherry picks the coolest ideas from higher maths and presents them in a readable form. May require some base level of math to understand

EDIT: Further down the Napkin Project by Evan Chen was recommended by /u/banksyb00mb00m (http://www.mit.edu/~evanchen/napkin.html) which I think is awesome (it is an introduction to lots of areas of advanced maths for International Mathematics Olympiad competitors or just High School kids that are really interested in maths) but should really be approached post getting a strong foundation.

> At first black holes were just a concept that was possible.

So, in order to repair your non sequitor, you have translated it to the 18th century. I would suggest that your example might have been improved had you chosen something relevant to modernity (see: M-theory).

> In 2010 a theory was published and peer reviewed that said that black holes could be wormholes to other universes. Scientist do not widely accept this or other alternate theories of black holes. They believe (because they cannot know) that black holes are collapsed stars.

Do you really believe that our understanding of black holes, or any topic of science, is a matter of taste? Do you really know so little of philosophy of science, and the practical establishment of scientific consensus?

> I do see secondary evidence [for theism] such as the universe, DNA, the precise strength of gravity to support life, the precise strength of the strong nuclear force to support life, the nearly unique properties of water.

Surely you can appreciate that a unifying characteristic of cosmogony, abiogenesis, and the origins of physical constants is scientific ignorance. So why are you so eager to connect that trait to your faith? Do you not understand how such a commitment is demonstrably hazardous to scientific literacy?

> My theory is that god exists and much like John Michell and Simon Pierre LaPlace in the 18th century I am waiting for science to catch up.

The mechanism by which science "catches up" is known as experiment.

What experiments could be performed to corroborate the existence of God?

English.
Cosmos is written By Carl Sagan. Amazon sure has it.
If not, google it. It's pretty popular/famous book.
 
I guess you're pretty young because you didn't recognize Carl Sagan.
Carl Sagan was american researcher, astronomer and educator, very famous in public because his involvement as host/narator for Cosmos TV Series.
The new Cosmos TV Series is being hosted by Neil deGrasse Tyson btw.
 

If you have finished Cosmos, read his sci-fi Novel "Contact"
Really good.
Ridiculously good.
Same book was adapted to movie with same title :
http://www.imdb.com/title/tt0118884/
Starring Jodie Foster, Matthew McConaughey

 
Interesting trivia:
Carl Sagan is also the one who design/head committee of Voyager Golden Record.
https://en.wikipedia.org/wiki/Voyager_Golden_Record
His legacy literally will go on forever, unless it bump into celestial object :)

 
I'm glad you found the beauty in old literature.
Huge fans of Agatha Christie myself.

 
edit (add Amazon link):
https://www.amazon.com/Cosmos-Carl-Sagan/dp/0345331354

The answer to this is much, much deeper than any of the comments so far. The answer to "How does" is not "4%". The answer is in Quantum Electrodynamics.

I have to run to work, and Richard Feynman is much better at explaining things than me, so I'll point you to his book QED which is dedicated to answering this question as a way to explain QED.

Sorry to have to run because this is fascinating, but to give an accurate answer that really hits on the principles behind it, takes about 20 pages from one of the smartest men who ever lived. I couldn't recommend the book more - it is accessible to anyone of reasonable intelligence willing to read it carefully, and unlocks one of the great mysteries of nature in an entertaining and exciting way.

> moving very slowly through time (i.e, the jiggling atoms are slower

Those are not the same thing. You're getting it backwards. Moving slowly through space doesn't mean you're moving slowly through time. It just means it takes longer to get to where you're going in space.

If you put a clock on an airplane, and you synchronize it with your watch, and then the airplane flies around the world, when it lands, your watch will have measured more elapsed time than the clock on the plane. (People have actually done this with atomic clocks, and it really happens.)

The movement of the airplane through space "uses up" some of its movement through time, so the airplane has moved through less time than you have while you were standing still. The clock (and everything else, like how hungry the passengers are) reflects this. Note that for an airplane, the difference is a tiny fraction of a second, but it's real and has to be compensated for in GPS satellites for example.

(Note that if neither of you speeds up or slows down, each of you is moving slower than the other, which is one of the weird things about relativity and why it's called "relativity".)

When you cool an object, the atoms move more slowly through space; that is correct. Their time doesn't slow down. Chemical reactions (like milk spoiling) progress more slowly, because it's less likely that when two molecules in the substance bump into them they're less likely to be going fast and hence bump together hard enough to react. Water evaporates more slowly when it's cold because any given water molecule getting to the surface is less likely to be going fast enough to pop free of the surface and into the air. But think about it like bumping two lumps of clay together: if you get the two lumps going faster, they're more likely to stick together.

If you make something very hot (like in a particle accelerator like the LHC) by making it move very fast, the time the particle experiences slows down, so a particle that would normally undergo radioactive decay in a billionth of a second sticks around long enough to see. The "cosmic rays" you sometimes hear about are particles coming in from space that only live a fraction of a second, but they're going so fast that their time is so slow (compared to ours) that they last long enough to get all the way from space down to the ground, several seconds.

Fun stuff.

If you want some basic normal every-day "here's how physics works" explained by the guy who won a Nobel prize for explaining to theoretical quantum mechanics theory guys how to understand quantum mechanics, try this: http://www.amazon.com/Six-Easy-Pieces-Essentials-Explained/dp/0465025277 No math involved.

If you want to learn why Einstein's relativity works the way it does, and you understand the Pythagorean Theorem about how long the sides of a right triangle are, try http://www.amazon.com/Six-Not-So-Easy-Pieces-Relativity-Space-Time/dp/B0009IINXE

Basically, if you understand https://www.youtube.com/watch?v=DxrlcLktcxU#t=32 you can understand why Relativity works the way it does. (Mind, you might not believe it... :-)

Forgive me if you already know this stuff and I'm just being confusing because I'm talking about it in a confusing way.

Don't skip proofs and wrestle through them. That's the only way; to struggle. Learning mathematics is generally a bit of a fight.

It's also true that computation theory is essentially all proofs. (Specifically, constructive proofs by contradiction).

You could try a book like this: https://www.amazon.com/Book-Proof-Richard-Hammack/dp/0989472108/ref=sr_1_1?ie=UTF8&qid=1537570440&sr=8-1&keywords=book+of+proof

But I think these books won't really make you proficient, just more familiar with the basics. To become proficient, you should write proofs in a proper rigorous setting for proper material.

Sheldon Axler's "Linear Algebra Done Right" is really what taught me to properly do a proof. Also, I'm sure you don't really understand Linear Algebra, as will become very apparent if you read his book. I believe it's also targeted towards students who have seen linear algebra in an applied setting, but never rigorous and are new to proof-writing. That is, it's meant just for people like you.

The book will surely benefit you in time. Both in better understanding linear algebra and computer science classics like isomorphisms and in becoming proficient at reading/understanding a mathematical texts and writing proofs to show it.

I strongly recommend the second addition over the third addition. You can also find a solutions PDF for it online. Try Library Genesis. You don't need to read the entire book, just the first half and you should be well-prepared.

I think the best answer is: since photons don't come with nametags, there's no way to tell, but in most cases, the light behaves as if it's the same photon. There are however some properties of light (diffraction, for instance) where thinking of each point in space as a source of new photons is useful.

For extra credit: the same is true of matter.

Not 100% related, but for more on this sort of thing check out Richard Feynman's short book "QED: The Strange Theory of Light and Matter". It's intended for ordinary laypeople, which says a lot about Feynman's confidence in laypeople, but it's great for the dedicated reader.

You might try here: http://www.reddit.com/r/askscience/search?q=fact&restrict_sr=on

and then ctr+F for "evolution" for a few previous instances of this question, or here:


http://www.reddit.com/r/askscience/search?q=evolution+fact&sort=top&restrict_sr=on

or other variations thereupon.

Anyways, we don't make a habit of letting these questions out all that often, as they never really do well, and when they do attract attention it's mostly people who don't really understand evolution all that well, trying to explain evolution to people who definitely don't understand it that well, and it just never really winds up being productive (while those of us who do know something about evolution squirm in agony at even attempting to undue all the damage this whole "fact vs theory" thing in a somewhat concise manner).

I'm keeping it spammed (you could also try searching in /r/evolution), but my honest suggestion would be to have her read something like Jerry Coyne's Why Evolution is True, if she's willing to (and perhaps you could sit down and read it yourself first, to be able to give it an honest recommendation). Alternatively Dawkins's The Greatest Show on Earth is supposed to be good (I haven't read it myself), although Coyne's writing style might be more appealing for the non-academic, and some people are allergic to Richard Dawkins, for obvious reasons if you know who he is.

What's her angle. Presumably she is of the faithful? If that's really her angle, then you might be hard pressed to convince her with a short paragraph or two that I could provide.

Group theory is important for theoretical physics and crystallography, but I think it takes a back seat to the topics I listed. I've survived to grad school without learning anything beyond the basics, though I would love to study it eventually. Unfortunately, I couldn't fit in an abstract algebra course during my undergrad, so I don't have a textbook to personally recommend, although Dummit and Foote is popular with others.

Also, pretty much every branch of math (except maybe number theory?) is useful in physics (category theory, combinatorics, topology, measure and probability theory etc) so it's hard to make a comprehensive list.

I learned a lot from getting a copy of Rudin (however, this book is very challenging and probably not the best to self study from. I was able to get to about continuity before taking my analysis course and it was challenging, but worth while). You can probably find it online somewhere for free.

A teacher lent Introduction to Analysis to me and suggested I use it instead of the book by Rudin. It was a well written book and had exercises which were much more approachable (although it included very difficult ones as well). The layout of this book (and I'd bet many others) is quite similar to that of Rudin. It was nice to be able to read them together.

For linear algebra, I can't speak to the quality of many books, but there are plenty which can fairly easily be found online. You will likely be recommended Linear Algebra Done Right however I found it a bit challenging as a first introduction to linear algebra and never got quite far.

My university course used Larson, Falvo Linear Algebra and it was enjoyable and helps you learn the computations very well and gives a decent understanding of proofs.

Square one...

You should have a solid base in math:

Introduction to Calculus and Analysis, Vol. 1 by Courant and John. Gotta have some basic knowledge of calculus.

Mathematical Methods in the Physical Sciences by Mary Boas. This is pretty high-level applied math, but it's the kind of stuff you deal with in serious physics/astrophysics.

You should have a solid base in physics:

They Feynman Lectures on Physics. Might be worth checking out. I think they're available free online.

You should have a solid base in astronomy/astrophysics:

The Physical Universe: An Introduction to Astronomy by Frank Shu. A bit outdated but a good textbook.

An Introduction to Modern Astrophysics by Carroll and Ostlie.

Astrophysics: A Very Short Introduction by James Binney. I haven't read this and there are no reviews, I think it was very recently published, but it looks promising.

It also might be worth checking out something like Coursera. They have free classes on math, physics, astrophysics, etc.

On evolution:

I urge you to read some books on the issue that aren't written with a fundamentalist Christian slant. The science is decisive, and the distinction between "macro" and "micro" is itself a religious confusion. (as others have already pointed out).

On the Big Bang: The biggest problem with the Big Bang is that we don't know how it happened. That is a problem, and scientists are working obsessively to solve it. But saying "God did it" buys you a whole host of new problems. How did God happen? Who created God? Why did he create the universe? You haven't answered anything by saying "God did it": you've just kicked the can down the road and added an additional unfalsifiable and unsupported assumption.

Also, the evidence for the Big Bang is all around you: look up background microwave radiation,distribution and evolution of galaxies, the abundance of light elements, and the expansion of space.

On the supernatural:

Any thinking that starts with "Do you think it's possible that..." is a HUGE RED FLAG. Almost anything is possible, but usually the sort of logic that must be defended with a "Well, it's possible..." is absurdly improbable. This is a good example. Yeah, it's possible that an entire other world could be layered on our own - but it's more improbable than winning the lottery, and I don't buy lottery tickets.

If I had to explain the fundamental difference between the way I think about the spiritual and the way you think about the spiritual, it would be this. You ask "Is it possible that..." and "Do you think that maybe..."

I ask "Is there empirical support for..." and "Does the evidence support the assertion that..."

As for the hope that human consciousness continues on....

Nope. This is it. That sucks, and I'm sorry. It's among the hardest pills to swallow about being an atheist - but it's true whether you believe it or not.

Well, Hardy & Wright is the classic book for elementary stuff. It has almost everything there is to know. There is also a nice book by Melvyn Nathanson called Elementary Methods in Number Theory which I really like and would probably be my first recommendation. Beyond that, you need to decide which flavour you like. Algebraic and analytic are the big branches.

For algebraic number theory you'll need a solid grounding in commutative algebra and Galois theory - say at the level of Dummit and Foote. Lang's book is pretty classic, but maybe a tough first read. I might try Number Fields by Marcus.

For analytic number theory, I think Davenport is the best option, although Montgomery and Vaughan is also popular.

Finally, Serre (who is often deemed the best math author ever) has the classic Course in Arithmetic which contains a bit of everything.

I made a comment in a another thread.

I second /u/ProfThrowawary17's recommendation for Strogatz and also suggest the undergrad text Hale and Kocak. Strogatz is a rare text that delivers both interesting math and well-motivated applications in a fairly accessible manner. I have not systematically read Hale and Kocak, but it also seems to provide a gentle yet rigorous introduction to ODE's from the modern dynamical systems point of view.

Like /u/dogdiarrhea, I also recommend the graduate text Hale. If you have a strong analysis background, working through Hale would be quite worthwhile. It's also a Dover publication! So if Hale doesn't work out for you in a first time reading, it would still be a useful reference later on.

Looking on their website it seems as if they do not let outside people borrow from their library, sorry :(.

I know many libraries have "partnerships" for the lack of a better word, where if you try to borrow a book from the library, and they don't have it, they will request it from somewhere else they are partnered with and get it for you.

Some ideas of books:

For my undergraduate astrophysics class I used - Foundations of Astrophysics by Ryden and Peterson, ISBN13: 978-0-321-59558-4

I have also used (more advanced, graduate level) - An Introduction to Modern Astrophysics by Carroll and Ostlie, ISBN13: 978-0-805-30402-2

There are plenty of other undergraduate text books for astrophysics, but those are the only two I have experience with.

Some other books that may be just fun reads and aren't text books:

A Brief History of Time - Hawking

QED: The Strange Theory of Light and Matter - Feynman

Random popular science books:

Parallel Worlds - Kaku (or anything else by him Michio Kaku)

Cosmos - Sagan

Dark Cosmos - Hooper

or anything by Green, Krauss, Tyson, etc.

Videos to watch:

I would also suggest, if you have an hour to burn, watching this video by Lawrence Krauss. I watched it early on in my physics career and loved it, check it out:

Lawrence Krauss - A Universe From Nothing

Also this video is some what related:

Sean Carroll - Origin of the Universe and the Arrow of Time

Hope you enjoy!

Edit: Formatting.

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

You could read Timothy Gowers' welcome to the math students at Oxford, which is filled with great advice and helpful links at the bottom.

You could read this collection of links on efficient study habits.

You could read this thread about what it takes to succeed at MIT (which really should apply everywhere). Tons of great discussion in the lower comments.

You could read How to Solve It and/or How to Prove It.

If you can work your way through these two books over the summer, you'll be better prepared than 90% of the incoming math majors (conservatively). They'll make your foundation rock solid.

Late to the game, but people always need more books...

The World Without Us was great, really interesting read about humanity's effects on the planet, with lots of references to expand on if you wanted to do that.

A Year of Living Biblically was interesting, even if you aren't a Christian or a Jew, if you find religion interesting.

And last but not least, Rocket Boys by Homer H. Hickam. This was made into the movie 'October Sky', and it's a memoir, one of the best I've ever read. But all the science of the rockets is in there too, I learned a lot about propellants and DeLavalle nozzles lol.

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.

Yes. I've read a lot of popular creationist books. I've also read a lot of popular evolution books. Please understand, I accept evolution not because I haven't considered creationism (heck I've practically studied it with all the papers and books I've read), but because the evidence is there. It's true. But don't take my word for it. Out of all the books I've read, Why Evolution is True is definitely the best book for the creation/evolution so-called debate. Please, read it.

Linear algebra is about is about linear functions and is typically taken in the first or second year of college. College algebra normally refers to a remedial class that covers what most people do in high school. I highly recommend watching this series of videos for getting an intuitive idea of linear algebra no matter what book you go with. The book you should use depends on how comfortable you are with proofs and what your goal is. If you just want to know how to calculate and apply it, I've heard Strang's book with the accompanying MIT opencourseware course is good. This book also looks good if you're mostly interested in programming applications. A more abstract book like Linear Algebra Done Right or Linear Algebra Done Wrong would probably be more useful if you were familiar with mathematical proofs beforehand. How to Prove it is a good choice for learning this.

I haven't seen boolean algebra used to refer to an entire course, but if you want to learn logic and some proof techniques you could look at How to Prove it.

Most calculus books cover both differential and integral calculus. Differential calculus refers to taking derivatives. A derivative essentially tells you how rapidly a function changes at a certain point. Integral calculus covers finding areas under curves(aka definite integrals) and their relationship with derivatives. This series gives some excellent explanations for most of the ideas in calculus.

Analysis is more advanced, and is typically only done by math majors. You can think of it as calculus with complete proofs for everything and more abstraction. I would not recommend trying to learn this without having a strong understanding of calculus first. Spivak's Calculus is a good compromise between full on analysis and a standard calculus class. It's possible to use this as a first exposure to calculus, but it would be difficult.

Things you'll want:
This book: http://www.amazon.com/Turn-Left-Orion-Hundred-Telescope/dp/0521781906/ref=sr_1_3?s=books&ie=UTF8&qid=1324830331&sr=1-3

Teflon pads as it is likely the pads on your dob suck and will make moving it suck as well.

A high field of view set of optics. I recommend any of the following (I have an 8" dob, you want a good wide-angle eye piece as it makes viewing a pleasure. Magnification is far from all important, esp. with a small telescope).

• http://www.universityoptics.com/eyepieces.html
  
• http://www.optcorp.com/ProductList.aspx?uid=30-718-1044-1046 (Baader planetarium)
  
• When picking out eye pieces, consider the magnification you'll get with your telescope (equations found online), the eye relief (bigger tends to be easier to use, basically how far your eye needs to be from the lens to be in focus), and the field of view (just how much of the sky you'll see).
  
  You need to collomate your telescope. http://en.wikipedia.org/wiki/Collimated_light. Basically, your telescope's mirror is likely very off center. A dobsonian like what you have is two mirrors, the main mirror (the big one), and the little post mirror that reflects light off the main mirror into your eye piece. You need a laser collomator that will shine a light from the eye piece into the telescope. If your telescope was properly collomated, the laser would bounce off of the post mirror, hit the dead center of the main mirror, reflect back onto the post mirror, and back into the collomator. Look online for more information.
  
  Lastly, you probably want a Telrad. It makes pointing your telescope very, very simple, and almost eliminates the need to use a finder scope. http://www.amazon.com/Telrad-Finder-Sight/dp/B0000ALKAN (you don't need any accessories for this. Its wonderful).
  
  Happy stargazing!
  
  Edit: feel the need to qualify why I suggest Teflon pads. your telescope moves around on two axises, up and down, and left and right. Unlike a "conventional" refractor telescope (the ones that we think of as a good "my first telescope"), a lot of weight is placed on those bottom pads. If you replace the pads that came with your telescope's base with teflon pads, it will make it a lot easier to move it along that particular axis, asthere is less friction.

Besides what has been said here, why don't you ask your parents to purchase you a fun math textbook? You'll have to do some research but why not just have some initiative and pick up your own algebra textbook and learn at your own pace? Maybe you might in interested in the Art of Problem Solving Series. You have an entire school of math teachers to ask for help if you get stuck somewhere. You have the internet (here being one of the places you can ask about anything math related; StackExchange is another good place). If I recall correctly, you can even "enroll" in online courses using edX that you can do on your own time. I often recommend to people Basic Mathematics because it covers everything that you should know math-wise before college. Some of the material might be advanced to you now but you can work through the book easily if what you claim about knowing all the material for your class is true.

For those that just think it's funny because it might be something you see in a textbook, it's not just that. This joke is a direct reference to Fermat's Last Theorem, which was proposed in 1637 and the text above was scribbled in the sidebar of the paper. It wasn't actually proven until 1994, 350+ years later.

Interestingly enough, it's unlikely that the current proof, which I think was around 300 pages, was anything like Fermat's proof that he alluded to (and possibly never had, which makes him an amazing troll). The current proof used methods that were not developed until recently, and I believe the author of the proof even developed some new mathematics in order to solve it.

https://en.wikipedia.org/wiki/Fermat's_Last_Theorem

Here's a great book on it, and the guy that finally provided the proof. Definitely worth reading, it's not boring at all: http://www.amazon.com/Fermats-Enigma-Greatest-Mathematical-Problem/dp/0385493622

Here are some books I'd recommend.

General Books

These are general books that are more focused on proving things per se. They'll use examples from basic set theory, geometry, and so on.

1. How to Prove It: A Structured Approach by Daniel Velleman
   
2. How to Solve It: A New Aspect of Mathematical Method by George Pólya
   
   Topical Books
   
   For learning topically, I'd suggest starting with a topic you're already familiar with or can become easily familiar with, and try to develop more rigor around it. For example, discrete math is a nice playground to learn about proving things because the topic is both deep and approachable by a beginning math student. Similarly, if you've taken AP or IB-level calculus then you'll get a lot of out a more rigorous treatment of calculus.
   
   

• An Invitation to Discrete Mathematics by Jiří Matoušek and Jaroslav Nešetřil
  
• Discrete Mathematics: Elementary and Beyond by László Lovász and Jaroslav Pelikan
  
• Proofs from THE BOOK by Martin Aigner and Günter Ziegler
  
• Calculus by Michael Spivak
  
  I have a special place in my hear for Spivak's Calculus, which I think is probably the best introduction out there to math-as-she-is-spoke. I used it for my first-year undergraduate calculus course and realized within the first week that the "math" I learned in high school — which I found tedious and rote — was not really math at all. The folks over at /r/calculusstudygroup are slowly working their way through it if you want to work alongside similarly motivated people.
  
  General Advice
  
  One way to get accustomed to "proof" is to go back to, say, your Algebra II course in high school. Let's take something I'm sure you've memorized inside and out like the quadratic formula. Can you prove it?
  
  I don't even mean derive it, necessarily. It's easy to check that the quadratic formula gives you two roots for the polynomial, but how do you know there aren't other roots? You're told that a quadratic polynomial has at most two distinct roots, a cubic polynomial has a most three, a quartic as most four, and perhaps even told that in general an n^(th) degree polynomial has at most n distinct roots.
  
  But how do you know? How do you know there's not a third root lurking out there somewhere?
  
  To answer this you'll have to develop a deeper understanding of what polynomials really are, how you can manipulate them, how different properties of polynomials are affected by those manipulations, and so on.
  
  Anyways, you can revisit pretty much any topic you want from high school and ask yourself, "But how do I really know?" That way rigor (and proofs) lie. :)

This has been a respectful back and forth, and I appreciate that. This will be my concluding comment.

> Religion has been the single greatest force limiting advancement in human history
>


This is the claim of the likes of Sam Harris. And this was the point that Nassim Taleb tried to make to him, although quite clumsily- religious thought has greatly contributed to building the Western world. For example, much of science has it's foundations in the presumptions produced by a religious worldview. Religion provides answers to existential questions that need to addressed before any scientific inquiry can be made. For example, one must have the presumption that the world is intelligible and comprehensible before engaging in scientific inquiry. If you don't start with that presumption, you cannot do science.

If you're interested in learning more about the philosophical presumptions that form the basis for scientific inquiry, check out The Structure of Scientific Revolutions by Thomas Kuhn


Peace.

There's a lot of ground to cover in math, but completely doable. I'm going to recommend a dense book, but I truly think it's worth the read.

Let me leave you with this. You understand how number work correct? 1 + 1 = 2. It's a matter of fact. It's not up for debate and to question it would see you insane.

This is all of math. You need to truly understand

1 + 1 = 2

a + a = b everything is a function. There are laws to everything, even if people wish to deny it. If we don't understand it, it's easier to state that there are no laws that govern it, but there are. You just don't know them yet. Math isn't overwhelming when you think of it that way, at least to me. It's whole.

Ask yourself, 'why does 1 + 1 = 2 ?' If you were given 1 + x = 2, how would you solve it? Why exactly would you solve it that way? What governing set of rules are you using to solve the equation? You don't need to memorize the names of the rules, but how to use them. Understand the terminology in math, or any language, and it's easier to grasp that language.

The book Mathematics

I didn't study biology in high school because I had a full course load of physics, chemistry and mathematics in preparation for engineering school. That being said, biology is one of the courses I regret not taking.

It really is the Greatest Show on Earth. No other scientific concept explains so much about our visible world while being simple and elegant. If you like biology, but have not read any of Dawkin's biology books, I highly recommend them. In addition to the one I already linked, another excellent one is The Ancestor's Tale. Evolution is capable of explaining why species, as you put it, are built they way they are and why they function the way they do. Evolution explains the why of it all. Of course, you don't need to abandon your concept of God, either. Evolution is perfectly compatible with theology.

I don't really want to comment on your postulates or discourage your thinking, but I would recommend the book, The Cosmic Serpent, in which an anthropologist examines shamanic traditions in the Amazon.

The question of how these shamans discovered the use of specific hundreds of assorted plants in the Amazon, out of the choice of tens of thousands, that cured, nourished, or tripped-out their people for millenia is central to the book, and doesn't require recourse to divine inspiration-- but it is perhaps as recondite and mysterious. It seems like a similar path of inquiry, and a wholly illuminating book of quality ethnobotany and anthropology.

Good luck in the search for truth... but it might not be wheat.

You even listen to Terrence McKenna?? Lol you'll be fine! I say go for it.

The thing about Terrence McKenna is that, like his brother Dennis said,if he's right about even 1% of his claims, that's a very important thing in the world.

I read a book once on ayahausca and DNA where this geneticist did an anthropology thing where he went and did ayahuasca with tribes in South America to scientifically prove a connection between ayahausca and DNA. It's a VERY interesting read. He does a great job at dumbing it down to laymen's terms so that someone who's not a scientist can read the book and understand it. Then the second half of the book is all works cited. Sources for every single claim he makes during the book. So if someone wanted to they could see proof for all the things he was claiming. He does great at not adding any of his personal beliefs into the book as well, it is purely scientific. It's called the cosmic serpent : Cosmic Serpent: DNA and the Origins of Knowledge https://www.amazon.com/dp/0874779642/ref=cm_sw_r_cp_apa_5QgMBbG18AQY8

Intro Calculus, in American sense, could as well be renamed "Physics 101" or some such since it's not a very mathematical course. Since Intro Calculus won't teach you how to think you're gonna need a book like How to Solve Word Problems in Calculus by Eugene Don and Benay Don pretty soon.

Aside from that, try these:

Excursions In Calculus by Robert Young.

Calculus:A Liberal Art by William McGowen Priestley.

Calculus for the Ambitious by T. W. KORNER.

Calculus: Concepts and Methods by Ken Binmore and Joan Davies

You can also start with "Calculus proper" = Analysis. The Bible of not-quite-analysis is:

[Calculus by Michael Spivak] (http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?s=books&ie=UTF8&qid=1413311074&sr=1-1&keywords=spivak+calculus).

Also, Analysis is all about inequalities as opposed to Algebra(identities), so you want to be familiar with them:

Introduction to Inequalities by Edwin F. Beckenbach, R. Bellman.

Analytic Inequalities by Nicholas D. Kazarinoff.

As for Linear Algebra, this subject is all over the place. There is about a million books of all levels written every year on this subject, many of which is trash.

My plan would go like this:

1. Learn the geometry of LA and how to prove things in LA:

Linear Algebra Through Geometry by Thomas Banchoff and John Wermer.

Linear Algebra, Third Edition: Algorithms, Applications, and Techniques
by Richard Bronson and Gabriel B. Costa.

2. Getting a bit more sophisticated:

Linear Algebra Done Right by Sheldon Axler.

Linear Algebra: An Introduction to Abstract Mathematics by Robert J. Valenza.

Linear Algebra Done Wrong by Sergei Treil.

3. Turn into the LinAl's 1% :)

Advanced Linear Algebra by Steven Roman.

Good Luck.

Hijacked is too strong a word, but I think two points are notable. First, arguably most of the really popular and notable books on evolution released in the last twenty years were penned by New Atheists proper or by authors who basically fit the New Atheist mold but aren't one of the four specific authors. A big part of the reason for that is simply Richard Dawkins. He's a popular writer and a biologist, so it was almost inevitable that he'd pen books about Darwin and that they'd hit the bestsellers lists. And if it were limited to Dawkins, I'd think nothing of it, but there's Dennett and Shermer, and I wouldn't be surprised to see Harris release one before long. Another part of the reason is that a number of the other books about Darwinian evolution that have sold well in past decades were penned by creationists like Michael Behe, so a certain measure of response is, from my perspective at least, welcome. At that point, it's about market share, and we don't want creationists having too big a piece of the market share. Their point of view is, after all, problematic to say the least. If it weren't for my second point, it wouldn't even be problematic that a) popular books on evolution are basically split between creationists and New Atheists, and b) that New Atheists make up such a large share of that market.

But my second point is this: New Atheists aren't just popularizing or "standing up for" Darwinian evolution; they're attaching a political and ideological agenda to that effort, and that runs several risks, the most obvious being that it can polarize people against evolution, as some commentators have warned it might do in Muslim countries. To my mind, the more insidious risk is that, once you've connected a scientific theory to a political or ideological effort, it becomes all to easy for its patrons to see it in those terms even when it has nothing to do with that effort. Without much noticing it, pro-Darwinians may start seeing barely articulated associations as part and parcel of evolution, until evolution is something more than a scientific model. Dawkins, for example, has turned evolution into a theological disproof with the subtitle of "The Blind Watchmaker". The title of Shermer's "Why Darwin Matters" sums up the achievement of evolutionary theory as a form of polemic against intelligent design theory. Dawkins, at least, is close enough to the professional practice of biology that he probably doesn't need reminding that evolution isn't really about atheism, but all of these guys are writing books for people who don't have the continual reminder of working in the field where evolutionary theory is most functional.

I say none of this in defense of the Guardian article, but I do think there's something to be said for the idea that our society stands to lose by leaving it up to the New Atheists to give evolution its popularly received meaning.

Indeed yes, there isn't so much absorbtion and reemission of quanta as i understand it as does the substance act like a matrix or diffraction grating. Then within the substance you have lots of little broken up waves all interacting with each other, canceling each other out in parts and bolstering each other in others. The 'super wave' made up of all these interactions propagates at slower than light speed, and potentially at an angle. Come out the other side (into a vaccum again) and there's no diffraction, no 'super wave' but back to light propagating at 'light speed again'.

There's probably a good quantum analogy too, but I don't recall it.

The thing to always remember is that these forces aren't quantum particles or idealized waves, those are just the best models we have for something we don't fully understand.

Read Feynman's QED, its short, written for the layman and completely awesome. It will also blow your freaking mind.

Simon Singh explains.

edit: Hey, I didn't expect this to become the top comment. Neat. Might as well abuse it, by providing bonus material:

This is the same Simon Singh discussed in this recent and popular Reddit post; he is a superhero of science popularization. He has written some excellent and highly rated books:

• Big Bang: The Origin of the Universe
  
• The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
  
• Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem
  
• Trick or Treatment: The Undeniable Facts about Alternative Medicine
  
  (full disclosure: I have nothing to disclose, other than that I'm a fan of his work.)

Hello, fellow Sacramentan here.

Our light-polluted cities limit what we can see. But even a small telescope can bring out details that are completely invisible to our eyes. I assume by now you've looked at the Moon and planets like Jupiter and Saturn. They never cease to amaze.

The ETX-70 doesn't have a very large aperture, so it won't suck in the photons like a larger reflector or SCT. But you'll still be able to make out deep sky objects (DSOs) like the Orion Nebula, some globular clusters, Albireo, and some galaxies (faintly, on a good night).

Your scope is light and portable. Take it away from the city lights! Even a few miles outside the cities makes a huge difference.

Getting eyepieces to increase magnification doesn't always help. It makes the image larger, but also dimmer. They work better on planets and the moon, but for DSOs you want all the light you can get.

Get your hands on a copy of Turn Left at Orion. It's a fantastic guide to the night sky and includes details about what you'll be able to see through a small telescope.

Finally, think about attending one of the monthly star parties hosted by the Sacramento Valley Astronomical Society (svaa.org). They are up at Blue Canyon where it is very dark on a moonless night.

For introductory physics, I'd recommend Giancoli, Physics for Scientists and Engineers. You may want something in addition to this for deeper math, but Giancoli is fantastic for getting the core ideas and integrating them across different phenomena. After Giancoli, you will understand almost everything a lot better.

After Giancoli, things get a lot rougher. Your next objective is Classical Mechanics. You cannot learn Quantum Mechanics without studying Classical Mechanics in depth. You can try, as I did, but you are in for a world of pain that you won't fully grasp until you take Classical Mechanics seriously. You will especially want to pay attention to periodic and harmonic systems. Giancoli's main disadvantage is a weak treatment of periodic systems. Any Classical Mechanics book will make up for this.

At this point you will also need a companion book to take you through Classical Mechanics and everything that follows (Statistical Mechanics, Electrodynamics, Quantum Mechanics). That book is Mary L. Boas' Mathematical Methods in the Physical Sciences. Frankly, upper level undergraduate physics textbooks assume you have this knowledge. It's a fantastic book and it would have saved me a world of pain if I'd known about it right from the beginning.

Anyhow, after Giancoli you should look at Boas, then you may choose "Classical Mechanics" by Thornton & Marion. This book assumes you have Boas. Then you can plunge into Griffiths' Introduction to Quantum Mechanics, which assumes you have Boas. However, you'll have an easier time of the material if you read Griffiths' E&M book first, which assumes you have Boas. You'll also be well-served with a Statistical Mechanics textbook. Blundell & Blundell (Introduction to Thermal Physics) is a wonderful book conceptually, except that it lacks solutions. The mathematical and conceptual ideas in each of these subjects were fundamental to the development of Quantum Mechanics, and familiarity with the subjects is assumed by QM textbook authors.

Azcel wrote a good book on Fermat's Last Theorem and Wiles' solution. Amazon

Simon Singh's book on the same subject is also good, but Amazon has it at $10.17 whereas Azcel's is $0.71 better at $10.88.

Either way you get an enjoyable read of one man's dedication to solve a notoriously tricky problem and just enough of the mathematical landscape to get a sense of what was involved.

Another fun & light holiday read is Polya's 'How To Solve it' - read the glowing reviews over at Amazon

I really good textbook is probably what you want. Good math textbooks are engaging and have lots of interesting problems. They have an advantage (in pure math) that they don't have to worry about teaching you specific tools (which IMO can make things boring). Lots of people love this one: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536

Also here is a really good lecture series (on a different topic): https://www.youtube.com/watch?v=7G4SqIboeig&list=PLMsYJgjgZE8hh6d6ia2dP1NI0BKNRXbiw

Also if you have a bit of a programming bent or want to learn a little bit of programming, you might like Project Euler:https://projecteuler.net/

I am a master's student with interests in algebraic geometry and number theory. And I have a good collection of textbooks on various topics in these two fields. Also, as part of my undergraduate curriculum, I learnt abstract algebra from the books by Dummit-Foote, Hoffman-Kunze, Atiyah-MacDonald and James-Liebeck; analysis from the books by Bartle-Sherbert, Simmons, Conway, Bollobás and Stein-Shakarchi; topology from the books by Munkres and Hatcher; and discrete mathematics from the books by Brualdi and Clark-Holton. I also had basic courses in differential geometry and multivariable calculus but no particular textbook was followed. (Please note that none of the above-mentioned textbooks was read from cover to cover).

As you can see, I didn't learn much geometry during my past 4 years of undergraduate mathematics. In high school, I learnt a good amount of Euclidean geometry but after coming to university geometry appears very mystical to me. I keep hearing terms like hyperbolic/spherical geometry, projective geometry, differential geometry, Riemannian manifold etc. and have read general maths books on them, like the books by Hartshorne, Ueno-Shiga-Morita-Sunada and Thorpe.

I will be grateful if you could suggest a series of books on geometry (like Stein-Shakarchi's Princeton Lectures in Analysis) or a book discussing various flavours of geometry (like Dummit-Foote for algbera). I am aware that Coxeter has written a series of textbooks in geometry, and I have read Geometry Revisited in high school (which I enjoyed). If these are the ideal textbooks, then where to start? Also, what about the geometry books by Hilbert?

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.

All the video sources I'm finding seem... spotty, but Richard Feynman's lectures on physics are the best in my opinion. He starts out with the basic foundations modern physics and progresses into much more difficult territory. They're well written, and definitely a good read for anyone who wants a basic understanding of physics.

I have these copies of his lectures which I like because they split up the easy and the hard topics in to separate books. But this is just personal opinion, and there are many, many copies of his works out there.

While it isn't strictly a science book, Douglas Adam's "Last Chance to See" Is a really great book on a few endangered species he toured around the world to go and try to find. Its short and hilarious and also does a really wonderful job at showing you how silly humans can be and how our silliness actually has pretty detrimental effects on the other animals we share this world with.

If you know anything about Douglas Adams and his Hitch Hikers Guide book then you will probably really enjoy this. It's an overlooked gem in his body of work.

http://www.amazon.com/Last-Chance-See-Douglas-Adams/dp/0345371984

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. :)

Most universities have a physics 101 class tailored to people like you. If you are already in school, you could express your interest to the teacher and ask to sit in on the class. I've done this for several classes and never had a teacher refuse my request, but if they say no, you can always just pay a little money and audit the class. The cost varies per school, but at my university it was only $30.

If you are looking for a book, I'd suggest Richard Feynman's Six Easy Pieces. I don't remember it containing any math at all, but is excellent for understanding some of the fundamental concepts of physics.

If you have a particular concept you'd like to understand, you can ask me! I would love to talk about physics to anyone at anytime.

For a fun read, I love The Disappearing Spoon.

For a while, I've been meaning to read Salt which is another fun read.

I also just love the Periodic Table of Videos YouTube channel for other fun stuff.

Textbook-wise, you can't beat Stumm and Morgan or Metcalf and Eddy for your water chemistry/water treatment needs.

I'll stick to recommending science communication books (those that don't require a deep background on biological concepts):

• On the Origin of Species by Means of Natural Selection - Charles Darwin, bonus points if you can get a 1st edition reprint (before his colleagues made him change a lot of important things); it is a must-read but it might need quite some time to truly understand it, it is a heavy read.
  
  
• A lot of people recommend the Selfish Gene by Richard Dawkins but that one is one of his most controversial books and if you decide to read it, you should take everything with a pinch of salt; for Dawkins I prefer to recommend the Greatest Show on Earth: The Evidence for Evolution and the Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design. Just beware of Dawkins, he's a little dogmatic in his approach.
  
  
• The Dialectical Biologist - Richard Levins & Richard Lewontin.
  
  
• The Structure of Scientific Revolutions - Thomas Kuhn, this one will change forever your conception of science as a whole.
  
  
• The Red Queen: Sex and the Evolution of Human Nature - Matt Ridley.
  
  
• Wonderful Life: The Burgess Shale and the Nature of History, and the Panda's Thumb: More Reflections in Natural History - Stephen J. Gould.
  
  
• The Ghosts of Evolution: Non-sensical Fruit, Missing Partners, and Other Ecological Anachronisms - Connie Barlow.
  
  
• Are We Smart Enough to Know How Smart Animals Are? - Frans de Waal, this one is about animal cognition but has an incredible underline of all the deficiencies and prejudges on science.
  
  
• Microbe Hunters - Paul de Kruif.
  
  
• Symbiotic Planet: A New Look at Evolution, and What is Life? - Lynn Margulis.
  
  
• The Demon-Haunted World: Science as a Candle in the Dark - Carl Sagan & Ann Druyan.
  
  
• A Short Story of Nearly Everything - Bill Bryson.
  
  ---
  
  For books that everyone studying biology ends up reading, my candidate would be Lehninger's Principles of Biochemistry, by Nelson & Cox but that's a textbook.

So if you find this even mildly interesting, you must read “The Disappearing Spoon”. It’s basically the stories behind the elements and their discovery. Before you yawn and move along, it reads like a badass Indiana Jones novel and is a page turner. The name is from Gallium which was used in a tea party and shaped like spoons. When the patrons stirred their tea the spoon disappeared and everyone was delighted (health concerns?). Anyways, you’ll never look at elements the same way:

The Disappearing Spoon: And Other True Tales of Madness, Love, and the History of the World from the Periodic Table of the Elements https://www.amazon.com/dp/0316051632/ref=cm_sw_r_cp_api_i_XCUVDbVXGT9JM

Feynman's Six Easy Pieces is a great introduction to quantum mechanics. Gary Zukov's book The Dancing Wu Li Masters doesn't have a great reputation among physicists because it strays a bit into mysticism, but I think it's a pretty good read. Capra's Tao of Physics is in the same category. For an easy-to-understand discussion of the weirdness of quantum mechanics, Fred Kuttner and Bruce Rosenblum's Quantum Enigma: Physics Encounters Consciousness is excellent.

This is an Amazon list of books on the subject that I found helpful:

Robert Kroese, author of Schrödinger's Gat

I'll throw out some of my favorite books from my book shelf when it comes to Computer Science, User Experience, and Mathematics - all will be essential as you begin your journey into app development:

Universal Principles of Design

Dieter Rams: As Little Design as Possible

Rework by 37signals

Clean Code

The Art of Programming

The Mythical Man-Month

The Pragmatic Programmer

Design Patterns - "Gang of Four"

Programming Language Pragmatics

Compilers - "The Dragon Book"

The Language of Mathematics

A Mathematician's Lament

The Joy of x

Mathematics: Its Content, Methods, and Meaning

Introduction to Algorithms (MIT)

If time isn't a factor, and you're not needing to steamroll into this to make money, then I'd highly encourage you to start by using a lower-level programming language like C first - or, start from the database side of things and begin learning SQL and playing around with database development.

I feel like truly understanding data structures from the lowest level is one of the most important things you can do as a budding developer.

QED - Richard Feynman QED is a small book that's an excellent introduction into Quantum Mechanics by one of the pre-eminent physicists of the 20th century. If you want to understand the double slit experiment, this is the book to read.

Time, Love, Memory - Jonathan Weiner A biography of Seymour Benzer, a physicist turned biologist whose lab demonstrated the existence of some fundamental genes. One of the more interesting series of experiments demonstrated how the brains of homosexual fruit flies were wired differently than heterosexual fruit flies.

I second scottkarr's "Misquoting Jesus." recommondation. It's a very interesting read on how the bible morphed over time. Read it after reading Time, Love, Memory and the analogies Benzer uses to describe gene mutation will really resonate.

You could consider starting with a book like Velleman's How to Prove It. It doesn't have to be that book, there are also free options online, but learning some logic and set theory from a book like that is a good way to figure out how to work with the other subjects you're working on.

Then, you could find a rigorous treatment of the subjects you want to learn. Something like Axler's Linear Algebra Done Right or Spivak's Calculus.

Learning math from textbooks like this is harder, but you end up with a better understanding of the math.

It's probably not quite as directly tied to the specifics of first-year curriculum as Klein, but Feynman's Six Easy Pieces is a great intro to the big picture in physics. If you really want to understand physics, Feynman is one of your best resources.

I suggest you read a couple of books that present the evidence for evolution very clearly:

Why Evolution Is True

The Greatest Show on Earth: The Evidence for Evolution

Evolution itself is a simple concept, but the evidence for it is broad and detailed across many scientific disciplines, and it all fits together.

Regarding the existence of God, one can't prove that your God doesn't exist, or that any of the other thousands of gods that have been worshiped through the ages don't exist. The real question is whether there is enough evidence to positively prove the existence of any one of those gods.

First read about these guys in 'Last Chance to See' by Douglas Adams. Worth a read.

Edit: Ah, what the hell...

Of these, the kakapo is the strangest. Well, I suppose the penguin is a pretty peculiar kind of creature when you think about it, but it's quite a robust kind of peculiarness, and the bird is perfectly well adapted to the world in which it finds itself, in a way the kakapo is not. The kakapo is a bird out of time. If you look one in its large, round, greeny-brown face, it has a look of serenely innocent incomprehension that makes you want to hug it and tell it that everything will be all right, though you know that it probably will not be.

It is an extremely fat bird. A good-sized adult will weigh about six or seven pounds, and its wings are just about good for waggling a bit if it thinks it's about to trip over something - but flying is completely out of the question. Sadly, however, it seems that not only has the kakapo forgotten how to fly, but it has also forgotten that it has forgotten how to fly. Apparently, a seriously worried kakapo will sometimes run up a tree and jump out of it, whereupon it flies like a brick and lands in a graceless heap on the ground.*

I think any ELI5 will be oversimplified. You'll come away feeling like you've gained an insight, but the explanation won't match what nature really does.

If you want an understanding of how nature behaves, then you'll need to spend time reading a book called QED. It's actually very readable, even for dummies like me who have no math or physics training whatsoever.

There's a quote floating around that goes like, "According to Feynman, to learn QED you have two choices: you can go through seven years of physics education or read this book". And it's quite true.


You can find the book here or you can watch the videos here.

EDIT: For the truly curious, you can read part of the book here.

Was thinking that this is far enough into the future that former cities have been almost completely subsumed by nature - New growth, the rise and fall of sea levels, even geological processes. Think like, 20,000 years after some sort of apocalypse, an ice age come and gone. The most intact traces of the ancients are akin to like, Angkor Wat or Stonehenge, all but the most permanent construction completely erased, by the time the former civilization was wiped out perhaps there already wasn't much left to be preserved. The current population understands that there were grand civilizations at some point in the past and they know where these ruins are but that's about it. Maybe warnings against whatever ideology begat the ancient's downfall are preserved as whispers among the current population's elders, kept secret from those not wise enough to be trusted with the preventative knowledge.

I read The World Without Us, a pop science book speculating about the life of infrastructure if humans were to disappear, and was surprised by the convincing arguments regarding just how fast things would crumble to dust. So I went with that. Related, I was kind of let down by how 'preserved' the ancient structures in Horizon Zero Dawn seemed, considering how far in the future it's supposed to be. A lot of my game is inspired by Nausicaa of the Valley of the Wind, and in that story most of the ancient's world has been washed away by completely new and alien ecosystems. But not wanting such a 'harsh' and dangerous world in my game I'm instead aiming for something positive and pastoral. The kind of imagery that cyclists like to look at while they're climbing a mountain pass :)

My favorite science-related leisure reading is Derek Lowe's blog In The Pipeline. He covers new developments in chemistry/biology, the drug discovery industry, and occasionally some other stuff. He writes it in a way would be interesting to anyone that like chemistry and biology regardless of their level of education. I always look forward to reading it over lunch.

​

If you are looking for a book, The Disappearing Spoon is a great set of true short stories about chemistry that is a really fun read.

OK, folks may call me a nut, but you might want to try Evolution by Loxton. It's for younger readers, but you could literally jumpstart yourself in an hour.

Then, read Why Evolution is True by Jerry Coyne as well as The Greatest Show on Earth by Dawkins.

Honorable mention goes to Dawkins' An Ancestor's Tale.

>All I'm saying is that the origin of a claim contains zero evidence as to that claim's truth.

I had a look back though your other posts and found this, which explains a lot, for me anyway. Most people would put some more options in there - yes, no, im pretty sure, its extremely unlikely etc..

Heres what I think is the problem, and why I think you need to change the way you are thinking - Your whole concept of what is "logical" or what is "using reason" seems to be constrained to what is formally known as deductive logic. You seem to have a really thorough understanding of this type of logic and have really latched on to it. Deductive logic is just a subset of logic. There is more to it than that.

I was searching for something to show you on other forms of logic and came across this book - "Probability Theory - The Logic of Science" Which looks awesome, Im going to read it myself, it gets great reviews. Ive only skimmed the first chapter... but that seems to be a good summary of how science works- why it does not use just deductive logic. Science draws most of its conclusions from probability, deductive logic is only appropriate in specific cases.

Conclusions based on probability - "Im pretty sure", "This is likely/unlikely" are extremely valid - and rational. Your forcing yourself to use deductive logic, and only deductive logic, where its inappropriate.

>You have no way of knowing, and finding out that this person regularly hallucinates them tells you nothing about their actual existence.

Yeah I think with the info you've said we have it would be to little to draw a conclusion or even start to draw one. Agreed. It wouldnt take much more info for us to start having a conversation about probabilities though - Say we had another person from the planet and he says its actually the red striped jagerwappas that are actually taking over - and that these two creatures are fundamentally incompatible. ie. if x exists y can't and vice-versa.

I will give you the same answer I give every one of my students, and that one of my mentors gave me: don't think that there is a logical progression to approaching mathematics. The reason that people think there is such a thing as a logical order to mathematics is due to the school system, which teaches things in a particular order before university, and then structures university classes using prerequisites, making you think that, for example, you need trigonometry before you do calculus. This simply isn't true. I could say more about this, but it won't answer your question.

Here is my suggestion. Go to the mathematics section of a library, yank any book off the shelf, and go to town. Most books aimed at advanced undergrad/grad students (which is the level you're looking for) will say in the introduction something to the effect of "there are no real prerequisites for this book other than mathematical maturity," and this is nearly always true. You probably won't have mathematical maturity starting out, which can be frustrating, but you'll develop it over time. You will encounter things that you don't understand in these books, and the correct response to this is to go find another book on that topic. You can't learn mathematics just by compiling a list of theorems and techniques.

So all you really need is a starting point. Looking at what you're interested in, I'd recommend this book, which is extremely practical. You'll find more computational things in there than mathematical things, but it has a pretty broad spectrum of techniques whose theoretical underpinnings you can pursue. This course of action is the only one I can recommend, because it's the one I took. The only math class I took in college was calculus, and now I do research in mathematics in grad school. The frustrating thing about this approach is that there's no quantitative way to measure your progress. On the other hand, you get a real feeling for why and how people came up with various aspects of mathematics, which is a feeling you can't get from a curriculum.

Any book by Mary Roach- her books are hilarious, random, and informative. I like Jon Krakauer's, Sarah Vowell's, and Bill Bryson's books as well.

Some of my favorites that I can think of offhand (as another poster mentioned, I loved Devil in the White City)

No Picnic on Mount Kenya

Guns, Germs, and Steel

Collapse

The Closing of the Western Mind

What is the What

A Long Way Gone

Alliance of Enemies

The Lucifer Effect

The World Without Us

What the Dog Saw

The God Delusion (you'd probably enjoy Richard Dawkins' other books as well if you like science)

One Down, One Dead

Lust for Life

Lost in Shangri-La

Endurance

True Story

Havana Nocturne

I'm in no way qualified enough to talk about it myself but since nobody else has said anything particularly helpful, Richard Dawkins does a great job covering this stuff in a clear and easy to understand way in Ancestor's Tale

Going to try and post books that are related, but not actually "atheist".

Cosmos by Carl Sagan

Ishmael by Daniel Quinn

The first one for obvious reasons. Sagan is the secular Jesus, and I'd say the second is an interesting read for anyone religious or otherwise, but I feel like it would be better received if you don't actually believe in Christianity. It's a great read though

Wellll I'm going to speak in some obscene generalities here.

There are some philosophical reasons and some practical reasons that being a "pure" Bayesian isn't really a thing as much as it used to be. But to get there, you first have to understand what a "pure" Bayesian is: you develop reasonable prior information based on your current state of knowledge about a parameter / research question. You codify that in terms of probability, and then you proceed with your analysis based on the data. When you look at the posterior distributions (or posterior predictive distribution), it should then correctly correspond to the rational "new" state of information about a problem because you've coded your prior information and the data, right?

WELL let's touch on the theoretical problems first: prior information. First off, it can be very tricky to code actual prior information into a true probability distribution. This is one of the big turn-offs for frequentists when it comes to Bayesian analysis. "Pure" Bayesian analysis sees prior information as necessarily coming before the data is ever seen. However, suppose you define a "prior" whereby a parameter must be greater than zero, but it turns out that your state of knowledge is wrong? What if you cannot codify your state of knowledge as a prior? What if your state of knowledge is correctly codified but makes up an "improper" prior distribution so that your posterior isn't defined?

Now'a'days, Bayesians tend to think of the prior as having several purposes, but they also view it as part of your modeling assumptions - something that must be tested to determine if your conclusions are robust. So you might use a weakly regularizing prior for the purposes of getting a model to converge, or you might look at the effects of a strong prior based on other studies, or the effects of a non-informative prior to see what the data is telling you absent other information. By taking stock of the differences, you can come to a better understanding of what a good prediction might be based on the information available to you. But to a "pure" Bayesian, this is a big no-no because you are selecting the prior to fit together with the data and seeing what happens. The "prior" is called that because it's supposed to come before, not after. It's supposed to codify the current state of knowledge, but now'a'days Bayesians see it as serving a more functional purpose.

Then there are some practical considerations. As I mentioned before, Bayesian analysis can be very computationally expensive when data sets are large. So in some instances, it's just not practical to go full Bayes. It may be preferable, but it's not practical. So you wind up with some shortcuts. I think that in this sense, modern Bayesians are still Bayesian - they review answers in reference to their theoretical understanding of what is going on with the distributions - but they can be somewhat restricted by the tools available to them.

As always with Bayesian statistics, Andrew Gelman has a lot to say about this. Example here and here and he has some papers that are worth looking into on the topic.

There are probably a lot of other answers. Like, you could get into how to even define a probability distribution and whether it has to be based on sigma algebras or what. Jaynes has some stuff to say about that.

If you want a good primer on Bayesian statistics that has a lot of talking and not that much math (although what math it does have is kind of challenging, I admit, though not unreachable), read this book. I promise it will only try to brainwash you a LITTLE.

As utterly retarded as the catholics are, I have to say they are pretty clued up on science. Instead of the typical USA 'tard evangalist denying the simple facts in front of them, the pope simply moves the goalposts and accepts what reality is, but makes out the "big-bang" is "god-diddit".

There is also a brilliant book for kids (and I admit myself too!) by the Vatican astronomer Guy Consolmagno

There is no religious rubbish in that book and it is excellent. I would love to see a "tea-party" right-wing christian guide to the stars... hohoho...

(Atheist here BTW, but I don't have a problem with religious scientists who stick to the science!)

I can offer a general layman's overview of you like (global studies ftw)

I'm not sure if this is what you're getting at but:

"Humans comprise about 100 million tonnes of the Earth's dry biomass, domesticated animals about 700 million tonnes, ..."

http://en.m.wikipedia.org/wiki/Biomass_%28ecology%29

I think human lifestyle might be a bigger issue. If you include indirect human usage like domesticated animals (and the resulting sewage pools) etc.

You might really like this book:
http://www.amazon.com/The-World-Without-Alan-Weisman/dp/0312427905

Edit: hopefully as technology progresses we can be less disruptive towards our environment. I'm convinced that bio diversity will be a huge scientific/economic boom in terms of finding out what kind of genetic/mathematical/physical models work well as trial tested by time/evolution (granted they're not all winners but...) A lot of solid architecture and medicine has come straight out of nature. Seems like a shame we're just pissing it away for short term goals/benefits.

I also look forward to the day all science merged into one and there's something better out there to run society than what humans/computers/programs are limited to at the moment.

Good post. I must say i follow a similar train of thought considering most matters you have discussed. It seems scientific thought plays a big role, and hence would be wise to understand the philosophical stance of science, or at least the attempts that have been made to understand it. A book i haven't read yet, but will embark on soon is titled What is this thing called science which as far as i'm aware is the go to introduction to philosophy of science text, also among universities. Also there is a good series on youtube that i've watched which covers some of the main ideas in philosophy of science such as inductivism, deductivism, paradigm theory and systematicity. That's a good watch, ~ 12 lectures that go for about an hour or so each. I can give you the lecture slides if you want. Also in relation to philosophy of science, The Structure of Scientific Revolutions is also very popular in which Kuhn puts forth paradigm theory.

First you need Algebra and Trig. From this stage you mainly need to be able to manipulate equations (e.g. take x^2 + y^3 + z^2 = k^2 / n^2 and solve for x, it's one of the easier parts of algebra) and to understand exponents/logarithms. From trig you need to know how to break a vector into components, how to find angles, how sines/cosines/etc are defined, and all those nasty trig identities (e.g 1 - sin^2 = cos^2). You don't need to memorize them (usually, some professors are insane) but it helps to be kinda-sorta familiar with them.

If you've mastered all that, you want to study calculus. If you can take derivatives and solve integrals you're probably good enough to start, but the more you understand the better. It's a lot easier to solve physics problems when you're not struggling with the math you need to solve them.

If you get a book like this and work through it you'll get a lot of what you need, but it's not really necessary to go that far-- that is stuff you won't need until your fourth or fifth semester. Some of it is grad school math.

tl;dr: Trig, Algebra, and basic Calculus for sure. That's what you need for year 1. You can go further if you want, but there is no need to kill yourself to learn advanced math before taking intro physics.

• Grab your copy of Stellarium
  
• Learn these astronomy basics
  
• Then look high at the brightest stars first, check their names,
  
• Find the story behind them (constellations got stories in greek, roman, american, asian mythology...),
  
• Ask yourself how big is that star, what temperature is it on surface, what's the difference between a blue star and a red giant star.
  
• Whenever you see an object in space, try to find what it is it made of, its distance...
  
• Find out the answers - many good websites provide this info.
  
• Don't try to locate as much objects as possible (forget about the galaxies for now). Discover them slowly. Aim for the moon/planets and the brightest stars first. One object per night.
  
• Plan your nights. Stellarium and here at /r/astronomy will help you.
  
• As you advance, read about astronomy actually... Turn Left at Orion and more books...
  
• Then it will be time to go deeper in space for the clusters, nebulae and galaxies. Fellow astronomers at Reddit are already recommending how to upgrade your equipment to a telescope.
  
  Welcome aboard.

I had to deal with the no internet thing for some time.
Find some place with free wi-fi(you are using phone?).
Download ebook/pdf reader, FBreader + PDF plugin is good (Assuming that you are using Android phone).
Install Firefox and this add-on Save Page WE, it also work for phones (tested with Android).

Then you can save pages from some of these web sites or Wikipedia:

• mathsisfun
  
  
• purplemath
  
  
• sosmath
  
  
• tutorial.math.lamar
  
  
• themathpage
  
  
  
  
  
  Poor man's library:
  
  http://gen.lib.rus.ec/
  http://b-ok.org/
  https://archive.org/
  
  Some books:
  
  [Harold Jacobs - Elementary Algebra] (https://www.amazon.com/Elementary-Algebra-Harold-R-Jacobs/dp/0716710471) (that's the most friendly and still not bullshit introduction I was able to find)
  
  [Basic Mathematics by Serge Lang] (https://www.amazon.com/Basic-Mathematics-Serge-Lang/dp/0387967877) - Make sure that you understand the first 100-150 pages from the first book if you want to start this one.
  
  Precalculus by David Cohen - Lang's Basic Mathematics is harder (and much more interesting) than this...
  
  Use the three web sites written above to download them. PDF for better performance (and some times quality) on cheap phone, epub/djvu for the smaller size.
  
  I think that free wi-fi will be easy to find. Reading books wouldn't be like watching videos but you will actually learn more. Compass, straightedge and protractor would be really useful.
  

This is a phenomenon described thoroughly by Douglas Adams in his less-fictional-than-usual account of a zoologically-focused trip he'd taken.

In a certain chapter, he gives the details of a bird with a specific sort of problem: this bird has invented something to make its life easier.

Most birds need to spend time incubating their nests, but the bird he describes creates a heap of material which warms the egg, so that it's free to go and do other things, such as hunt for food.

The inherent difficulty here is that the body of the bird regulates its own temperature, where the heap does not.
Thus, the bird has to constantly attend to the matter, adding here, subtracting there, in order to maintain the exact temperatures needed to incubate their young.


He then compared that to his own interest in computers, especially that he might spend the entire afternoon creating a program which will calculate a very close approximation the volume of the heaps created by these birds, instead of just figuring it out on paper, and then getting on with writing the rest of the book.

For Cosmology, check out Carl Sagan's Cosmos. It is a fantastic book and a favorite of many astronomy, cosmology enthusiast. It was also produced into a TV series which you can watch online for free. It's a bit dated, as it came out in the 80's, but still a fantastic read and very good for a layman understanding of a lot of science.

I think I could possibly answer a part of your question in this post that I already made, but let me elaborate further since it isn't everyday that I'm able to have deep conversation IRL. My room-mates are muggles.

>But, what you're saying is that any such identity is acceptable and that one has to possess at least one such identity to be alive?

Yes. That's what I feel. As long as I (what is this 'I' in the first place) have an identity which ever it may be, as long as I'm self-aware I don't mind.

After all, can you imagine how the world was before you were born? How it will be after you die or 'die'? It's simply unimaginable. Coming back to our identity, I'd rather be someone since hey, if I'm that someone, I wouldn't know about this 'me' or would I? What guarantee do I have against the fact that every night when I go to sleep, my mannerism are completely altered, and my memories retroactively correct themselves.

Not to sound depressing (since I'm not depressed or anything) but mind, brain, body, life, existence seem pretty puny when compared to the vast scales of space and time that exists. Yes, I'm reading that and each moment I spend reading it, I get angrier at humans for the false sense of pride.

If you're interested in this topic, I highly recommend Dawkins "The Ancestor's Tale." It starts with modern humans, and then it works it's way back through our ancestors (explaining as it goes along when our "cousins" join the family tree; or to put it differently, it explains, in real time (rather than going backwards), our cousins departure from our common ancestor to the place they hold today). It doesn't focus exclusively on hominids or "transitional fossils," but the scope of the book will definitely give you an idea of the mountains of evidence we have for determining our ancestors, our cousins, and our family tree. I'm only about halfway through, but I've enjoyed it quite a bit so far. Take a look at the reviews online, and if it looks good, pick it up.

http://www.amazon.com/The-Ancestors-Tale-Pilgrimage-Evolution/dp/061861916X

I really love Probability Theory: The Logic of Science by Jaynes. While it is not a physics book, it was written by one. It is very well written, and is filled with common sense (which is a good thing). I really enjoy how probability theory is built up within it. It is also very interesting if you have read some of Jaynes' more famous works on applying maximum entropy to Statistical Mechanics.

You can download the full episodes at:
http://www.radiolab.org/archive/

The podcasts are short, but the full hour-long episodes are available. It's one of my favorite programs. That, and Philosophy Talk.

Radio Lab tends to feature one of my favorite mathematicians, Steven Strogatz, in several episodes (Emergence was great). He has a good presentation style (see YouTube) and I've really enjoyed his book: http://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-Nonlinearity/dp/0738204536

What kind of nerd am I to have a favorite mathematician? I'm not sure I want to know.

just some of my standard answers.


The Disappearing Spoon- yes, it's chemistry but I found it very interesting.


Abraham Lincoln's DNA- if you have a good background in genetics you might already know many of these stories. Read the table of contents first.


New Guinea Tapeworms and Jewish Grandmothers- disease based biology. There is a follow up book if it turns out you like it.


Stiff- more than you wanted to know about dead bodies.


And by the same author but space based... Packing for Mars.

I hope these help... Cheers.

Hey, girl in chemistry here. First I wanted to comment on the beaker glasses idea. If you do get something like that, go with a beaker mug and try to pick something with thicker glass. Regular beakers heat up easily and if she pours hot beverage, it will get too hot to hold in a few minutes even if there is a handle (this was tested out in a field by many chemists). Does she like to read? If so, get her The Disappearing Spoon by Sam Kean (http://www.amazon.com/Disappearing-Spoon-Madness-Periodic-Elements/dp/0316051632/ref=sr_1_1?ie=UTF8&qid=1417607692&sr=8-1&keywords=disappearing+spoon). It's a book full of true, fun and sometimes weird stories about many elements. Any chemist would appreciate that. Also, anything periodic table will be appreciated, in addition to shower curtain idea there are fridge magnets. T-shirts are tough since most of them are really cheesy. Recently I came across this one which is not bad http://www.amazon.com/Never-Everything-Science-Unisex-T-shirt/dp/B00HWEHM6M/ref=pd_sim_a_32?ie=UTF8&refRID=09FK7M4D48KR5RD8K80H. Anything with moles and avogadro will do, example http://www.amazon.com/CafePress-Mole-Problems-Mug-Multi-color/dp/B00INLA6RU/ref=sr_1_8?ie=UTF8&qid=1417609281&sr=8-8&keywords=avogadro+number. Can't really think of anything else right now, but if you want to run a specific idea by me, feel free to do it.

Do not enroll in a precalculus class until you have a solid grasp on the foundations of precalculus. Precalculus is generally considered to be the fundamentals required for calculus and beyond (obviously), and a strong understanding of precalculus will serve you well, but in order to do well in precalculus you still need a solid understanding of what comes before, and there is quite a bit.

I do not mean to sound discouraging, but I was tutoring a guy in an adult learning program from about December 2017-July 2018...I helped him with his homework and answered any questions that he had, but when he asked me to really get into the meat of algebra (he needed it for chemistry to become a nurse) I found a precalculus book at the library and asked him to go over the prerequisite chapter and it went completely over his head. Perhaps this is my fault as a tutor, but I do not believe so.

What I am saying is that you need a good foundation in the absolute basics before doing precalculus and I do not believe that you should enroll in a precalculus course ASAP because you may end up being let down and then give up completely. I would recommend pairing Basic Mathematics by Serge Lang with The Humongous Book of Algebra Problems (though any book with emphasis on practice will suffice) and using websites like khanacademy for additional practice problems and instructions. Once you have a good handle on this, start looking at what math courses are offered at your nearest CC and then use your best judgment to decide which course(s) to take.

I do not know how old you are, but if you are anything like me, you probably feel like you are running out of time and need to rush. Take your time and practice as much as possible. Do practice problems until it hurts to hold the pencil.

If you're doing both applied and pure abstract algebra rather than elementary algebra, then you'll probably need to learn to write proofs for the pure side. I recommend Numbers, Groups, and Codes by J. F. Humphreys for an introduction to the basics and to some applied abstract algebra. If you need more work on proofs, the free Book of Proofs can help, and Fraleigh's A First Course in Abstract Algebra is a good book for pure abstract algebra. If you want something more advanced, I recommend the massive Abstract Algebra by Dummit and Foote.

Strogatz's Nonlinear Dynamics and Chaos (https://www.amazon.ca/Nonlinear-Dynamics-Chaos-Applications-Engineering/dp/0738204536) is a good book to introduce applications of differential equations. It's an easy read that focuses on concepts and motivation rather than rigour.


Differential equations describe how things change based on what state they are in. An easy example is that the larger a population is the faster is grows. Or the more predators and the less food it has, the slower it grows. One can build a system that takes all variables thought to be relevant and construct a system that describes how all these things affect each other's growth rate, and then see how this system changes in time. Other examples include chemical reactions, as the rate of change of the ingredients depends on how much of each ingredient is in the mixture. Economics: the change of a market depends on the state of all other relevant markets. Physics: the change in velocity of a satellite depends on its position relevant to a large body. The change in weather depends on the pressure, temperature, and air velocity all over the earth (this is getting into PDEs, but the basic motivation remains).


Of course, the connection of such models to the real world depends on how well the model is constructed and how well it can be analyzed. It's a matter of balancing robustness and usability with accurateness, and there are reasons to explore either side of that spectrum based on what your goals are. Many times we may not even bother to solve them, but rather focus on qualitative properties of the model, such as whether or not an equilibrium is stable, the existence of periodic solutions or chaos, whether a variable goes to zero or persists, etc. Differential equations is probably the largest field in applied math, and in my opinion probably the most important use of math in science other than maybe statistics and probability.

Hi. The book Basic Mathematics by Serge Lang covers high school math in a way that is similar to most texts on higher mathematics, with theorems and proofs. As such, I think it would make a great stepping stone to higher maths, and some reviewers on Amazon agree. It gives you a solid foundation, and a little bit of an idea what's in store for you if you choose to pursue math. I think it would be a great place to start.

Send me a PM if you need help obtaining (a digital version of) the book.

I've read some good reviews of Basic Mathematics by Serge Lang. It should prepare the reader for calculus.

Otherwise, many online and free books are already available. Here you find a list of free books approved by the American Institute of Mathematics.

If you want to understand the WHY, then you need to read proofs and at least be familiar with basic concepts of logic. I've found this site really helpful. It's a source for definitions and proofs.

There's no single book that's right for everyone: a suitable book will depend upon (1) your current background, (2) the material you want to study, (3) the level at which you want to study it (e.g., undergraduate- versus graduate-level), and (4) the "flavor" of book you prefer, so to speak. (E.g., do you want lots of worked-out examples? Plenty of exercises? Something which will be useful as a reference book later on?)

That said, here's a preliminary list of titles, many of which inevitably get recommended for requests like yours:

1. Undergraduate Algebra by Serge Lang
   
   
2. Topics in Algebra, 2nd edition, by I. N. Herstein
   
   
3. Algebra, 2nd edition, by Michael Artin
   
   
4. Algebra: Chapter 0 by Paolo Aluffi
   
   
5. Abstract Algebra, 3rd edition, by David S. Dummit and Richard M. Foote
   
   
6. Basic Algebra I and its sequel Basic Algebra II, both by Nathan Jacobson
   
   
7. Algebra by Thomas Hungerford
   
   
8. Algebra by Serge Lang
   
   Good luck finding something useful!

I think pockets of extreme ingenuity were present in certain places, Asimov has some great non fiction books that explore the nature of these types of discoveries and sciences... Its a look at human intuition, ill post links when I get home!

Edit: As promised, here is the link to the Asimov book: The Edge of Tomorrow. It's a great book that combines non-fiction stories and science-fiction stories to stir the imagination and provide a framework as to how/why humans and their intuition lead to the amazing fantasies in science-fiction (which often lead the way for future discoveries).

Another great book to read is Carl Segans: The Cosmos, I know the TV series was wicked awesome (and inspired a generation of great scientists) but the book is that much better... being able to break down the math and explore core concepts in much more depth is very eye opening. The book is written in a way that the technical information provided can be figured out by a lay person while not losing to much of the concepts in the translation.

Similarly, McQuarrie Physical Chemistry may be helpful.

At my school, pchem was divided into a first semester which covered the quantum chemistry of individual atoms/molecules, and a second semester which used some of these quantum ideas (but mostly statistics and thermo) to talk about the statistical mechanics of collections of particles. I believe that McQuarrie's Physical Chemistry covers both, but note that the "mathematical review" sections are just brief interludes. For a more thorough treatment of math methods for physical scientists, consider the Mary Boas book. This book mostly focuses on physics applications, but from my experience in pchem, I would argue that it's just a very "applied" or "specific" version of quantum (or thermal, E&M, etc.) physics.

Also, for quantum chem, it is of utmost importance to be familiar with matrices, vectors, and ideally some of the more fancy portions of a first course in linear algebra, like bases and diagonalization. Although the relative importance of calculus/DE vs. linear algebra might depend on whether your course follows a "Schrodinger" vs. "Heisenberg" (not the Walter White one) approach, respectively.

Sure, I personally know of many examples; that's why I mentioned it before. Also, your second paragraph did not seem remotely offensive to me; it just sounded like you were trying to clearly articulate your point! In response, I think there might be two helpful things to raise at this point before going into specific examples:

• There is a difference between critical inquiry and what I guess I'd call mere criticism. For example, scientists are perpetually engaged in critical inquiry, testing both the results of and also the basis of their discipline, but they are in general disinterested in mere criticism--exploring whether or not science is loopy or of any value whatsoever. I think you may be mistaking this difference in the way you address religion, but a parallel set of conditions obtains. I know very few religious people who engage in mere criticism of religion (although there are some out there!), but I know of quite a substantial number who engage in critical inquiry.
  
  
• It sounds like you may be transferring a lot of your personal experience with religion to other people's expressions of their experience. This might not be the case--you may actually be encountering a lot of people who engage in pseudo-critical thought about their religious beliefs--but I'd wager that this sentence is bordering a self-fulfilling prophecy in the strictly, psychological sense of the term:
  > when I read of how people "question their faith" I see a similarity. I see myself in their words. So far, I haven't seen anything deviate from this.
  
  Two concluding caveats; despite how frequently this point is raised in debate, it is not substantial:
  
  > a dozen religions believe contradictory things
  
  The way this is usually developed to merely criticize religion is like saying "because a dozen philosophies or aesthetic theories or anthropological worldviews believe contradictory things, they are all wrong." Just because two different religious loci make wildly different claims does not mean that they are both equally, wildly incorrect. On the other hand, this is a very good point:
  
  > some of these "self-criticisms" are no better than a person who's in love with someone who is emotionally abusive towards them but they can't bring themselves to leave. Any sort of "evaluating the relationship" is simply a joke. Any example of misconduct is explained away by rationalizing that "but everything else is OK and it feels good on top of that."
  
  I think what we are dealing with here is something that is not specific to religious belief but to any belief that is radicalized in the case of religion. This was part of the point Kuhn so famously made in The Structure of Scientific Revolutions, that there is a strong effect of personal bias and comfort and perceived upheaval in the way that any discipline develops. In other words, I would absolutely grant your point that a lot of religious people are sub-critical and self-deluded when it comes to their reflections on their own religion, but I would attribute this to a condition of humanity in general given its prevalence in other realms of rational endeavor and not just as something particular to religion.
  
  Perhaps this is so obviously prevalent in the case of religion for two reasons:
  
  
• Religion necessarily deals with things close to the bone. There's a lot at personal stake for most people when it comes to whether or not Jesus rose from the dead circa 30 CE, but there's little personally at stake for most people when it comes to whether Marc Anthony married Cleopatra circa 32 BCE. It's more difficult to be critical about beliefs that are "close."
  
  
• We live in a society that rarely speaks openly and pointedly about religious matters. Hence, people have difficulty treating them as a "subject" of a debate or a study without taking things very, very personally. This has been the case in the past for other disciplines in other contexts; for example, it is said that the followers of Pythagorous threw one of their own out of a boat to drown when he demonstrated that the square root of two was an irrational number. People take their religion much more personally now than they take their mathematics; hence, they tend to be ill-adept at a healthy sort of critical inquiry when it comes to religion in general.
  
  Nevertheless, I maintain that there are a lot of religious people who are healthily critical of their own beliefs.

You can get by without enrolling in upper-level courses. There is some great free coursework out there if you want to go that route without paying money. Otherwise there are great introductory texts on the subject, like Why Evolution is True.

> There are some philosophical reasons and some practical reasons that being a "pure" Bayesian isn't really a thing as much as it used to be. But to get there, you first have to understand what a "pure" Bayesian is: you develop reasonable prior information based on your current state of knowledge about a parameter / research question. You codify that in terms of probability, and then you proceed with your analysis based on the data. When you look at the posterior distributions (or posterior predictive distribution), it should then correctly correspond to the rational "new" state of information about a problem because you've coded your prior information and the data, right?

Sounds good. I'm with you here.

> However, suppose you define a "prior" whereby a parameter must be greater than zero, but it turns out that your state of knowledge is wrong?

Isn't that prior then just an error like any other, like assuming that 2 + 2 = 5 and making calculations based on that?

> What if you cannot codify your state of knowledge as a prior?

Do you mean a state of knowledge that is impossible to encode as a prior, or one that we just don't know how to encode?

> What if your state of knowledge is correctly codified but makes up an "improper" prior distribution so that your posterior isn't defined?

Good question. Is it settled how one should construct the strictly correct priors? Do we know that the correct procedure ever leads to improper distributions? Personally, I'm not sure I know how to create priors for any problem other than the one the prior is spread evenly over a finite set of indistinguishable hypotheses.

The thing about trying different priors, to see if it makes much of a difference, seems like a legitimate approximation technique that needn't shake any philosophical underpinnings. As far as I can see, it's akin to plugging in different values of an unknown parameter in a formula, to see if one needs to figure out the unknown parameter, or if the formula produces approximately the same result anyway.

> read this book. I promise it will only try to brainwash you a LITTLE.

I read it and I loved it so much for its uncompromising attitude. Jaynes made me a militant radical. ;-)

I have an uncomfortable feeling that Gelman sometimes strays from the straight and narrow. Nevertheless, I looked forward to reading the page about Prior Choice Recommendations that he links to in one of the posts you mention. In it, though, I find the puzzling "Some principles we don't like: invariance, Jeffreys, entropy". Do you know why they write that?

If you're really interested in this kind of stuff, check out The Ancestor's Tale by Richard Dawkins. In it, he examines our common ancestors with other life in backwards chronological order (our common ancestor with chimps, then our and chimps' common ancestor with the other apes, then apes' common ancestor with all primates, etc). There's lots of interesting information about how genes express and get selected for. For example, one particularly fascinating chapter covers the origin of our tri-chromal color vision, as opposed to the vision of most other mammals, like dogs, and what happened in our genes to bring about that change.

This is a question I have grappled with, since it is something I will eventually face if I ever have children. I feel like the only reasonable route is to provide my child with a copy of this, this, and this, as well as a copy of the Bible, and encourage them to ask questions about anything they're trying to understand. I'll tell them the truth: that many people believe in a god or gods, but that there's no proof that any of it is actually true, and tell them that it's important to understand it for themselves instead of relying on someone stating that something is true and refusing to allow them to question it.

Question everything, even the most mundane detail, until you understand why anything is said to be true or false. That will hopefully be the legacy that I can leave to a child.

Santa Claus will also be a problem.

A couple good ones to get started are:

• A Classical Introduction to Modern Number Theory - Ireland & Rosen
  
  
• Primes of the form x^(2)+ny^(2) - David Cox
  
  These will introduce a lot of the main ideas in a way that you can understand with only the basics of abstract algebra. Having background in Galois Theory helps (you can use Dummit & Foote for a solid intro). Cox's book is probably one of the best reads in the subject. Then there are a few that introduce the basic formalism rigorously:
  
  
• First two/three chapters of Algebraic Number Theory - Neukirch
  
  
• Milne's Online Notes (PDF)
  
  
• A Course in Arithmetic - Serre (PDF)
  
  These cover the basics and can be found from many sources via amazon and google. After this, you can look at some more specialized stuff, though the two main directions are Analytic Number Theory and Langlands Program:
  
  
• Analytic Number Theory: Introduction to Analytic Number Theory - Apostal
  
  
  
• Local Fields: Local Fields - Serre
  
  
• Cyclotomic Fields: Introduction to Cyclotomic Fields - Washington
  
  
• Class Field Theory: Algebraic Number Theory - Cassels & Frolich, the final chapters of Neukirch, Artin L-Functions: A Historical Approach - Snyder (PDF)
  
  
• Elliptic Curves: Rational Points on Elliptic Curves - Silverman (undergrad level), The Arithmetic of Elliptic Curves - Silverman
  
  
• Modular Forms: A First Course in Modular Forms - Diamond & Shurman, Introduction to Elliptic Curves and Modular Forms - Koblitz, Modular Functions and Modular Forms - Milne (PDF), Automorphic Forms and Representations - Bump
  
  
• Langlands Program: (The theory that ties absolutely everything together) An Introduction to Langlands Program - Various, An Elementary Introduction to the Langlands Program - Gelbart (PDF)
  
  
• Prerequisites for the Langlands Program - Knapp (PDF) - This has a basic overview of most everything encountered in algebraic number theory along with many more references. Check it out!
  
  This may be looking far into the future, for someone just getting into Algebraic Number Theory, but I figure it's good to have a reference to point people to. I have my own biases and preferences, if anyone else wants to add something, go for it!

Evolution makes testable predictions which are proved true, and many things in biology and geobiology only make sense in light of evolution.

The discovery of Tiktaalik is one of the better examples.

It's an important transitional fossil, which was found very intentionally.

The scientists wanted to find a particular transition, so they figured out what time period it should be in, then which layer of the earth's crust that should be in because of that time period. Then they looked on maps for where that layer would be exposed, traveled there, and found the fossil exactly where their predictions said.

There's lots of articles and videos on the topic, and it is featured in the excellent book, Why Evolution is True that is filled with many such evidences. If you could get someone to agree to read one bok on evolution, I would recommend that one.

The best advice to get better at solving these problems is to persist. You should have to try, to think, to fail slowly building a picture until you find the solution. Have patience with not knowing exactly what to do.

For more technical general advice Polya's lovely book How to Solve it is excellent.

For those who have not read Douglas Adams' book Last Chance to See I highly recommend it.

This encounter took place as Douglas' friend Stephen traveled to the same places Douglas went in an attempt to see how things had changed since the original publishing of the book.

The bird in this clip is a Kakapo, and it was one of the most touching and funny parts of the original book. There was no porn in the original though.

You're not really doing higher math right now as much as you're learning tricks to solve problems. Once you start proving stuff that'll be a big jump. Usually people start doing that around Real Analysis like your father said. Higher math classes almost entirely consist of proofs. It's a lot of fun once you get the hang of it, but if you've never done it much before it can be jarring to learn how. The goal is to develop mathematical maturity.

Start learning some geometry proofs or pick up a book called "Calculus" by Spivak if you want to start proving stuff now. The Spivak book will give you a massive head start if you read it before college. Differential equations will feel like a joke after this book. It's called calculus but it's really more like real analysis for beginners with a lot of the harder stuff cut out. If you can get through the first 8 chapters or so, which are the hardest ones, you'll understand a lot of mathematics much more deeply than you do now. I'd also look into a book called Linear Algebra done right. This one might be harder to jump into at first but it's overall easier than the other book.

Bayes is the way to go: Ed Jayne's text Probability Theory is fundamental and a great read. Free chapter samples are here. Slightly off topic, David Mackay's free text is also wonderfully engaging.

I also encourage:

"Last Chance to See"

"The Deeper Meaning of Liff"

Both are excellent books. Honestly he was a great writer, and greatly missed.

I enjoyed this one by the same author: Fermat's Enigma. Maybe 1/3 to 1/2 of the book tells the story of Andrew Wiles trying to prove Fermat's Last Theorem (and the significance of it), and mixed in throughout is information about all sorts of mathematical history.

This is not a highly advanced or hard-to-read book. Anybody with an interest in mathematics could enjoy it. If you're looking for some higher-level mathematical knowledge, this is not the book to read. I haven't read The Code Book, so I don't know how similar it is.

EDIT: The first review starts with "After enjoying Singh's "The Code Book"..." The reviewer gave it 5 stars.