The Princeton Companion to Mathematics is a good resource consisting of a huge collection of detailed articles on many mathematical subjects by knowledgeable contributors. It requires no specialized background and is curated by Fields Medalist Tim Gowers. Whoever reads it from cover to cover is my hero, but failing that there's always an interesting article to jump to. Don't just be a consumer but write something as soon as you're inspired. I wish there were more emphasis on writing mathematics in school prior to the graduate level. Leslie Lamport says if you're thinking but not writing…
Definitely! I have both the Princeton Companion to Mathematics and Princeton Companion to Applied Mathematics and both are well worth the money. One of the difficulties in studying the breadth of mathematics is that the huge amount of jargon/notation of the different branches/models/tools all seem complex/unrelated and hence a single volume where you can jump back and forth between different views is very much necessary to appreciate the unity of Mathematics. It is also an invaluable aid in understanding new terminologies/techniques that one may come across while studying other subjects. The…
May I present one of the greatest math books for general audience: Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent’ev. http://www.amazon.com/Mathematics-Its-Content-Methods-Meanin... Math books rarely move from the Soviet Union to west, but this did and for really good reason. Just look at the list of writers included. So far I have not seen any math books that come even close to this. Reading this book together with the The Princeton Companion to Mathematics was real treat.
This is a wonderful book. A word of caution though: don't get the Kindle version from Amazon. I thought I'd get it for the Kindle, because the print version is huge and I sometimes like to read in bed and don't want to lug the dead tree version I own around, but I had to return it because of the standard problems with garbled notation (some symbols appearing as a square box or some other incorrect symbol) that affects every math book I've ever purchased on Amazon for the Kindle. There error rate was much lower than in any other math book I've tried, but still much too high.
Yes and it's conveniently available on Safari [0] if the sticker shock of the print edition is too much. Also, the editor Tim Gowers wrote Mathematics: A Very Short Introduction [1]. 0: http://my.safaribooksonline.com/book/math/9781400830398 1: http://www.amazon.com/dp/B000SEP2T2/
Books are fantastic. I definitely would judge a person that has books for display only. It is easy to tell too. Books are not only novels and the best sellers you find at airports. You can check a fact or a chapter of a textbook to learn or refresh some math problem. You can revisit your own notes on a margin of a novel. You can lend them. Books promote curiosity. While they can be superficial I think dismissing them like that is just anti-intellectual. Other posts in this thread say you can find the books online. As an example, I challenge anyone to find the Princeton Companion to…
If you want thickness: https://www.cis.upenn.edu/~jean/gbooks/geomath.html If you want proofs: https://cseweb.ucsd.edu/~gill/CILASite/ If you want dictionary: https://press.princeton.edu/books/hardcover/9780691118802/th... If you want usefullness: any mathematical physics book will do
I'm suggesting it because, whatever practical tutorials the poster is looking for, the Companion will make for fascinating reading. When I was in school and plodding through physics and chemistry class, I was wildly excited by other, more advanced books, which I devoured. Ditto for biology. I wish the Companion was out then, for I would have loved it (although, my love for mathematics wasn't in any way diminished). Sure, the book is not going to teach you K-12 stuff, but it is almost like standing on the edge of mountain, giving you a vista of the wonderful world of math.
- The Rise of the Western World: A New Economic History, 1973 (Douglas North, Robert Thomas): Nobel Economic Historian North explains how institutions and property rights determine how human beings got along with each other through history; this is important, so they don't think we're mass murderers by design - some school biology book on natural selection, evolution - The Princeton Companion to Mathematics - Goedel, Escher, Bach: introduction to the "weirdness" of the human brain - the little prince (Antoine de Saint-Exupéry): human beings and their quirks - Several editions of Popular…
I’m going to go with a few assumptions here: a) You don’t do this full time. b) By “bottoms up” you just mean “with firm grasp on fundamentals”, not logic/set/category/type theory approach. c) You are skilled with programming/software in general. In a way, you’re ahead of math peers in that you don’t need to do a lot of problems by hand, and can develop intuition much faster through many software tools available. Even charting simple tables goes a long way. Another thing you have going for yourself is - you can basically skip high school math and jump right in for the good stuff. I’d…