This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.
105
votes
35answers
7k views
Fun but serious mathematics books to gift advanced undergraduates.
I am looking for fun, interesting mathematics textbooks which would make good studious holiday gifts for advanced mathematics undergraduates or beginning graduate students. They should be serious but ...
104
votes
2answers
5k views
The Integral that Stumped Feynman?
In "Surely You're Joking, Mr. Feynman!," Nobel-prize winning Physicist Richard Feynman said that he challenged his colleagues to give him an integral that they could evaluate with only complex methods ...
56
votes
3answers
1k views
Is there a definitive guide to speaking mathematics?
Is there a definitive guide to speaking mathematics to avoid ambiguity? I'm writing a program to generate text for a variety of mathematical expressions and would like to code it so that it adheres ...
53
votes
25answers
5k views
What is the single most influential book every mathematician should read?
If you could go back in time and tell yourself to read a specific book at the beginning of your career as a mathematician, which book would it be?
51
votes
7answers
2k views
A Case Against the “Math Gene”
I'm currently teaching a mathematics course for elementary educators (think of it as math methods, but with less focus on methods and more focus on content). In a student's essay, I encountered the ...
49
votes
13answers
7k views
Mathematical equivalent of Feynman's Lectures on Physics?
I'm slowly reading through Feynman's Lectures on Physics and I find myself wondering, is there an analogous book (or books) for math?
48
votes
5answers
1k views
Defining a manifold without reference to the reals
The standard definition I've seen for a manifold is basically that it's something that's locally the same as $\mathbb{R}^n$, without the metric structure normally associated with $\mathbb{R}^n$. ...
47
votes
24answers
10k views
Best book ever on Number Theory
Which is the single best book for Number Theory that everyone who loves Mathematics should read?
47
votes
7answers
3k views
Why do books titled “Abstract Algebra” mostly deal with groups/rings/fields?
As a computer science graduate who had only a basic course in abstract algebra, I want to study some abstract algebra in my free time. I've been looking through some books on the topic, and most seem ...
46
votes
21answers
4k views
Complete course of self-study
I am about 16 years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study ...
43
votes
1answer
806 views
A fleshed-out version of the Noncommutative Geometry proof of the Gauss-Bonnet Theorem?
In Connes's book on noncommutative geometry, he outlines a rather short "algebraic" proof of the Gauss-Bonnet theorem that uses multilinear forms. (Start reading on page 19 of the book) This is given ...
40
votes
3answers
874 views
Paul Erdos's Two-Line Functional Analysis Proof
Legends hold that once upon a time, some mathematicians were rather pleased about a 30-ish page result in functional analysis. Paul Erdos, upon learning of the problem, spent ten or so minutes ...
39
votes
5answers
1k views
What are the issues in modern set theory?
This is spurred by the comments to my answer here. I'm unfamiliar with set theory beyond Cohen's proof of the independence of the continuum hypothesis from ZFC. In particular, I haven't witnessed ...
37
votes
16answers
1k views
The Best of Dover Books (a.k.a the best cheap mathematical texts)
Perhaps this is a repeat question -- let me know if it is -- but I am interested in knowing the best of Dover mathematics books. The reason is because Dover books are very cheap and most other books ...
31
votes
5answers
3k views
Completion of rational numbers via Cauchy sequences
Can anyone recommend a good self-contained reference for completion of rationals to get reals using Cauchy sequences?
