5
votes
4answers
1k views

Advice for number theory library

Hi I just got a faculty position and it comes with a generous start up funds for "office supplies", which I must use or lose. What does a pure mathematician need? I have good computers already. I ...
17
votes
2answers
1k views

Papers better than books?

Not so long ago I took a class called "Discrete analysis". I remember that I couldn't find any "novice" level material on Mobius functions in combinatorics. So then I went to the roots and read Rota's ...
25
votes
65answers
7k views

Fiction books about mathematicians? [closed]

What are some fiction books about mathematicians? It seems to me rather difficult for writers to create good books on this subject. Some years ago I thought there were no such books at all. There ...
11
votes
6answers
2k views

Graduate ODE textbook

Suppose that a hypothetical math grad student was pretty comfortable with first-year real variables and algebra, and had even studied some other things (algebraic geometry, Riemannian geometry, ...
16
votes
17answers
3k views

Which book would you like to see “texified”? [closed]

Let's see if we could use MO to put some pressure on certain publishers... Although it is wonderful that it has been put online, I think it would make an even greater read if "Hodge Cycles, Motives ...
12
votes
19answers
7k views

Textbook recommendations for undergraduate proof-writing class

I am teaching the proof-writing class (for the 3rd time) in the Fall and plan to buck the party line and use a different text than the default Bond and Keane. My parameters are as follows: Logic, ...
6
votes
5answers
931 views

Suggestions for mathematics encyclopedia

On daily basis I need to check (and re-check and re-check...) some definitions and main theorems that are not in my research area. Usually I accomplish this by a Google-search and/or a visit to our ...
34
votes
26answers
11k views

A Book You Would Like to Write

Writing a book from the beginning to the end is (so I heard) a very hard process. Planning a book is easier. This question is dual in a sense to the question "Books you would like to read (if somebody ...
10
votes
2answers
968 views

Social Reading Platform for Math or LaTeX texts

Social reading is considered to be one of the big trends that could be catalysing learning by reading. Features could include: Highlighting or annotating paragraphs or single steps in a proof for ...
23
votes
13answers
20k views

Good differential equations text for undergraduates who want to become pure mathematicians

Alright, so I have been taking a while to soak in as much advanced mathematics as an undergraduate as possible, taking courses in algebra, topology, complex analysis (a less rigorous undergraduate ...
15
votes
9answers
3k views

Mathematics and autodidactism

Mathematics is not typically considered (by mathematicians) to be a solo sport; on the contrary, some amount of mathematical interaction with others is often deemed crucial. Courses are the student's ...
6
votes
6answers
432 views

Reference Request: Perspective Painting

What is a good book/article explaining the mathematics behind perspective painting? I have already looked at the wikipedia article on the topic, so I am looking for something more advanced than this. ...
26
votes
32answers
5k views

What out-of-print books would you like to see re-printed?

It's excellent news that the LMS are to re-publish Cassels & Fröhlich. There are many other excellent mathematics books which are just about impossible (or at least very expensive) to get hold ...
93
votes
22answers
9k views

Why do so many textbooks have so much technical detail and so little enlightenment? [closed]

I think/hope this is okay for MO. I often find that textbooks provide very little in the way of motivation or context. As a simple example, consider group theory. Every textbook I have seen that ...
15
votes
4answers
6k views

Famous exercise from Lang's Algebra

There's a famous story about an exercise from Lang's Algebra that says something along the lines of "pick up a homological algebra book and prove all of the theorems yourself". I cannot find it in ...
15
votes
29answers
10k views

Alternative Undergraduate Analysis Texts

Other than the standard baby Rudin, Spivak, and Stein-Shakarchi, are there other alternative and comprehensive analysis texts at the undergraduate level? For example something that has general results ...
56
votes
61answers
22k views

Favorite popular math book [closed]

Christmas is almost here, so imagine you want to buy a good popular math book for your aunt (or whoever you want). Which book would you buy or recommend? It would be nice if you could answer in the ...
8
votes
4answers
3k views

Number theory textbook with an algebraic perspective

Most of the number theory textbooks I've dealt with take a very classical approach to the subject. I'm looking for a textbook that's something like a first course in number theory for people who have ...
9
votes
3answers
780 views

How to sufficiently motivate organization of proofs in math books

Hello, I have a bit of a general question about math books. I get the feeling that in a lot of math books, the organization for the theorems and lemmas are not explained well (ex. Topics in Algebra ...
5
votes
5answers
978 views

Texts In Non-Commutative Harmonic Analysis

What texts/books are available for progressing into non-commutative harmonic analysis?
23
votes
9answers
4k views

Introductory text on geometric group theory?

Can someone indicate me a good introductory text on geometric group theory?
27
votes
11answers
7k views

Homological Algebra texts

I would like to hear the communities' ideas on good Homological Algebra textbooks / references. The standard example is of course Weibel (which I'll leave for someone else to describe). As usual, ...
21
votes
14answers
5k views

Learning LaTeX properly

I have never learned how to use Latex properly. Whenever writing a paper, I use hacks to override behavior of the underlying template. What would be an intermediate to advanced book on learning how to ...