Questions asking for recommendations of textbooks on some subject. It can be helpful to indicate whether the request is for self-study, for use in a course one teaches, for use accompanying a course one takes etc., and to give some additional details on the context. Typically, additional tags are ...

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2
votes
1answer
557 views

Knowledge base about topology [closed]

We are studying topology. There are a lot of definitions and theorems. I wonder if there somewhere knowledge base about topology and reasoning system exists. So I expect some tool that systematizes ...
10
votes
8answers
3k views

Leibnizian calculus textbook

Where can I find a calculus textbook that emphasizes differentials? Is there such a book that I could realistically require my calculus students to use? I want a textbook that supports me when I tell ...
9
votes
11answers
3k views

What advanced Area of Mathematics can be delved into with only basic Calculus and Linear Algebra

Hello Mathoverflow Community, I would really appreciate some advice on this: All I know is Basic Calculus and Basic Linear Algebra, I want to start learning more advanced material on my own while ...
6
votes
5answers
6k views

Beginners text on calculus of variations

I want to begin learning Calculus of Variations. What texts would MathOverflow recommend? Amazon shows up quite a few options: http://tinyurl.com/36koaq4 I work on Machine Learning, and that where ...
10
votes
14answers
7k views

undergraduate logic textbook

I am going to teach the standard undergraduate Logic course for math and engineering majors. What are good (bad) text-books and why. I have not taught that course for a while and wonder if there are ...
12
votes
7answers
3k views

Book on Symplectic Geometry

Can someone please tell me some introductory book on symplectic geometry? I have no prior idea of the subject but I do know about Lagrangian and Hamiltonian dynamics (at the level of Landau-Lifschitz ...
13
votes
12answers
4k views

The best text to study both incompleteness theorems

Hi! What text on both incompleteness theorems you would recommend for beginner? Specifically, I'm looking for the text with the following properties: 1) The proofs should be finitistic, in Godel's ...
15
votes
5answers
4k views

Textbook or lecture notes in topological K-Theory

I am looking for a good introductory level textbook (or set of lecture notes) on classical topological K-Theory that would be suitable for a one-semester graduate course. Ideally, it would require ...
18
votes
19answers
14k views

Good combinatorics textbooks for teaching undergraduates?

Hello, can anyone recommend good combinatorics textbooks for undergraduates? I will be teaching a 10-week course on the subject at Stanford, and I assume that the students will be strong and motivated ...
20
votes
3answers
3k views

Real algebraic geometry vs. algebraic geometry

This question is predicated on my understanding that real algebraic geometry (henceforth RAG) is the version of algebraic geometry (AG) one gets when replacing (esp. algebraically closed) fields with ...
15
votes
1answer
5k views

Matsumura: “Commutative Algebra” versus “Commutative Ring Theory”

There are two books by Matsumura on commutative algebra. The earlier one is called Commutative Algebra and is frequently cited in Hartshorne. The more recent version is called Commutative Ring ...
11
votes
10answers
3k views

Math History books

I'm teaching a course over the summer (it's a sort of make-your-own course for non-majors) and I'm planning on organizing it as a math history course, hitting on major threads through about 1900, and ...
28
votes
16answers
8k views

introductory book on spectral sequences

I have studied some basic homological algebra. But I can't send to get started on spectral sequences. I find Weibel and McCleary hard to understand. Are there books or web resources that serve as ...
18
votes
10answers
9k views

Riemannian Geometry Introductory Text

I have studied differential geometry, and am looking for basic introductory texts on Riemmanian geometry. My target is eventually Kähler geometry, but certain topics like geodesics, curvature, ...
14
votes
10answers
3k views

nonstandard analysis book recommendation

I wish to learn nonstandard analysis. Are there any good book recommendations? I'm familiar with the ZFC system, and learnt analysis the classical way. I've found some undergraduate texts, but they ...
33
votes
11answers
12k views

Algebraic Topology Beyond the Basics:Any Texts Bridging The Gap?

Peter May said famously that algebraic topology is a subject poorly served by it's textbooks. Sadly,I have to agree. Although we have a frieghtcar full of excellent first-year algebraic topology ...
3
votes
7answers
2k views

Books about polynomials [closed]

Hi,have you a good reference (books) for the study of polynomials with one variable or many variables ? Thanks for your help. Don't hesitate to correct my English.
16
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13answers
5k views

Looking for an introductory textbook on algebraic geometry for an undergraduate lecture course

I am now supposed to organize a tiny lecture course on algebraic geometry for undergraduate students who have an interest in this subject. I wonder whether there are some basic algebraic geometry ...
34
votes
6answers
7k views

Good lattice theory books?

A recent answer motivated me to post about this. I've always had a vague, unpleasant feeling that somehow lattice theory has been completely robbed of the important place it deserves in mathematics - ...
20
votes
10answers
12k views

A book for problems in Functional Analysis

I want to know if there's any book that categorizes problems by subjects of Functional Analysis. I'm studying Functional Analysis now a days and I really need to solve some problems in order to ...
19
votes
15answers
18k views

Good Algebraic Number Theory Books

I have just finished a master's degree in Mathematics and want to learn everything possible about algebraic number fields and especially applications to the generalized Pell equation (my thesis ...
20
votes
17answers
33k views

Suggestions for a good Measure Theory book

I have taken analysis and have looked at different measures, but I am currently looking at realizing a certain problem in a different light and feel that I need a better background in various measures ...
21
votes
29answers
14k 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 ...
12
votes
15answers
11k views

Learning Topology

EDIT (Harry): Since this question in its original form was poorly stated (asked about topology rather than graph theory), but we have a list of Topology books in the answers, I guess you should go ...
15
votes
17answers
14k views

Undergraduate Differential Geometry Texts

Can anyone suggest any basic undergraduate differential geometry texts on the same level as Manfredo do Carmo's Differential Geometry of Curves and Surfaces other than that particular one? (I know a ...
5
votes
3answers
1k views

Suggested reading for thermodynamic formalism

Are there any good books out there that can serve as an introduction to thermodynamical formalism in dynamical systems? I know only Zinsmeister's short "Thermodynamical formalism and holomorphic ...
24
votes
11answers
8k views

Lecture notes on representations of finite groups

Next term I am supposed to teach a course on representation of finite groups. This is a third year course for undegrads. I was thinking to use the book of Grodon James and Martin Liebeck ...
5
votes
5answers
1k views

Texts In Non-Commutative Harmonic Analysis

What texts/books are available for progressing into non-commutative harmonic analysis?
17
votes
21answers
24k views

Text for an introductory Real Analysis course.

Any suggestions on a good text to use for teaching an introductory Real Analysis course? Specifically what have you found to be useful about the approach taken in specific texts?
33
votes
12answers
11k 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, ...
122
votes
33answers
70k views

Best Algebraic Geometry text book? (other than Hartshorne)

I think (almost) everyone agrees that Hartshorne's Algebraic Geometry is still the best. Then what might be the 2nd best? It can be a book, preprint, online lecture note, webpage, etc. One suggestion ...
13
votes
7answers
2k views

What is lambda calculus related to?

So I'm not much of a math guy but I've really enjoyed programming in Lisp and have become interested in the ideas of lambda calculus which it is based. I was wondering if anyone had a suggestion ...