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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2answers
99 views

Mathematical statistical qm book-recommendation

I feel that there are quite a few good and rigorous books on the mathematical foundations of quantum mechanics, but I am currently looking for a book that covers mathematical statistical quantum ...
6
votes
0answers
486 views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-modules and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, A Primer of Algebraic D-Modules ...
7
votes
4answers
2k views

Help me find good math questions for my students

I am a teacher at 西铁一中。 I teach mathematics in English for students going abroad. Now this is my problem, there are few mathematics books written in English that are at the level of high school, ...
13
votes
17answers
11k 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 ...
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 ...
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 ...
2
votes
3answers
374 views

First Explicit Irreducible Representations

Although the classification of simple Lie Algebras and their representations is fully understood, I wonder whether there is some book with exhaustive tables describing explicit irreducible ...
10
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19answers
19k 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?
17
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19answers
3k views

Math books for advanced high school students

I'm working in a program for teaching a group of students selected in a Olympiad competition. The program is aimed to acquaint the students with the diverse aspects of higher mathematics in a way ...
5
votes
3answers
936 views

Signal Analysis/Processing Textbook

Can anybody recommend me a decent Signal Analysis/Processing textbook. If possible one that deals a little with MATLAB. I have an little knowledge of Real Analysis and fourier transforms. Wavelets i ...
5
votes
2answers
268 views

Combinatorial designs textbook recommendation

Good evening, I am currently taking a class which has combinatorial designs as the first topic, we are using Peter Cameron's book Designs, Graphs, Codes and their Links which I am finding extremely ...
4
votes
1answer
211 views

Survey on Structural Complexity

Alot of the proofs I've been recently reading: IP / PSpace / MIP / NEXP / randomized reductions have a certain flavour involving proofs showing equivalence/relation between various complexity ...
18
votes
14answers
2k views

Insightful books about elementary mathematics

What are some books that discuss elementary mathematical topics ('school mathematics'), like arithmetic, basic non-abstract algebra, plane & solid geometry, trigonometry, etc, in an insightful ...
1
vote
2answers
160 views

Defining Gauss-Kronecker curvature for submanifolds of $\Bbb R^n$ and relation with ${\rm d}{\bf N}_i$'s

I'm trying to find a definition for Gauss-Kronecker curvature of submanifolds of $\Bbb R^n$, but I'm only finding it for hypersurfaces. I would like to know if someone knows any text which works in ...
27
votes
1answer
12k views

If I want to study Jacob Lurie's books “Higher Topoi Theory”, “Derived AG”, what prerequisites should I have?

I've been told that it's important to know modern physics, Differential Geometry and Algebraic Topology for understanding higher structures. Is there any other prerequisite for understanding Lurie's ...
1
vote
1answer
166 views

Book on Convergence Concepts in Probability without Measure Theory [closed]

I am looking for a comprehensive book on Probability which discusses Convergence of Random Variables in detail, excluding portions of Measure Theory. Allan Gut's "Probability: A Graduate Course" seems ...
8
votes
5answers
1k views

What is a good book on topological groups?

I am looking for a good book on Topological Groups. I have read Pontryagin myself, and I looked some other in the library but they all seem to go in length into some esoteric topics. I would love ...
10
votes
9answers
4k views

Textbooks for PDE between Strauss and Folland

Walter A. Strauss's Partial Differential Equations: An Introduction is a classic PDE textbook for the undergraduate students. While Folland's Introduction to Partial Differential Equations, is a nice ...
43
votes
1answer
2k views

Wanted: a “Coq for the working mathematician”

Sorry for a possibly off-topic question -- there are four StackExchange subs each of which could be construed as the proper place for this question, and I've just picked the one I'm most familiar ...
93
votes
33answers
56k 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 ...
12
votes
12answers
3k 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 ...
5
votes
1answer
889 views

textbooks on modern algebraic geometry for 21st-century starters

As for learners in algebraic geometry in 21st century, is there a textbook, lecture note or anything like that to introduce algebraic geometry utilizing the language of derived categories and stacks? ...
3
votes
1answer
273 views

A More Advanced Version of Aluffi's Chapter 0

This is a crosspost of this question from MSE. Paulo Aluffi's Book, Algebra, Chapter 0 aims to teach basic algebra from a categorical viewpoint. The first chapters of the book, however, introduce ...
11
votes
5answers
881 views

Differential Algebra Book

I'm looking for a couple good textbooks covering differential algebra. I'm a prospective Ph.D. student, and this is potentially applicable to my specialization. As such, I'm not afraid of depth; I've ...
2
votes
0answers
152 views

Good Pre-Calculus book? [closed]

I was reading this article and the author mentioned I should come here and get some advice. I'm 17, currently taking Pre-Calc in high schooling doing really good, but I feel like I'm not getting the ...
8
votes
2answers
441 views

Are there some tables or handbooks of homology and homotopy groups of every manifold which has been calculated?

Are there some tables or handbooks of homology and homotopy groups of every manifold which has been calculated? Or are there some tables or handbooks which list some common calculated results of ...
8
votes
4answers
914 views

Books on advanced galois theory

I have been studying galois theory on my own and find it very fascinating. I have gone through Ian Stewarts book: http://www.amazon.co.uk/Galois-Theory-Third-Chapman-Mathematics/dp/1584883936. I am ...
2
votes
1answer
136 views

books on very large scale linear optimization

Recently in my material science research, I have encountered problems of very large scale linear optimization. I read the introductory book "Introduction to Linear Optimization (Athena Scientific ...
0
votes
4answers
373 views
4
votes
3answers
439 views

Textbook request for class field theory [duplicate]

I am studying class field theory. I need good reference books, notes, or other materials which explain the following topics: ideles and ideals, Haar measure and integration on local fields, Fourier ...
6
votes
5answers
4k views

Mathematical Physics Book Recommendation

I want to learn contemporary mathematical physics, so that, for example, I can read Witten's latest paper without checking other sources again and again to find some basic definitions and theorems. I ...
13
votes
10answers
3k views

Good book on Riemann surfaces and Galois theory?

I'm supervising an undergraduate project on Galois theory and covering spaces. I want to have him read about the fact that from a branched cover of a Riemann surface you get an extension of its field ...
3
votes
2answers
383 views

Textbook for Partial Differential Equations with a viewpoint towards Geometry

I don't know whether I should ask this question here or not but I asked this question on MSE but didn't get any answer so I am posting it here. Though similar questions have been asked at ...
7
votes
6answers
2k views

Discrete Mathematics textbooks for undergraduates

For the first time, I will be teaching a course on Discrete Mathematics for electrical and computer undergraduates students. I intend to focus on practical applications. I would be grateful if ...
0
votes
2answers
208 views

A book about almost periodic functions [closed]

Can anyone give me suggestions for new books about Besicovitch's almost periodic functions? Thanks a lot.
7
votes
2answers
462 views

Ergodic theory and dynamical systems books references

I am arranging a weekly meeting of 2 hours with postgraduate students in ergodic theory (for a period of 3 weeks). I am asking here for an advice of a book (or maybe a set of papers) to look at ...
5
votes
1answer
412 views

Serious introduction to the Langlands program for nonspecialist

I recently became interested in the Langlands program and hope to learn more. For context, I am an analytic number theorist but have some light background in algebraic number theory and modular ...
12
votes
19answers
9k 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, ...
2
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.
5
votes
1answer
257 views

Where can I find resources for creating a mathematics “bridge course”?

My department is in the very early stages of developing a "bridge course" or "introduction to proofs" course, motivated by our lower-level courses not currently doing a good job of preparing our ...
13
votes
13answers
4k 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 ...
6
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 ...
3
votes
3answers
318 views

undergraduate handle decomposition. Reference

As the title says, I'm searching for a nice textbook for introducing the theory of handle decomposition of manifolds to undergraduate students.
10
votes
7answers
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 ...
1
vote
1answer
163 views

Which book will discuss torsion tensor and affine connection in detail? [closed]

Which book about differential geometry will have these formula about torsion tensor? $$\nabla_{j}T^{i}_{kl}+\nabla_{k}T^{i}_{lj}+\nabla_{l}T^{i}_{jk}=R^{i}_{jkl}+R^{i}_{klj}+R^{i}_{ljk}$$ ...
19
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 ...
1
vote
2answers
218 views

Introductory text on Group Cohomology [closed]

What are good introductory textbooks available on Cohomology of Groups?
18
votes
15answers
15k 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 ...
5
votes
1answer
284 views

Learning representation theory of real reductive lie groups

I am interested in any sources that can be helpful for learning the representation theory of real reductive groups. I am currently reading Wallach book, but I feel that I don't understand the subject ...
2
votes
0answers
89 views

Learning resources for Probability Distributions/Models [closed]

I've a good background in basic probability. I need to learn and get a good grip on the probability distributions and stochastic processes, counting processes, and other related topics. I am already ...