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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6
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5answers
3k 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
254 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 ...
4
votes
3answers
769 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
659 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
0answers
67 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
2answers
176 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.
6
votes
2answers
385 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
305 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
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, ...
2
votes
7answers
1k 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.
4
votes
1answer
226 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 ...
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 ...
3
votes
3answers
299 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
119 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? $$\nabla_{j}T^{i}_{kl}+\nabla_{k}T^{i}_{lj}+\nabla_{l}T^{i}_{jk}=R^{i}_{jkl}+R^{i}_{klj}+R^{i}_{ljk}$$ ...
8
votes
9answers
3k 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 ...
19
votes
3answers
2k 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
173 views

Introductory text on Group Cohomology [closed]

What are good introductory textbooks available on Cohomology of Groups?
17
votes
15answers
14k 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
228 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
80 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 ...
-1
votes
1answer
342 views

Fuzzy topology : references [closed]

Hey. I'm looking for references in fuzzy topology. Does anyone know a good book ?
12
votes
18answers
16k views

A good book of functional analysis

I'm a student (I've been studying mathematics 4 years at the university) and I like functional analysis and topology, but I only studied 6 credits of functional analysis and 7 in topology (the ...
12
votes
9answers
2k views

Book recommendation for ergodic theory and/or topological dynamics?

Hello, I'd like to hear your opinion for ergodic theory books which would suit a beginner (with background in measure theory, real analysis and topological groups). I am looking for something well ...
8
votes
6answers
3k views
10
votes
4answers
736 views

Calculus book in the spirit of the 18th century

I have been reading a lovely 18th century book by John Rowe called An Introduction to the Doctrine of Fluxions. It presents calculus completely motivated by geometric questions - finding tangents to ...
2
votes
1answer
535 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 ...
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 ...
14
votes
1answer
4k 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 ...
18
votes
5answers
2k views

A toolbox for algebraic topology

This question has a very general part and a rather concrete part. General: When one wants to prove something in algebraic topology (actually in all parts of mathematics) one obviously needs some ...
33
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 ...
1
vote
4answers
1k views

Textbooks to use as reference for standard calculus and probability topics

I am currently working on a paper to be submitted to a US journal (addressed primarily to non-mathematicians’ audience) where I use (1) some standard calculus stuff (e.g. limits, Taylor expansions, ...
14
votes
19answers
11k 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 ...
5
votes
4answers
713 views

“Introduction to mathematical logic” book from a formalist perspective

I'm looking for books that introduce the reader to mathematical logic assuming the perspective of a formalist. I've found that many books are more or less written for the platonist - like Kunen's ...
5
votes
1answer
317 views

Background to understand Gromov's green book

I have a decent background in differential geometry. I have read John Lee's introduction to smooth manifolds and doCarmo's Riemannian Geometry. I was trying to read Misha Gromov's Metric structures ...
2
votes
6answers
1k views

Differential geometry study materials

I want to start studying differential geometry but I can't seem to find a proper starting path. Whenever I try to search for differential geometry books/articles I get a huge list. I know that it is a ...
13
votes
6answers
1k views

Text for Algebraic Number Theory

I have the privilege of teaching an algebraic number theory course next fall, a rare treat for an algebraic topologist, and have been pondering the choice of text. The students will know some ...
21
votes
3answers
3k views

Elementary Number Theory Text from a Categorical Perspective

My question is somewhat similar to this previous question, but from a slightly different perspective. Is there any textbook on elementary number theory that develops the properties of $\mathbb{Z}$ as, ...
5
votes
5answers
2k views

Exponential sums for beginner.

What are the good books, online lecture notes or starting material on exponentials sums with applications in number theory for a beginner, apart from N. M. Korobov's book? The book or notes should ...
7
votes
10answers
4k views

College (Euclidean) geometry textbook recommendations

I will be teaching a mid-level undergraduate course in Euclidean geometry this fall. Has anyone taught such a course, who can recommend a good textbook? My students will mostly be future high school ...
14
votes
12answers
5k views

A book in topology

I will have to teach a topology course: it starts in point set topology and ends at fundamental group of $S^1$. In the past I have used two different books: Elementary Topology. Textbook in ...
20
votes
1answer
1k views

Why not a Roadmap for Homotopy Theory and Spectra?

MO has seen plenty of roadmap questions but oddly enough I haven't seen one for homotopy theory. As an algebraic geometer who's fond of derived categories I would like some guidance on how to build up ...
5
votes
3answers
968 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 ...
26
votes
6answers
4k views

Book on mathematical “rigorous” String Theory?

I've been looking high and low for a mathematical Book on String Theory. The only Book I could find was "A Mathematical Introduction to String Theory" by Albeverio, Jost, Paycha and Scarlatti. I only ...
6
votes
6answers
628 views

What books approach group theory through transformation/permutation groups?

What are some books that discuss transformation groups (or permutation groups) before abstract groups? Some quotes to motivate the question: from V. I. Arnold, 'On Teaching Mathematics': What ...
3
votes
6answers
8k views

What are your favorite calculus books for math majors of various levels? [closed]

Since I'll be working ("I" being the original poster, Andrew L) as either a high school math teacher or adjunct at a university as well as private tutoring, to make ends meet for the next year or so ...
2
votes
1answer
360 views

Books on the Hardy-Littlewood circle method

Are there any good books providing an introduction to the Hardy-Littlewood method that do not require much of a background in complex analysis?