**8**

votes

**2**answers

376 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 ...

**4**

votes

**3**answers

794 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 ...

**7**

votes

**4**answers

812 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

**1**answer

114 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 ...

**15**

votes

**16**answers

2k 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 ...

**0**

votes

**4**answers

306 views

### Which are the recommended books for an introductory study of complex manifolds? [closed]

Are there any good introductory type of books that is focus on complex manifolds?
Thanks.

**4**

votes

**3**answers

343 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

**5**answers

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

**10**answers

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

**2**answers

298 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

**6**answers

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

**2**answers

182 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

**2**answers

414 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

**1**answer

345 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

**19**answers

8k 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

**7**answers

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.

**4**

votes

**1**answer

240 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

**13**answers

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

**4**answers

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

**3**answers

305 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

**7**answers

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

**1**answer

130 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

**9**answers

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

**3**answers

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

**2**answers

187 views

### Introductory text on Group Cohomology [closed]

What are good introductory textbooks available on Cohomology of Groups?

**17**

votes

**15**answers

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

**1**answer

241 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

**0**answers

82 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

**1**answer

345 views

### Fuzzy topology : references [closed]

Hey. I'm looking for references in fuzzy topology. Does anyone know a good book ?

**12**

votes

**18**answers

17k 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

**9**answers

3k 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

**6**answers

3k views

**10**

votes

**4**answers

748 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

**1**answer

537 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

**29**answers

11k 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

**1**answer

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 ...

**19**

votes

**5**answers

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 ...

**34**

votes

**1**answer

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

**4**answers

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

**19**answers

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

**4**answers

803 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

**1**answer

324 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

**6**answers

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

**6**answers

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 ...

**22**

votes

**3**answers

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

**5**answers

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

**10**answers

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

**12**answers

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

**1**answer

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

**3**answers

972 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 ...