**0**

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**0**answers

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### Algebra textbook recommandation for person already familiar with algebra [migrated]

Can you guys please recommend me a good textbook on algebra, given that I am already familiar with lots of algebra stuff and I want to revisit, and deepen my knowledge?
(Little backstory: I started ...

**0**

votes

**1**answer

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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**

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**5**answers

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I would love ...

**10**

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**4**

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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 ...

**42**

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**88**

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**33**answers

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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

**12**answers

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### 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

**1**answer

823 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

**1**answer

235 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**

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**5**answers

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**2**

votes

**0**answers

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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 ...

**10**

votes

**18**answers

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### 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?

**8**

votes

**2**answers

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### 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 ...

**7**

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**4**answers

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**2**

votes

**1**answer

124 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 ...

**16**

votes

**16**answers

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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

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### 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**

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**3**answers

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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

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### 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**

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**10**answers

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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

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Though similar questions have been asked at ...

**7**

votes

**6**answers

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I intend to focus on practical applications.
I would be grateful if ...

**0**

votes

**2**answers

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### 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**

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**2**answers

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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

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### 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

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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

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### 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

250 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

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### 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

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### 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

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### 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

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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

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### 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

**3**answers

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### Real algebraic geometry vs. algebraic geometry

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**1**

vote

**2**answers

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### Introductory text on Group Cohomology [closed]

What are good introductory textbooks available on Cohomology of Groups?

**17**

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**15**answers

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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

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### 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

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### 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

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### Fuzzy topology : references [closed]

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

**12**

votes

**18**answers

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**12**

votes

**9**answers

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### 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

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**10**

votes

**4**answers

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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

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### 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

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### 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

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### 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

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### 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 ...

**1**

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**4**answers

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### Textbooks to use as reference for standard calculus and probability topics

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**15**

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**19**answers

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### 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 ...