**1**

vote

**0**answers

1k views

### Textbook suggestion for advanced algebra? [closed]

After having a solid year long undergraduate course in abstract algebra, I'm interested in learning algebra at a more advanced level, especially in the context of category theory.
I've done some ...

**3**

votes

**3**answers

1k views

### What to teach in a second graduate course in algebra? What textbook to use?

There is a standard syllabus for a first graduate course in algebra. One teaches groups,
rings, fields, perhaps a little bit of Galois theory, perhaps a little bit of
category theory, perhaps a ...

**4**

votes

**2**answers

616 views

### Reference for general linear groups

I want to find a comprehensive reference on general linear groups, which has depth discussion about its subgroups (like solvable subgroups, Abelian subgroups, and so on). Can anyone help me with this? ...

**20**

votes

**2**answers

6k views

### Introductory text on Galois representations

Could someone please recommend a good introductory text on Galois representations? In particular, something that might help with reading Serre's "Abelian l-Adic Representations and Elliptic Curves" ...

**5**

votes

**6**answers

3k views

### A book about model theory

I am looking for a good book about model theory. As this is obviously too vague, let me
explain what I am looking for and why.
First I am interested about the basics and foundations of model theory. ...

**4**

votes

**5**answers

1k views

### What is a basic textbook to studying symmetric spaces?

I want to study basic properties of symmetric spaces.
What is a basic textbook?

**4**

votes

**3**answers

618 views

### What is the best paper or book studying the P homomorphism, J homomorphism and Hopf invariant in Homotopy theory?

I want to study P & J homomorphisms and Hopf invariant in Homotopy theory.
I have some paper, but I don't know what is first and what is nice.
Please recommend to me.

**1**

vote

**2**answers

499 views

### Weil bound for characters sums. (reference-request )

Do you know on any good reference on Weil bound for charcter sums over algebraic curves.
I prefer reference which assume few previous knowlage.

**9**

votes

**4**answers

658 views

### Introductory reading on the Scholz reflection principle?

The Scholz reflection principle says, among other things, that if $D < 0$ is a negative fundamental discriminant, not $-3$, then the 3-ranks of the class group of $\mathbb{Q}(\sqrt{D})$ is either ...

**5**

votes

**2**answers

525 views

### frechet manifolds book

hi, does anyone know a good book or some lecture notes on the theory of frechet manifolds ?

**4**

votes

**1**answer

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 ...

**2**

votes

**2**answers

826 views

### torsion free modules over general ring

i want to know how to prove a torsion free modules over general ring is flat. (in "lecture on ring and modules, T.Y.Lam prove in case R is interal domain). please help me prove it or give me some ...

**30**

votes

**1**answer

13k 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 ...

**11**

votes

**1**answer

3k views

### Intersection between category theory and graph theory

I'm a graduate student who has been spending a lot of time working with categories (model categories, derived categories, triangulated categories...) but I used to love graph theory and have always ...

**6**

votes

**2**answers

873 views

### A book on Banach Manifold for a Dynamicist

Hi all,
Could you give me a suggestion of suitable book about Banach Manifolds for someone that have background in functional analysis at the level of Conway's book and Do Carmo's book on Riemannian ...

**10**

votes

**6**answers

3k views

**1**

vote

**1**answer

340 views

### References For Important Hopf Algebras

Where can I find references that discuss important classes of Infinite Hopf Algebras. By important classes, I mean heavily used in research and of relevance to Hopf Algebraist(s),Physicists, ...

**6**

votes

**2**answers

594 views

### Book on mixed Hodge structures?

Is there any English textbook about Deligne's mixed Hodge structures? Can you tell me about a reference where they are introduced at least for smooth quasi-projective varieties?

**0**

votes

**1**answer

775 views

### Abelian Variety and Tangent Bundle ----Reference Request

I am looking for the reference where I can find the proof of the following:
If $A$ is an abelian variety then its tangent bundle is trivial.

**1**

vote

**0**answers

180 views

### What is the MP pseudoinverse's role in statistical learning and Self-Organizing Maps?

During a discussion in our lab last month, a professor mentioned to me that the behavior of Self-Organizing Maps can be described in terms of repeated applications of the Moore-Penrose psuedoinverse, ...

**7**

votes

**4**answers

2k views

### Hopf Algebras and Quantum Groups

I have studied graduate abstract algebra and would like to learn about Hopf algebras and quantum groups. What book or books would you recommend? Are there other subjects that I should learn first ...

**15**

votes

**3**answers

2k views

### A reference for geometric class field theory?

The classic reference of this topic is Serre's Algebraic Groups and Class Fields. However, many parts of this book use Weil's language, which I find quite hard to follow. Is there another reference ...

**2**

votes

**0**answers

578 views

### Elliptic Curves and cryptography. Recommended Reading [closed]

I have been studying RSA cryptography and want to extend this to ECC. I am interested in any books on the topic, that start off with basic principles of elliptic curves as I have almost zero knowledge ...

**14**

votes

**18**answers

24k 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 ...

**14**

votes

**11**answers

5k 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 ...

**30**

votes

**6**answers

5k 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 ...

**7**

votes

**4**answers

1k views

### Introduction to L-series and Dirichlet characters?

I'm looking for an introductory text on Dirichlet characters and the L-series of a field K, specifically for quartic extensions of $\mathbb{Q}$. I have Davenport's Multiplicative Number Theory, ...

**2**

votes

**0**answers

163 views

### Are there any recommended texts that cover Turing Tilings?

I have read the original paper by Wang, as well as a paper by Boas [1996] entitled 'the Convenience of Tilings', but wanted to know if there were any other texts that people could recommend that ...

**8**

votes

**2**answers

1k views

### good books on Dirichlet's class number formula

i refrained from asking the technical questions ,may be everyone didnt like my attitude ,atleast help me finding the good books
can anyone suggest any good book that gives a complete reference to ...

**5**

votes

**7**answers

6k views

### What is some good introduction to lambda calculus?

I have some background in set theory and automata and I am looking for a good place to start with lambda calculus.

**48**

votes

**7**answers

15k views

### Is Mac Lane still the best place to learn category theory?

For a student embarking on a study of algebraic topology, requiring a knowledge of basic category theory, with a long-term view toward higher/stable/derived category theory, ...
Is Mac Lane still ...

**4**

votes

**2**answers

470 views

### Reading Material on Couplings

Does anybody have suggestions on what to read to learn more about couplings pertaining to statistics?
I'm working on a research project on Poisson approximations and am looking to perform a coupling ...

**5**

votes

**2**answers

828 views

### Survey of Algebraic K-Theory Since 1980?

I just came across Charles Weibel's Development of Algebraic K-Theory until 1980, and found it really helpful. Is there been anything analogous which surveys the developments in the last 30 years? ...

**0**

votes

**1**answer

664 views

### Does it make sense that “Representations of groups over finite ring” ?

I am an undergrad student who wants to know about the representation theory over
arbitrary finite fields or finite rings of characteristic p (p a prime). (called modular
representation theory.)
In ...

**16**

votes

**14**answers

2k views

### Teaching a pedagogy course

At my institution incoming graduate students must take a semester long course on pedagogy taught by current grad students. I may soon be in the position of having to teach this course and I'm looking ...

**24**

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, ...

**0**

votes

**0**answers

445 views

### Linear Representations of the Groups

Does anyone know a good book on Linear Representations of the finite Groups which does not assumes a lot of background. Book which will be good to study for computer science and will cover all( at ...

**8**

votes

**5**answers

3k views

### Good introductory text book on Matroid Theory?

I am looking for a good text book on Matroid theory. Ideally, one that might be better suited to engineers than pure mathematicians...but any book that is well written/organized would do.
I have ...

**10**

votes

**2**answers

1k views

### Literature on the Springer resolution

Could you suggest me a basic reading list on the Springer resolution? Is there a textbook I can refer to? Or do I need to start with the original paper?
Unfortunately googling for "Springer" and ...

**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 ...

**43**

votes

**8**answers

4k views

### Natural transformations as categorical homotopies

Every text book I've ever read about Category Theory gives the definition of natural transformation as a collection of morphisms which make the well known diagrams commute.
There is another possible ...

**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, ...

**4**

votes

**7**answers

2k views

### probability and math puzzle books/references

Hi All,
I'd like to solve some math puzzles, especially in the context of probability theory, but I'm open to other areas too. The kind of problems that does not require much knowledge of mathematics, ...

**13**

votes

**19**answers

10k 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, ...

**4**

votes

**10**answers

3k views

### Best introduction to probability spaces, convergence, spectral analysis

I'm not sure if this stuff all falls under what most would just term "probability", but I'm researching applied macroeconomics and need to get a handle on the following concepts ASAP:
probability ...

**2**

votes

**1**answer

549 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

**8**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 ...

**9**

votes

**11**answers

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 ...

**5**

votes

**5**answers

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

**14**answers

6k 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 ...