**3**

votes

**2**answers

313 views

### what is the definition of the Picard group of a (non necessarilly commutative) Ring?

Hi. I have only able to find the definition of $Pic(R)$ for a commutative ring $R.$ Which is the isomorphism classes of projective $R$-modules of rank $1,$ and the product given by $[A][B]=[A\otimes_R ...

**4**

votes

**4**answers

511 views

### Synthetic approach to hyperbolic geometry?

Hello,
I am looking for a source that discusses and teaches hyperbolic geometry from a synthetic approach (As opposed to the common analytinc approach in the poincare disk). I am looking for ...

**8**

votes

**5**answers

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 ...

**8**

votes

**5**answers

1k views

### Measure theory treatment geared toward the Riesz representation theorem

I'm looking for recommendations for books (or lecture notes) that develop measure theory in sufficient detail to state and prove the Riesz representation theorem (which is the characterization of the ...

**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 ...

**4**

votes

**0**answers

382 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
...

**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 ...

**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 ...

**3**

votes

**1**answer

472 views

### Searching for text for studying Spectral sequence

I'm a graduate student studying algebraic geometry
I saw Spectral sequence is important in deformation theory, and many other places in algebraic geometry.
Can you recommand me some good text for ...

**4**

votes

**5**answers

979 views

### searching for text for studying representation theory

I'm a graduate student studying algebraic geometry.
Recently, When I studying Hodge theory, I saw sl2-representation is used in Hodge theory.
So I think that studying representation theory may be ...

**12**

votes

**11**answers

2k views

### Approachable French Masters

It has been my general desire for a few years to acquire the basics in other European languages for the purpose of reading some of the classics in their original language, in a similar vein to this ...

**3**

votes

**1**answer

634 views

### Books on logic for someone aiming to go to grad school in the field?

I have taken two introductory courses on logic. One was an undergraduate level and the second one was at the graduate level. Both used a set of notes written by the instructor. I'm thinking about ...

**3**

votes

**1**answer

471 views

### Math background needed for Stakgold's Boundary Value Problems & Green's Functions Book

I saw a reference in Jackson's "Classical Electrodynamics" book for Stakgold's book on "Boundary Value Problems and Green's Functions" as a reference for Green's functions. The text is sort of clear, ...

**9**

votes

**2**answers

571 views

### Tor sheaves: what do they tell us about geometry

Hi!
I fear that I am up to ask a very vague question, but more than an answer I need a suggestion of references I should look up.
I need to know everything about Tor sheaves and what do they tell ...

**3**

votes

**3**answers

484 views

### Finite, abelian, yet “fugitive” orthogonal subgroups

Update July 29, 2013.
I have still not found a good textbook for this topic, if you point one to me I will be grateful :) I have accepted BS's answer anyway, since their explanation was useful to me ...

**4**

votes

**3**answers

861 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 ...

**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 ...

**-1**

votes

**1**answer

357 views

### Fuzzy topology : references [closed]

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

**6**

votes

**4**answers

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, ...

**1**

vote

**1**answer

734 views

### Algebraic approaches to modular forms

I'd like to learn about modular forms. My background is mostly computational algebra and group theory, and I've had little-to-no training in complex analysis. I've briefly seen modular forms in a ...

**4**

votes

**2**answers

983 views

### Any suggestions for a course in Mathematical Logic?

I am teaching a topics course for Mathematics majors (at Temple), and am considering Logic as the topic. I was wondering if people (a) have suggestions for an appropriate text and (b) how much might ...

**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 ...

**6**

votes

**5**answers

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 ...

**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 ...

**11**

votes

**6**answers

2k views

### Graduate ODE textbook

Suppose that a hypothetical math grad student was pretty comfortable with first-year real variables and algebra, and had even studied some other things (algebraic geometry, Riemannian geometry, ...

**3**

votes

**3**answers

981 views

### looking for a book on banach manifolds

Hi,
I am looking for a book on Banach manifolds. Can somebody recommend me something.
Thanks in advance.
leo

**17**

votes

**5**answers

4k views

**1**

vote

**0**answers

981 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

598 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? ...

**16**

votes

**2**answers

5k 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" ...

**4**

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. ...

**3**

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

581 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

449 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

620 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 ...

**4**

votes

**2**answers

507 views

### frechet manifolds book

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

**2**

votes

**1**answer

180 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 ...

**0**

votes

**2**answers

740 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 ...

**22**

votes

**1**answer

11k 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 ...

**8**

votes

**1**answer

2k 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

808 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 ...

**8**

votes

**6**answers

3k views

**1**

vote

**1**answer

316 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

560 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

719 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

176 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

558 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 ...