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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12
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2answers
2k views

Learning path for the proof of the Weil Conjectures

Assume you are an algebraic geometry advanced student who has mastered Hartshorne's book supplemented on the arithmetic side by the introduction of Lorenzini - "An Invitation to Arithmetic Geometry" ...
1
vote
1answer
399 views
8
votes
7answers
2k views

Any good books on numerical methods for ordinary differential equations?

I need to find some masters-level exercises about numerical methods for solving ODEs. Are there any good references?
8
votes
11answers
2k views

Textbook for undergraduate course in geometry

I've been assigned to teach our undergraduate course in geometry next semester. This course originally was intended for future high-school teachers and focused on axiomatic, Euclid-style geometry ...
-4
votes
3answers
616 views

Books on analytic functions on Banach spaces over a non-Archimedean field

I'm looking for good textbooks on analytic functions on Banach spaces over a non-Archimedean field. If you know one(s), please let me know.
4
votes
2answers
327 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 ...
5
votes
4answers
526 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
5answers
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
5answers
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
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 ...
6
votes
0answers
499 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
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 ...
7
votes
10answers
5k 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
1answer
479 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
5answers
1k 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
11answers
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
1answer
674 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
1answer
485 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
2answers
592 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
3answers
486 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 ...
5
votes
3answers
945 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
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 ...
-1
votes
1answer
371 views

Fuzzy topology : references [closed]

Hey. I'm looking for references in fuzzy topology. Does anyone know a good book ?
7
votes
4answers
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
1answer
770 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
2answers
992 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
12answers
6k 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
5answers
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
9answers
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
6answers
3k 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
3answers
1k 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
5answers
5k views

Textbook for Etale Cohomology

What is the best textbook (or book) for studying Etale cohomology?
1
vote
0answers
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
3answers
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
2answers
605 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? ...
17
votes
2answers
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" ...
4
votes
6answers
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
5answers
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
3answers
610 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
2answers
462 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
4answers
634 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
2answers
515 views

frechet manifolds book

hi, does anyone know a good book or some lecture notes on the theory of frechet manifolds ?
4
votes
1answer
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 ...
0
votes
2answers
778 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 ...
28
votes
1answer
12k 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
1answer
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
2answers
834 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 ...
1
vote
1answer
319 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
2answers
579 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?