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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3
votes
1answer
182 views

How to learn concepts of Functional Analysis which are common in PDE

I am a master student and working in PDE area. I am trying to gain deep understanding of some of the concepts in functional analysis which are common tools in PDE research, such as weak*-topology, ...
2
votes
1answer
30 views

Specific discrete system $x_n = A(n,u)\cdot x_{n-1}$ control papers

Basic discrete control theory mostly studies systems which can be represented as $x_n=A(n)x_{n-1}+B(n)u_n$. I wonder if optimal control of specific discrete systems of the type $x_n = A(n,u)\cdot ...
36
votes
5answers
1k views

Undergraduate ODE textbook following Rota

I imagine many people are familiar with the extremely entertaining article "Ten Lessons I Wish I Had Learned Before I Started Teaching Differential Equations" by Gian-Carlo Rota. (If you're not, do ...
21
votes
6answers
1k views

Book recommendation for cobordism theory

I am planning to organize a seminar on cobordism theory and I'm looking for a reference. Such a reference is preferably a book, but I'm open to other ideas. The audience is familiar with ...
9
votes
3answers
350 views

Braided Hopf algebras and Quantum Field Theories

It is well-known, that there are a lot of applications of classical Hopf algebras in QFT, e.g. Connes-Kreimer renormalization, Birkhoff decomposition, Zimmermann formula, properties of Rota-Baxter ...
24
votes
12answers
10k views

Introductory text on Riemannian geometry

I have studied differential geometry, and am looking for basic introductory texts on Riemannian geometry. My target is eventually Kähler geometry, but certain topics like geodesics, curvature, ...
21
votes
24answers
26k views

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?
60
votes
7answers
18k 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 ...
24
votes
18answers
30k 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 ...
3
votes
3answers
578 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 ...
8
votes
3answers
275 views

Combinatorial aspects of continued fractions

Recently, I got interested in the study of the combinatorial aspects of continued fractions. Precisely, I read of the following lemma of Flajolet (see here): Lemma. It holds $$\sum_{\omega} ...
-1
votes
1answer
81 views

What would be a suitable textbook of ordinary differential equations for such content? [closed]

I'm a first year undergraduate in Math. And I'm going to take the course "Analysis II" in the next semester. Half of the course will be spent on ODEs, but from the content of the lecture notes I ...
19
votes
22answers
13k 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, ...
1
vote
1answer
223 views

Good graph theory and combinatorics book

I am looking for a book about graph theory and combinatorics. I am studying the routing problem in communication networks, therefore my interest is on a book with a wide set of problems and examples. ...
39
votes
18answers
36k views

Linear Algebra Texts?

Can anyone suggest a relatively gentle linear algebra text that integrates vector spaces and matrix algebra right from the start? I've found in the past that students react in very negative ways to ...
9
votes
6answers
2k 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 ...
2
votes
1answer
135 views

reference request: simple facts about vector-valued $L^p$ spaces [closed]

I learned basic results (regarding weak convergence) about Banach-space valued functions of a single real variable when learning PDE. (See e.g. Appendix E in Evans's Partial Differential Equations) I ...
15
votes
10answers
3k views

nonstandard analysis book recommendation

I wish to learn nonstandard analysis. Are there any good book recommendations? I'm familiar with the ZFC system, and learnt analysis the classical way. I've found some undergraduate texts, but they ...
15
votes
5answers
4k views

Textbook or lecture notes in topological K-Theory

I am looking for a good introductory level textbook (or set of lecture notes) on classical topological K-Theory that would be suitable for a one-semester graduate course. Ideally, it would require ...
1
vote
1answer
321 views

Mathematics Book on Yang-Mills Equation [duplicate]

I am planning to read two papers - Atiyah-Bott's paper on Yang-Mills equations on Riemann surfaces and Hitchin's Self-Duality equations on Riemann Surface. Can someone please suggest some book where ...
3
votes
3answers
592 views

Intuitive functional analysis book

I want to know functional analysis book like Terence tao's real analysis and measure theory book, full of intuition. I am aware of linear algebra, real analysis, measure theory, Probability theory.
21
votes
10answers
13k views

A book for problems in Functional Analysis

I want to know if there's any book that categorizes problems by subjects of Functional Analysis. I'm studying Functional Analysis now a days and I really need to solve some problems in order to ...
0
votes
0answers
33 views

going from basic category theory to 2-category theory [duplicate]

It seems to me that 2-category is the natural frame to express many of the interesting concepts in computer science : monoidal categories and the various monoids (inc monades etc..) end and coend as ...
23
votes
17answers
35k views

Suggestions for a good Measure Theory book

I have taken analysis and have looked at different measures, but I am currently looking at realizing a certain problem in a different light and feel that I need a better background in various measures ...
11
votes
6answers
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 ...
34
votes
12answers
12k views

Homological Algebra texts

I would like to hear the communities' ideas on good Homological Algebra textbooks / references. The standard example is of course Weibel (which I'll leave for someone else to describe). As usual, ...
21
votes
29answers
15k 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 ...
7
votes
4answers
2k views

Good book on Calculus of Variations

What is a good book on the Calculus of Variations, for a second year PhD student?
35
votes
6answers
8k views

Good lattice theory books?

A recent answer motivated me to post about this. I've always had a vague, unpleasant feeling that somehow lattice theory has been completely robbed of the important place it deserves in mathematics - ...
25
votes
6answers
3k 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 ...
13
votes
7answers
3k views

Book on Symplectic Geometry

Can someone please tell me some introductory book on symplectic geometry? I have no prior idea of the subject but I do know about Lagrangian and Hamiltonian dynamics (at the level of Landau-Lifschitz ...
5
votes
0answers
482 views

Grothendieck problem

Could you suggest me a book or a link where I can find some information about the Grothendieck problem about differential equations? The Grothendieck problem that I am reffering to is the following: ...
127
votes
33answers
74k views

Best Algebraic Geometry text book? (other than Hartshorne)

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 ...
4
votes
2answers
249 views

Notes on flag varieties and Grassmannians for beginners

Can you suggest books or lecture notes (for beginners) covering basic material about flag varieties and Grassmannians (of reductive groups), with emphasis on the usual flag variety, i.e. flag variety ...
13
votes
1answer
363 views

An introduction to Macdonald polynomials other (better?!) than SFHP

Long story short, I personally find Macdonald's celebrated book Symmetric Functions and Hall Polynomials somewhat difficult to read for various reasons. I also know for a fact that I'm not the only ...
8
votes
3answers
879 views

Category theory for Algebraic Geometry

How much of category theory should I know to view schemes, sheaves and cohomology concepts as concrete cases of abstract categorical concepts? Is there a textbook of category theory for AG people?
23
votes
9answers
2k views

Advanced Differential Geometry Textbook

I tried this post on StackExchange with no luck. Hopefully the experts at MathOverflow can help. In algebraic topology there are two canonical "advanced" textbooks that go quite far beyond the usual ...
6
votes
5answers
7k 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 ...
8
votes
6answers
854 views

What books approach group theory through transformation/permutation groups?

What are some books that discuss transformation groups (or permutation groups) before abstract groups? Some quotes to motivate the question: from V. I. Arnold, 'On Teaching Mathematics': What ...
12
votes
1answer
445 views

Springer GTM Reprints in China?

I apologise if this is not the sort of question appropriate for MO; it does however seem that mathematicians are the most likely to know the answer: Many of the Chinese mathematicians and graduate ...
3
votes
1answer
136 views

Good broad review of agent-based modeling? [closed]

Trying to find some good review of agent-based models and networks, specifically models that are defined by a graph of interacting nodes, that covers analysis of collective behavior based on model of ...
10
votes
2answers
652 views

What's a good introduction to category theory for someone doing analysis?

I do functional analysis, and diagrams are popping all over the place. It is about time I learned me some category theory. Any recommendations?
1
vote
0answers
40 views

Basic results for chi square processes

I could not find any introductory material with basic results regarding chi-square processes. Their definition from The Supremum of Chi-Square Processes is as a sum of $d$ squares of independent ...
5
votes
0answers
124 views

Reference for the Banach Manifold structure of $C^k(M,N)$

I'm completely new to the subject of banach manifolds and I'm looking for a reference of the following: Let $M$,$N$ be smooth (=$C^\infty$) finite-dimensional compact manifolds. Consider the set ...
34
votes
11answers
13k views

Algebraic Topology Beyond the Basics:Any Texts Bridging The Gap?

Peter May said famously that algebraic topology is a subject poorly served by it's textbooks. Sadly,I have to agree. Although we have a frieghtcar full of excellent first-year algebraic topology ...
0
votes
2answers
374 views

Linear Algebra classic books [closed]

I'm learning linear algebra at the moment, so I'm looking for some great old classic books. Something like Fermat's or Gauss books of some great mathematians. I don't really like the nowadays books ...
2
votes
0answers
445 views

Commutative algebra books representing the edge of research

Recently I have come across the books Combinatorial Commutative Algebra by Miller and Sturmfels along with Combinatorics and Commutative Algebra by Stanley. I will soon own a copy of each. I also ...
8
votes
8answers
4k 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?
10
votes
8answers
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 ...
2
votes
6answers
1k views

Good books on Geometric Theory of Dynamical Systems

I am looking for a good book on Geometric Theory of Dynamical Systems . I found Geometric Theory of Dynamical Systems by Jr. Palis myself,but it's very old, anyway i would like to find a pure ...