Tagged Questions

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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4
votes
3answers
324 views

Textbook request for class field theory [duplicate]

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 ...
2
votes
0answers
71 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 ...
3
votes
2answers
278 views

Textbook for Partial Differential Equations with a viewpoint towards Geometry

I don't know whether I should ask this question here or not but I asked this question on MSE but didn't get any answer so I am posting it here. Though similar questions have been asked at ...
0
votes
2answers
179 views

A book about almost periodic functions [closed]

Can anyone give me suggestions for new books about Besicovitch's almost periodic functions? Thanks a lot.
5
votes
1answer
319 views

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 ...
4
votes
1answer
230 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 ...
1
vote
1answer
123 views

Which book will discuss torsion tensor and affine connection in detail? [closed]

Which book about differential geometry will have these formula about torsion tensor? $$\nabla_{j}T^{i}_{kl}+\nabla_{k}T^{i}_{lj}+\nabla_{l}T^{i}_{jk}=R^{i}_{jkl}+R^{i}_{klj}+R^{i}_{ljk}$$ ...
1
vote
2answers
180 views

Introductory text on Group Cohomology [closed]

What are good introductory textbooks available on Cohomology of Groups?
5
votes
4answers
1k views

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 ...
5
votes
1answer
234 views

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
0answers
80 views

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 ...
3
votes
3answers
300 views

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.
6
votes
2answers
392 views

Ergodic theory and dynamical systems books references

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 ...
34
votes
1answer
2k views

Wanted: a “Coq for the working mathematician”

Sorry for a possibly off-topic question -- there are four StackExchange subs each of which could be construed as the proper place for this question, and I've just picked the one I'm most familiar ...
5
votes
4answers
734 views

“Introduction to mathematical logic” book from a formalist perspective

I'm looking for books that introduce the reader to mathematical logic assuming the perspective of a formalist. I've found that many books are more or less written for the platonist - like Kunen's ...
5
votes
1answer
318 views

Background to understand Gromov's green book

I have a decent background in differential geometry. I have read John Lee's introduction to smooth manifolds and doCarmo's Riemannian Geometry. I was trying to read Misha Gromov's Metric structures ...
13
votes
6answers
1k views

Text for Algebraic Number Theory

I have the privilege of teaching an algebraic number theory course next fall, a rare treat for an algebraic topologist, and have been pondering the choice of text. The students will know some ...
20
votes
1answer
1k views

Why not a Roadmap for Homotopy Theory and Spectra?

MO has seen plenty of roadmap questions but oddly enough I haven't seen one for homotopy theory. As an algebraic geometer who's fond of derived categories I would like some guidance on how to build up ...
2
votes
1answer
363 views

Books on the Hardy-Littlewood circle method

Are there any good books providing an introduction to the Hardy-Littlewood method that do not require much of a background in complex analysis?
16
votes
12answers
1k views

Insightful books about elementary mathematics

What are some books that discuss elementary mathematical topics ('school mathematics'), like arithmetic, basic non-abstract algebra, plane & solid geometry, trigonometry, etc, in an insightful ...
0
votes
1answer
344 views

Recomendation of Complex variables book [closed]

I'd like to ask for a book of complex variables that includes a "large" discussion about the Dirichlet problem, Neumann problem, and problems like that, I have now read "basic complex analysis - ...
1
vote
0answers
451 views

Linear Algebra Text Book

In our department we do not like our current linear algebra book and so we would want to find a better book. This is for the first course in linear algebra and the title of the course is Elementary ...
5
votes
1answer
975 views

Hodge Theory (Voisin)

I have a strong understanding of Representation Theory but am interested in learning from Voisin, Hodge Theory and Complex Algebraic Geometry. What are the prerequisites to learning from this ...
6
votes
6answers
631 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 ...
1
vote
2answers
116 views

Good introductory books on dilation theories?

Are there any good introductory type of books that contain dilation theories of Sz-Nagy, Rohlin and Akcoglu?
13
votes
5answers
1k views

Book Recommendation - PDE's for geometricians / topologists

I am looking for recommendations for a book on partial differential equations, which is not written for applied mathematicians but rather focused on geometry and applications in topology, as well as ...
3
votes
1answer
400 views
1
vote
2answers
353 views

Reference request: learn measure theory for PDEs

I am requesting some references to learn appropriate measure theory for PDEs. Specifically, I would like to learn all the measure theory necessary to understand well-posedness of PDEs with measure ...
24
votes
8answers
3k views

An “advanced beginner's” book on algebraic topology?

It has so happened that I have come this far knowing nothing on the subject of algebraic topology (as in homology theories of topological spaces and their applications). I've decided to finally read ...
11
votes
2answers
446 views

Book on the Three body Problem

Hi all, I am looking for a good book about the famous (infamous perhaps?) three body problem - both theoretical and numerical hardless and accomplishments. can you help? Thanks
10
votes
4answers
738 views

Calculus book in the spirit of the 18th century

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
0answers
326 views

Textbooks on Algorithmic Number Theory

I am looking for a good textbook suitable for graduate or advanced undergraduate students who want to explore algorithmic number theory. Specifically, algorithms for primality testing, and factoring ...
3
votes
4answers
1k views

Roadmap to reach Arithmetic Geometry for a Physics Major

Hi Everybody! I am physics major but I read mathematics for myself. my main fields of interest are number theory and geometry. it seems that due to the works of A.Grothendieck, algebraic geometry must ...
5
votes
2answers
671 views

Books on advanced galois theory

I have been studying galois theory on my own and find it very fascinating. I have gone through Ian Stewarts book: http://www.amazon.co.uk/Galois-Theory-Third-Chapman-Mathematics/dp/1584883936. I am ...
3
votes
2answers
231 views

Book on the Moment Problem

Is there a recently published book on the Classical Moment Problems and related theory? I have seen a couple of old books by Tamarkin and a few other books by Russian authors. Want to know what else ...
2
votes
6answers
1k views

Differential geometry study materials

I want to start studying differential geometry but I can't seem to find a proper starting path. Whenever I try to search for differential geometry books/articles I get a huge list. I know that it is a ...
1
vote
1answer
221 views

Recommend a book about compact subgroups

Hi, could you please recommend me some books/articles where I could find information about compact subgroups of metric topological compact (abelian) groups? Thanks in advance for any help.
12
votes
2answers
1k 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
290 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 ...
-5
votes
3answers
566 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.
2
votes
2answers
296 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
4answers
498 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 ...
4
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 ...
4
votes
0answers
365 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 ...
18
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
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 ...