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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Logic and Metamath book recommendation [migrated]

Recently, I got interested in Mathematical Logic and now I am looking for good introductory books on Mathematical Logic for beginners. In fact, I plan to read some good books on Metamathematics also. ...
2
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1answer
171 views

Open problems books [closed]

As the title might indicate , I would like to look for recommendations for mathematical book that present open problems in depth with commentary. The only book of this type that I've come across is ...
5
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3answers
321 views

Introductory texts to mathematics [closed]

I am interested in texts recomendations for a 14 years old boy who wants to study more mathematics than he does at school. He seems quite talented, but his knowledge of maths is rather low. I would ...
-1
votes
4answers
405 views

Studying topology: which first, algebraic or differential? [closed]

I have recently studying the basics of topology (ideas in point set, connectedness compactness) and I want to continue my studies but i'm interested in both differential and algebraic topology. which ...
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2answers
160 views

Mathematical statistical qm book-recommendation

I feel that there are quite a few good and rigorous books on the mathematical foundations of quantum mechanics, but I am currently looking for a book that covers mathematical statistical quantum ...
2
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3answers
386 views

First Explicit Irreducible Representations

Although the classification of simple Lie Algebras and their representations is fully understood, I wonder whether there is some book with exhaustive tables describing explicit irreducible ...
5
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2answers
288 views

Combinatorial designs textbook recommendation

Good evening, I am currently taking a class which has combinatorial designs as the first topic, we are using Peter Cameron's book Designs, Graphs, Codes and their Links which I am finding extremely ...
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2answers
187 views

Defining Gauss-Kronecker curvature for submanifolds of $\Bbb R^n$ and relation with ${\rm d}{\bf N}_i$'s

I'm trying to find a definition for Gauss-Kronecker curvature of submanifolds of $\Bbb R^n$, but I'm only finding it for hypersurfaces. I would like to know if someone knows any text which works in ...
1
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1answer
206 views

Book on Convergence Concepts in Probability without Measure Theory [closed]

I am looking for a comprehensive book on Probability which discusses Convergence of Random Variables in detail, excluding portions of Measure Theory. Allan Gut's "Probability: A Graduate Course" seems ...
3
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1answer
292 views

A More Advanced Version of Aluffi's Chapter 0

This is a crosspost of this question from MSE. Paulo Aluffi's Book, Algebra, Chapter 0 aims to teach basic algebra from a categorical viewpoint. The first chapters of the book, however, introduce ...
5
votes
1answer
935 views

textbooks on modern algebraic geometry for 21st-century starters

As for learners in algebraic geometry in 21st century, is there a textbook, lecture note or anything like that to introduce algebraic geometry utilizing the language of derived categories and stacks? ...
2
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0answers
163 views

Good Pre-Calculus book? [closed]

I was reading this article and the author mentioned I should come here and get some advice. I'm 17, currently taking Pre-Calc in high schooling doing really good, but I feel like I'm not getting the ...
11
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5answers
908 views

Differential Algebra Book

I'm looking for a couple good textbooks covering differential algebra. I'm a prospective Ph.D. student, and this is potentially applicable to my specialization. As such, I'm not afraid of depth; I've ...
8
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2answers
454 views

Are there some tables or handbooks of homology and homotopy groups of every manifold which has been calculated?

Are there some tables or handbooks of homology and homotopy groups of every manifold which has been calculated? Or are there some tables or handbooks which list some common calculated results of ...
0
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4answers
412 views

Which are the recommended books for an introductory study of complex manifolds? [closed]

Are there any good introductory type of books that is focus on complex manifolds? Thanks.
17
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19answers
3k views

Math books for advanced high school students

I'm working in a program for teaching a group of students selected in a Olympiad competition. The program is aimed to acquaint the students with the diverse aspects of higher mathematics in a way ...
4
votes
3answers
465 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
1answer
141 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
424 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
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2answers
224 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
447 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 ...
5
votes
1answer
262 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
170 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
235 views

Introductory text on Group Cohomology [closed]

What are good introductory textbooks available on Cohomology of Groups?
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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
303 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
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0answers
92 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
323 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.
7
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2answers
489 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 ...
43
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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
1k 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 ...
6
votes
1answer
362 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 ...
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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 ...
23
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
424 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?
18
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14answers
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 ...
1
vote
1answer
451 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
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0answers
514 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
1k 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
677 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
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2answers
126 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?
15
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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 ...
2
votes
1answer
462 views
1
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2answers
402 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 ...
27
votes
8answers
4k 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
485 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
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4answers
814 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
341 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 ...
9
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4answers
972 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 ...