Questions tagged [textbook-recommendation]

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 used to indicate the subject. For other questions on books, please use the tag books. Also, see reference-request for a related tag.

Filter by
Sorted by
Tagged with
249 votes
37 answers
168k views

Best algebraic geometry textbook? (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 ...
47 votes
7 answers
14k views

Classification of (compact) Lie groups

I would like to study/understand the (complete) classification of compact lie groups. I know there are a lot of books on this subject, but I'd like to hear what's the best route I can follow (in your ...
68 votes
12 answers
28k views

Algebraic topology beyond the basics: any texts bridging the gap?

Peter May said famously that algebraic topology is a subject poorly served by its textbooks. Sadly, I have to agree. Although we have a freightcar full of excellent first-year algebraic topology texts ...
49 votes
8 answers
25k views

Roadmap for studying arithmetic geometry

I have read Hartshorne's Algebraic Geometry from chapter 1 to chapter 4, so I'd like to find some suggestions about the next step to study arithmetic geometry. I want to know how to use scheme ...
16 votes
2 answers
2k views

Good introductory references on moduli (stacks), for arithmetic objects

I've studied some fundation of algebraic geometry, such as Hartshorne's "Algebraic Geometry", Liu's "Algebraic Geometry and Arithmetic Curves", Silverman's "The Arithmetic of Elliptic Curves", and ...
k.j.'s user avatar
  • 1,352
45 votes
8 answers
22k 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 ...
44 votes
11 answers
16k views

Resources for learning practical category theory

I've been doing functional programming, primarily in OCaml, for a couple years now, and have recently ventured into the land of monads. I'm able to work them now, and understand how to use them, but ...
41 votes
1 answer
9k 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 ...
John Salvatierrez's user avatar
38 votes
26 answers
56k 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?
16 votes
5 answers
3k 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 ...
Igor Khavkine's user avatar
136 votes
15 answers
35k views

Statistics for mathematicians

I'm looking for an overview of statistics suitable for the mathematically mature reader: someone familiar with measure theoretic probability at say Billingsley level, but almost completely ignorant of ...
63 votes
25 answers
68k 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 ...
52 votes
9 answers
6k 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 ...
50 votes
7 answers
14k 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 - ...
44 votes
6 answers
11k views

Book on mathematical "rigorous" String Theory?

I've been looking high and low for a mathematical book on String Theory. The only book I could find was "A Mathematical Introduction to String Theory" by Albeverio, Jost, Paycha and ...
44 votes
19 answers
16k views

introductory book on spectral sequences

I have studied some basic homological algebra. But I can't send to get started on spectral sequences. I find Weibel and McCleary hard to understand. Are there books or web resources that serve as ...
28 votes
5 answers
4k views

Modern source for spectra (including ring spectra)

I am looking for a modern introduction to spectra that improves on the treatment by Adams in his "Stable Homotopy and Generalized Homology" notes (by improves I mean taking into account what ...
28 votes
9 answers
14k views

Suggestions for good books on class field theory

Recently I tried to learn class field theory, but I find it is difficult. I have read the book "Algebraic Number Theory" by J. W. S. Cassels and A. Frohlich. In the book, the approach to class field ...
25 votes
1 answer
2k views

Reading list recommendation for a hep-ph student to start studying QFT at a more mathematically rigorous level?

Edition On July 15 2021, the description of the question has been considerably modified to meet the requirement of making this question more OP-independent and thus more useful for general readers. ...
Qi Tianluo's user avatar
20 votes
7 answers
8k views

Elementary reference for algebraic groups

I'm looking for a reference on algebraic groups which requires only knowledge of basic material on the theory of varieties which you could find in, for example, Basic Algebraic Geometry 1 by ...
David Corwin's user avatar
  • 15.1k
18 votes
15 answers
13k views

undergraduate logic textbook

I am going to teach the standard undergraduate Logic course for math and engineering majors. What are good (bad) text-books and why. I have not taught that course for a while and wonder if there are ...
18 votes
5 answers
4k views

Are there textbooks on logic where the references to set theory appear only after the construction of set theory?

This is cross posted from MathStackExchange. Since this is a reference request, I believe there will not be duplications of efforts in answers. This is also related to the question here. In textbooks ...
Sergei Akbarov's user avatar
16 votes
6 answers
7k 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 ...
6 votes
0 answers
1k views

Are French, original editions of Grothendieck's EGA&SGA out of sales?

I have been desperately searching for the hardcopies of Grothendieck's EGA and SGA trilogy, but I could not find available sales except for some used books at Amazon with ridiculously expensive prices....
MathWanderer's user avatar
4 votes
2 answers
914 views

Reference request: Oldest complex analysis books with (unsolved) exercises?

Per the title, what are some of the oldest complex analysis books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there. I am aware of the ...
Squid with Black Bean Sauce's user avatar
4 votes
1 answer
382 views

Reference request: Oldest (non-analytic) geometry books with (unsolved) exercises?

Per the title, what are some of the oldest (non-analytic) geometry books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there.
Squid with Black Bean Sauce's user avatar
148 votes
26 answers
27k views

Good "casual" advanced math books

I'm curious if there are any good math books out there that take a "casual approach" to higher level topics. I'm very interested in advanced math, but have lost the time as of late to study textbooks ...
90 votes
8 answers
12k views

Books on music theory intended for mathematicians

Some time ago I attended a colloquium given by Princeton music theorist Dmitri Tymoczko, where he gave a fascinating talk on the connection between music composition and certain geometric objects (as ...
82 votes
4 answers
7k 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 with....
darij grinberg's user avatar
63 votes
19 answers
95k 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 ...
59 votes
1 answer
32k 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 ...
Chuang 's user avatar
  • 609
53 votes
13 answers
87k views

Good differential equations text for undergraduates who want to become pure mathematicians

Alright, so I have been taking a while to soak in as much advanced mathematics as an undergraduate as possible, taking courses in algebra, topology, complex analysis (a less rigorous undergraduate ...
53 votes
17 answers
15k views

Computer science for mathematicians

This is a big-list community question, so I'm sorry in advance if it is deemed too soft but I haven't seen anything similar yet. I've seen computer scientists post questions looking to learn things ...
51 votes
14 answers
13k views

Introductory text on geometric group theory?

Can someone indicate me a good introductory text on geometric group theory?
41 votes
2 answers
16k 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" ...
41 votes
12 answers
28k 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, ...
35 votes
5 answers
8k 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 ...
QcH's user avatar
  • 805
32 votes
11 answers
13k views

Lecture notes on representations of finite groups

Next term I am supposed to teach a course on representation of finite groups. This is a third year course for undegrads. I was thinking to use the book of Grodon James and Martin Liebeck "...
28 votes
3 answers
8k 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" ...
Javier Álvarez's user avatar
27 votes
10 answers
10k 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 ...
27 votes
29 answers
29k 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 ...
25 votes
3 answers
5k views

Introductory References for Geometric Representation Theory

Would anyone be able to recommend text books that give an introduction to Geometric Representation Theory and survey papers that give an outline of the work that has been done in the field? I'm ...
Siddharth Venkatesh's user avatar
25 votes
5 answers
5k 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 ...
25 votes
19 answers
20k 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 ...
24 votes
9 answers
13k 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, ...
21 votes
6 answers
8k views

Any good reference for Tits Building?

For beginers, any suggestions?
20 votes
6 answers
2k views

Signal processing reference for pure mathematician

Before giving a more detailed question below, the basic one is: can anyone recommend a good signal-processing reference which would be maximally readable by a pure mathematician (who nevertheless ...
Pure mathematician's user avatar
18 votes
1 answer
6k 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 ...
David White's user avatar
  • 28.7k
17 votes
4 answers
1k 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 ...
mikis's user avatar
  • 797
17 votes
10 answers
16k 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 ...