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.

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11 votes
2 answers
2k views

Textbooks or notes on gradient flows in metric spaces

What is a good introduction in gradient flows in metric spaces? I know the book Gradient flows: in metric spaces and in the space of probability measures by Luigi Ambrosio, Nicola Gigli and Giuseppe ...
8 votes
1 answer
1k views

Textbook recommendation: Metric Geometry

I’m currently reading Burago, Burago, Ivanov’s book A Course in Metric Geometry. I’m really enjoying it so far - what would be a good continuation to the book once I’m done?
1 vote
0 answers
191 views

Constructing real numbers using Bolzano-Weierstrass Theorem? [closed]

$\mathbb{R}$ is generally constructed as equivalence classes of Cauchy sequences. As Cauchy Completeness and Archimedean Property together are equivalent to the Bolzano-Weierstrass Theorem, there ...
3 votes
1 answer
137 views

Literature on linear categories

I am trying to understand Deligne's 'Categories Tensorielles', and therefore I need some knowledge on linear categories. Looking at Wikipedia and nLab, I found some definitions and explanations, but I ...
7 votes
1 answer
484 views

Books to develop a unified view of statistics and information theory?

I hope to understand the connection between statistics and information theory in a deep philosophical sense. I suppose the best place to start would be David MacKay's Information Theory, Inference, ...
5 votes
1 answer
889 views

Continuous dependence on initial parameters of an ODE for non-Lipschitz functions?

For ODEs, the standard theorem of continuous dependence of initial parameters deals only with functions that are Lipschitz. Do there exist more general results holding for non-Lipschitz functions? If ...
18 votes
4 answers
3k views

Problems in advanced calculus

I have been teaching Advanced Calculus at the University of Pittsburgh for many years. The course is intended both for advanced undergraduate students and the first year graduate students who have to ...
3 votes
1 answer
225 views

Isometric immersions and metrics in the same conformal class

Let $\phi:\Sigma^2\to M^3$ an conformal isometric immersion into a Riemannian 3-manifold $(M,g)$. I would like to know what kind of informations is preserved (about the immersion) when we change $g$ ...
12 votes
4 answers
2k views

Book on manifolds from a sheaf-theoretic/locally ringed space PoV

I'm looking for an introductory (or rather, non-advanced) book on manifolds as locally ringed spaces, i.e., from the algebraic geometric viewpoint. Most introductory texts only introduce manifolds ...
2 votes
2 answers
569 views

Reference for weak*-semigroup

Let $X$ a dual Banach space (there exists a Banach space $Y$ such that $X=Y'$). A weak* semigroup on $X$ is a semigroup $(T_t)_{\geq 0}$ on $X$ such that, for all $x\in X$, we have $T_tx\to x$ in the ...
23 votes
12 answers
14k 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 (...
17 votes
1 answer
2k views

Best introductory texts on pointless topology

As I understand it, there are three canonical textbooks on pointless topology: the classic "Stone Spaces" by Johnstone, "Topology via Logic" by Steve Vickers, and the newer "Frames and Locales" by ...
41 votes
4 answers
6k views

Elementary number theory text from a categorical perspective

My question is somewhat similar to this previous question, but from a slightly different perspective. Is there any textbook on elementary number theory that develops the properties of $\mathbb{Z}$ as, ...
63 votes
19 answers
96k 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 ...
0 votes
0 answers
122 views

Ask for some percolation reference textbook

I try to learn Bernoulli percolation recently. Could anyone provide some lecture notes or textbooks to enter this field? Thanks.
26 votes
15 answers
18k views

Learning Topology

EDIT (Harry): Since this question in its original form was poorly stated (asked about topology rather than graph theory), but we have a list of Topology books in the answers, I guess you should go ...
10 votes
1 answer
599 views

Reference request about “internal language of categories”

I've tried to become familiar with the so-called "internal language of a category" for the last months. However, I'm still not confident enough when, for instance, I find a subobject (of a given ...
5 votes
1 answer
211 views

Translated version of a Caratheodory article

This excellent introduction to Compressive Sensing cites a couple of (seemingly) interesting Caratheodory papers from 1907-1911. These are: [46] C. Caratheodory. Uber den Variabilitätsbereich der ...
30 votes
6 answers
4k 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 ...
1 vote
0 answers
401 views

How to be able to understand Cédric Villani's work? [closed]

I'm a grad student and I find Villani's work profoundly interesting, though I'm not able to read his papers. My question is, how can i cover the prerequisites to read them?
24 votes
12 answers
8k 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 ...
11 votes
4 answers
630 views

Introductory textbook on geometry of hyperbolic space

I am looking for an introductory textbook to the geometry of the hyperbolic space $\mathbb{H}^n$. The book should include explicit description of geodesics and horospheres in various models (...
4 votes
4 answers
2k views

Reference request: any 20th century German critiques of Bourbaki? [closed]

Vladimir Arnold is known, among other things, for offering a scathing critique of Bourbaki: The Arnold – Serre debate Recently I've been reading some Nietzsche, and he chides some Germans in the ...
62 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 ...
0 votes
1 answer
367 views

Reference request: Oldest books on analytic geometry with unsolved exercises?

Per the title, what are some of the oldest books on analytic geometry out there with unsolved exercises? Maybe there are some hidden gems from before the 20th century out there.
34 votes
7 answers
13k views

Textbook for Etale Cohomology

What is the best textbook (or book) for studying Etale cohomology?
12 votes
2 answers
2k views

A second course in the representation theory

I've read Etingof's and then Fulton-Harris' books about the representation theory ("Intrdouction to representation theory" and "Representation theory. A first course" respectively) and found their ...
6 votes
1 answer
560 views

Survey article model theory research

I've taken a graduate course in model theory and I like it so much that I can imagine doing research in this area. Are there survey articles or review papers on the current research topics in model ...
3 votes
1 answer
293 views

Reference request: Oldest books on series with unsolved exercises?

Per the title, what are some of the oldest books on series out there with unsolved exercises? Maybe there are some hidden gems from before the 20th century out there.
6 votes
2 answers
1k views

Simple book on model theory

I was expressed by how Mendelson describes models in his Introduction to mathematical logic. Now I am looking for a nice model theory guide. The book (video source, etc.) must: Include the concrete ...
4 votes
2 answers
642 views

Reference request: Oldest books on algebraic curves with unsolved exercises?

Per the title, what are some of the oldest books on algebraic curves out there with unsolved exercises? Maybe there are some hidden gems from before the 20th century out there.
7 votes
2 answers
755 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 ...
2 votes
0 answers
279 views

Tracking down an elusive book

A few weeks ago I had a very engaging talk with a faculty member, where he told me lots of interesting things about quantum algebras, know theory and Reshetikhin-Turaev invariants (this field is not ...
3 votes
0 answers
3k views

Reading list in dynamical systems

So I’ve managed to gather from various sources, a plethora of books in dynamical systems. Now I’m wondering which of them to read, and in what order. So far these are the books I’ve found/been ...
10 votes
2 answers
1k 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 ...
5 votes
2 answers
1k views

Background needed to understand modern research on knot homology theories

I am a student of mathematics, and have some background in Algebraic Topology (Hatcher, Bott-Tu, Milnor-Stasheff), Differential Geometry (Lee, Kobayashi-Nomizu), Riemannian Geometry (Do Carmo), ...
5 votes
1 answer
277 views

Textbook recommendations: Weakly almost periodic functions

I am currently studying Ergodic Theory from Glasner’s book - in it, weakly almost periodic functions play a large role, as well as general “means” and unitary representations of groups on Hilbert ...
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, ...
7 votes
4 answers
3k views

Exercises in Lie group theory for physics

I teach a course on (Lie) group theory for physics at the level of senior undergraduates. I follow basically the book by Georgi "Lie algebras in particle physics". So I teach them the groups SU(2), ...
5 votes
3 answers
1k views

Problem based representation theory book

I am trying to find books similar in the spirit of Ram Murty's Problems in Analytic Number theory or Murty Esmonde's Problems in Algebraic number theory in the field of Representation Theory (of ...
3 votes
0 answers
306 views

Textbook covering superoperators and tensor products

I am looking for a textbook to cover the following tensor product (and, of course, the theory around it): Let $\otimes_1$ denote the tensor product on Hilbert spaces. Let $\otimes_2$ denote the ...
1 vote
0 answers
249 views

Functional Analysis book with graphical descriptions [closed]

I am looking for some book about functional analysis that has also graphical descriptions and images of the important concepts. Anyone knows some book like this?
24 votes
6 answers
14k views

What are the recommended books for an introductory study of elliptic curves?

I am currently doing a self study on algebraic geometry but my ultimate goal is to study more on elliptic curves. Which are the most recommended textbooks I can use to study? I need something not so ...
8 votes
0 answers
286 views

Explicit computations with crystalline cohomology

I am currently studying crystalline cohomology and while all the talk about crystalline topoi is nice, I would like to see some explicit computations. What are some references on this subject which ...
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 ...
4 votes
1 answer
173 views

Origin of the relations of Leavitt path algebras

I know the formal definition of Leavitt path algebras, but I want know why the relations defining Leavitt Path Algebras are defined in that way? what is special of this relations? My real hidden ...
6 votes
7 answers
6k 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
3 answers
1k views

Reference request: Dynamical systems

I’m currently reading Brin and Stuck’s Introduction to Dynamical Systems, and I think I like the field a lot so far. I haven’t finished it quite yet, but what are some other good textbooks I can read ...
3 votes
1 answer
2k views

Regarding learning Algebraic Topology [closed]

Recently, I read a little portion of homotopy theory from Bredon's 'Topology and Geometry' and found that I like it enough to want to continue reading material in Algebraic Topology. A little ...
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.

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