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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9
votes
4answers
569 views

An introductory text on expanders

I am looking for a book that covers expander graphs rigorously. Preferably a book aimed at beginners.
1
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0answers
92 views

Metrizable cellular topological spaces

For a CW-complex, locally compact, metrizable, first countable and locally finite are equivalent conditions. A proof is available in https://epub.ub.uni-muenchen.de/4524/1/4524.pdf. I need the same ...
1
vote
0answers
75 views

constructive type theory references books

What is the best book you recommend for a beginner in constructive type theory applied to computer science?
0
votes
0answers
125 views

Algebraic closure of field of fractions of multivariate polynomial ring over $\mathbb{R}$

I am searching for good references on the topic of the behaviour of the elements in the algebraic closed field $(\mathbb{R}[x_{1},\dots,x_{n}])^{\operatorname{alg}}.$ I imagine that, when we try to ...
1
vote
2answers
216 views

Reference for integral extensions of $\mathbb{Z}/p^k\mathbb{Z}$

I was looking for a reference which discusses the structure of finite integral extensions of $\mathbb{Z}/p^k\mathbb{Z}$. In particular, I am interested in understanding what the abelian group of its ...
115
votes
22answers
7k views

Books that teach other subjects, written for a mathematician

Say I am a mathematician who doesn't know any chemistry but would like to learn it. What books should I read? Or say I want to learn about Einstein's theory of relativity, but I don't even know much ...
0
votes
0answers
49 views

Reference request for additive persistence of a number

It is well known fact that each natural number can be represented uniquely in any base. So we can define digit sum function whose value is sum of digits of the natural number in given base. Let $f(n,b)...
1
vote
1answer
92 views

Can any one suggest a very basic book for fuzzy graph theory?

Can anyone help with a very basic book on fuzzy graph theory for a beginner to it with good explanations. Any video course online on fuzzy graph theory extensively to help understand please share link....
21
votes
10answers
5k views

Best Springer mathematics books [closed]

I received an email from zbMATH today to the effect that, as a result of their going open access in January 2021 (which is awesome), they will no longer be able to offer their reviewer discount for ...
1
vote
0answers
100 views

A gentle introduction to harnack curves

I am starting to study Harnack curves and I would like to read a very introductory and intuitive text, if it's possible with a lot of examples and with a clear exposition of general ideas.
15
votes
4answers
1k views

Which mathematics book would you wish theoretical physicists had read?

It is a well-known phenomenon that mathematicians and physicists working on closely-related topics (say in gauge theories, or in general relativity etc.) generally approach the problems from very ...
15
votes
2answers
1k views

Roadmap to learning the classification of finite simple groups

I want to learn the classification of finite simple groups. But it is often commented that it is a theorem spanning tens of thousands of pages of research papers. So it is quite intimidating to an ...
14
votes
3answers
555 views

What are some foundational authors/papers in dynamical systems?

I have just begun my first dynamical systems class, and I would like to try out the advice in the top answer here. To summarize, the answer suggests that when studying a new field, one should look at ...
3
votes
2answers
221 views

Reading material for an analytical aspect of Kähler Geometry

This question was originally posted on MSE. But I would like to post it here to see whether anyone could recommend some reference for me. I am currently reading the paper "Three-circle theorem ...
4
votes
1answer
379 views

Algebraic geometry reference for differential geometer

I am a graduate student in differential geometry and would like to learn more about algebraic geometry recently. Are there any recommended textbook/reference/lecture notes which is easier for a ...
3
votes
1answer
516 views

Is Axler's Linear Algebra done right insufficient for an introduction of the subject? [closed]

Is Axler's Linear algebra done right insufficient for an introduction of the subject? I have recognized the similar question, but I have a somewhat different situation. My familiarity with linear ...
15
votes
0answers
336 views

Grothendieck dessins d'enfants - current surveys or text you can recommend?

I was recommended this forum to be the leading site for algebraic geometry, so I would like to ask you a question about Grothendieck dessins d´enfants. My background is in maps on surfaces (graph ...
1
vote
0answers
74 views

Dislocations and Random Matrix Theory

Does anyone have a good reference book that works as a good starting point for an analyst to learn about the connection between Random Matrix Theory and Dislocations? Thank you for your help. By ...
7
votes
5answers
528 views

Reference for graduate-level text or monograph with focus on “the continuum”

I always had the dream to design a course for my graduate students like "mathematical models of the continuum". This course should cover history of real numbers, the Measure Problem, the ...
0
votes
3answers
427 views

Oldest abstract algebra book with exercises?

Per the title, what are some of the oldest abstract algebra books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there. I am already aware of ...
3
votes
2answers
655 views

What are your opinions on Zeidler's QFT books? [closed]

I am interested in mathematically rigorous treatment of quantum field theory, constructive QFT in particular. I have read 'QFT, A Tourist Guide for Mathematicians' and am going to read "Quantum ...
0
votes
0answers
42 views

Beginner's book on stochastic prediction theory

I read the papers of Wiener and Masani on stochastic prediction theory. I do not have a statistics background, but for some reason I need to know this subject. My questions are: Can someone please ...
4
votes
1answer
172 views

Books to develop a deep understanding of Algorithmic Information Theory?

I'm mathematical physicist working with hydrodynamics modelling. Recently, I had to turn to modelling of flows with particles and some questions I have I think are related to Algorithmic Information ...
5
votes
1answer
452 views

Canon in algebraic combinatorics and how to study

1) In subjects such as algebraic geometry, algebraic topology there is a very basic standard canonical syllabus of things one learns in order to get to reading research papers. Is there a similar ...
4
votes
0answers
99 views

Books on integration on semisimple Lie groups

Can anyone suggest me some good books where I can find integration theory on semisimple Lie groups (using KAK, KAN and other type of decompositions)? I have read Knapp's book "Lie groups beyond ...
6
votes
3answers
479 views

Bass-Serre theory textbook

I am a PhD freshman working on topological graph theory and geometric group theory. I would like to learn some Bass-Serre theory. What do you think is the best introductory textbook in this topic? ...
8
votes
1answer
689 views

Which books should I read in order to be prepared to study information geometry?

At the moment, I am preparing my master's thesis (in statistics) and I intend to keep studying in order to pursue a doctoral degree. To be precise, I am mainly interested in studying Information ...
6
votes
1answer
493 views

Books on foliations

I am looking for resources (books, notes, lecture video, etc. anything will do although printed material in English is preferable) on foliations which satisfy some or all of the following constraints. ...
6
votes
3answers
791 views

A recommendation for a book on perverse sheaves

I would like to learn about perverse sheaves. I will be grateful if someone could recommend me a book with the following structure. Introduction to basic homotopy theory (derived category and t-...
1
vote
0answers
109 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
1answer
124 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 ...
8
votes
1answer
196 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
1answer
229 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
4answers
2k 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 ...
4
votes
0answers
120 views

Introductory text on amenability

I am looking for a book that covers amenability rigorously. Preferably a book aimed at beginners.
2
votes
1answer
99 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 $g$ ...
11
votes
4answers
1k 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 ...
5
votes
3answers
1k views

More recent introductory text on Differential Geometry similar to Kobayashi/Nomizu

We began an introductory course on Differential Geometry this semester but the text we are using is Kobayashi/Nomizu, which I'm finding to be a little too advanced for an undergraduate introductory ...
15
votes
1answer
766 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 ...
0
votes
0answers
79 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.
10
votes
2answers
598 views

Road map to learn about $\mathrm{Out}{F_n}$

I'm a last year undergraduate student and I have taken a graduate course in geometric group theory. I'd like to start reading some more advanced stuff in geometric group theory and in particular ...
5
votes
1answer
164 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 ...
1
vote
0answers
317 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?
10
votes
4answers
525 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 (...
0
votes
1answer
286 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.
11
votes
2answers
1k 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 ...
7
votes
1answer
359 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
1answer
261 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.
4
votes
4answers
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 ...
6
votes
2answers
920 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 ...

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