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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Reference request: Left $R/k$-modules

In the paper titled: On the module of differentials of a noncommutative algebra and symmetric biderivations of a semiprime algebra I found the following definition: Let $k$ be a commutative ring with ...
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1 vote
0 answers
199 views

Advanced texts on analytic number theory?

So a friend of mine is very interested in analytic number theory, and is looking for resources past the basic level. He has studied analytic number theory from several books, among them are Hardy’s ...
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3 votes
2 answers
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Request for recommendation in probability and complex analysis

Could somebody kindly recommend to me some books which deal with the applications of the probabilistic method to problems in real and complex analysis or which consider probabilistic versions of some ...
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1 vote
0 answers
192 views

Reference request - Texts on geometric analysis with exercises

I’ve recently been studying some Riemannian geometry and geometric analysis, however I have found it difficult to find resources with exercises to practice. It seems that many textbooks past the ...
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7 votes
0 answers
160 views

Literature on the reals or their gaps in $L[0^\sharp]$?

I'm doing my Bachelor's Thesis on the continuum in $L$ and $L[0^\sharp]$. In $L$ I study the gaps without new reals (sets of natural numbers) in the hierarchy, as presented in Gaps in the ...
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3 votes
0 answers
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Book and article recommendations with the purpose of studying the intersection between probability theory and lattice theory

Lately, I have been studying probability theory and lattice theory separately and I would like to investigate ideas which relate both subjects together. Having said that, I would like to know if ...
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1 vote
0 answers
243 views

Stein's book on harmonic analysis

My background : I am a Math PhD student. I will most probably work in harmonic analysis on Euclidean spaces. I am a fan of Folland's Real analysis and I have thoroughly studied first 8 chapters of ...
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6 votes
0 answers
164 views

Recent literature on the gaps of reals on $L$ or other inner models?

I'm doing my Bachelor's Thesis on Gödel's constructible universe $L$. I'm interested in the gaps without new reals (sets of natural numbers) in the hierarchy, as presented in Gaps in the constructible ...
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38 votes
13 answers
4k views

Exposition of Grothendieck's mathematics

As Wikipedia says: In Grothendieck's retrospective Récoltes et Semailles, he identified twelve of his contributions which he believed qualified as "great ideas". In chronological order, ...
3 votes
1 answer
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Reference request for a general-to-specific text(book) on abstract dynamical systems

In all references on dynamical systems---encyclopedias, textbooks and articles---I have so far consulted, either there is from the beginning an emphasis on a certain class of dynamical system being ...
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2 votes
0 answers
394 views

Non standard/Advanced books in algebraic topology

Disclaimer: I was really uncertain about posting this question, because it is quite similar to this Algebraic Topology Beyond the Basics: Any Texts Bridging The Gap?. I don't know if it would be best ...
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2 votes
0 answers
106 views

"Equivalent" reference to "Quelques méthodes" by J-L. Lions

I've just started learning about some methods to deal with parabolic equations, and in a lot of papers they refer to the book "Quelques méthodes de résolution des problèmes aux limites non ...
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3 votes
0 answers
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Reference request for convex geometry?

I am looking for a reference for an elementary convex geometry. In Appendix A (page 1810) of this paper by Green and Tao, they cover some basic results from elementary convex geometry. The results ...
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2 votes
0 answers
113 views

Any concrete book for renormalization to recommend?

Any concrete book for renormalization to recommend? concrete Enough,and simple enough, both in mathematics and physics. Thanks in advance.
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3 votes
1 answer
356 views

Geometry book recommendation

Context and mathematical maturity: I have knowledge of the usual engineering math courses, meaning differential+integral+vector calculus, linear algebra, probability and statistics, etc. and some pure ...
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29 views

Rabinowitz global bifurcation

Do you have any (modern) references to recommend to learn the proof of the so called Rabinowitz Global Bifurcation Theorem? The original paper is not self-contained and I don’t find it very ...
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Reference request: Introduction to stochastic control theory

I’m looking for a nice readable introductory text to stochastic control theory. Background wise, I know some general stochastic analysis and deterministic optimal control theory. Some criterion I’m ...
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0 votes
1 answer
44 views

Correlation of centrality measure random vectors [closed]

Let's assume that we have 2 random vectors A=(a1,a2,a3) and B=(b1,b2,b3). Each of these elements is a centrality measure of a network. For instance a1 and b1 are the centrality measures of the same ...
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8 votes
3 answers
901 views

Further reading in algebraic geometry

I recently finished reading W. Fulton's "Algebraic Curves" and also attended a lecture series on moduli spaces and am interested in learning about them as well. I looked for a few books to ...
3 votes
0 answers
168 views

Textbooks/References for Solid Angles? [closed]

Are there any good textbooks that consider the properties of solid angles for polytopes? Being not the most well-versed in geometry, I am unsure of where to start looking. Thank you very much!
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0 votes
1 answer
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Centrality measures in a network with negative correlations

I have a bidirectional network where the weights of edges are based on partial correlation matrix. I have both positive and negative values as weights. Now, I want to compute centrality measures as ...
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24 votes
1 answer
1k 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. ...
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1 vote
0 answers
169 views

Reference request: Interpolation inequalities for Holder continuous functions

I’m looking for easy to read references on the topic of interpolation theory for Holder spaces. The references given in the post here, and the standard reference Gilbarg and Trudinger are (to me) ...
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1 vote
0 answers
108 views

Help to use Statistics and algebra books for community [closed]

My father has 2000 statistics and higher algebra books (schaum series etc). Need to use these for community since he passed away (India) kindly guide me I just need to know if we can donate these ...
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15 votes
8 answers
3k views

Books in advanced differential topology

I am looking for books or other sources in differential topology that include topics like: vector bundles, fibration, cobordism, and other related topics. In general, if anyone has recommendation of ...
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8 votes
2 answers
493 views

Books/References for Inequalities that take advantage of orders

Are there any good references/papers/books that specifically address inequalities that take advantage of orders or monotonicity? I have already browsed through the classical Cauchy-Schwarz Master ...
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11 votes
9 answers
3k views

List of problems for graduate topics?

When I study a new topic, I never feel satisfied until I have spent some time solving a long list of problems. I am looking for either a problem book or a list of problems on graduate math topics. ...
9 votes
4 answers
703 views

An introductory text on expanders

I am looking for a book that covers expander graphs rigorously. Preferably a book aimed at beginners.
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1 vote
0 answers
99 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 ...
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1 vote
0 answers
118 views

constructive type theory references books

What is the best book you recommend for a beginner in constructive type theory applied to computer science?
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0 votes
0 answers
177 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 ...
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1 vote
2 answers
235 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 ...
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124 votes
22 answers
8k 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
0 answers
62 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)...
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1 vote
1 answer
104 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....
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22 votes
10 answers
7k 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
0 answers
106 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.
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15 votes
4 answers
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 ...
17 votes
2 answers
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 ...
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15 votes
3 answers
613 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 ...
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3 votes
2 answers
332 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 ...
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4 votes
1 answer
501 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 ...
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3 votes
1 answer
973 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 ...
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15 votes
0 answers
373 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
0 answers
77 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 ...
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7 votes
5 answers
559 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 ...
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-1 votes
3 answers
514 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 ...
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3 votes
2 answers
834 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 ...
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3 votes
1 answer
337 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
2 answers
842 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 ...
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