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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2 votes
1 answer
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Does some published texbook take a particular approach (described here) to the transition from discrete to continuous probability distributions?

(I posted this question at matheducators.stackexchange.com and it seems to be considered an inappropriate question for that site. I don't understand why.) Imagine an introductory probability course ...
Michael Hardy's user avatar
9 votes
2 answers
528 views

Book for matroid polytopes

I have made a study of polytopes with the books of Ziegler and "Integer Programming" of Conforti, my main goal is to study matroid polytopes; to study matroids I have thought about the book &...
Wrloord's user avatar
  • 201
1 vote
0 answers
224 views

Is there any good book about mathematical physics? [closed]

Is there any book that generally introduces/talks about mathematical physics as a whole and that emphasizes on mathematics, not physics? Or is there no such single book because mathematical physics is ...
ale_7's user avatar
  • 33
4 votes
1 answer
407 views

Reference book on Riemann zeta function and random matrices

What is a reference book to understand the relation between the Riemann zeta function and random matrices?
Cosimo's user avatar
  • 43
0 votes
0 answers
218 views

Reference book on the relation between modular forms and elliptic curves

What is a modern reference book to understand the relation between modular forms and elliptic curves after the proof of the Taniyama–Shimura theorem?
Cosimo's user avatar
  • 43
1 vote
1 answer
320 views

Book on analysis and algebra at the undergraduate level [closed]

I am writing this post because I would like to know what are your references concerning math book showing the interplay between analysis and algebra at an undergraduate-advanced undergraduate level. ...
2 votes
1 answer
36 views

Questions on the "generalized" min. singular value of $A$ given $B$: $\min_{L \in \mathbb{R}^{n \times m}} \{\|BL\|_F: \det(A + BL) = 0\}$

Let $A \in \mathbb{R}^{n \times n}$ be a matrix. Recall $\sigma_{\min}(A)$ is the Frobenius distance between $A$ and the set of singular matrices: $$\sigma_\min(A) = \min_{E \in \mathbb{R}^{n \times n}...
Spencer Kraisler's user avatar
26 votes
1 answer
2k views

(Obscure) areas of mathematics that are largely inactive or forgotten today? [duplicate]

I am looking examples of a mathematical theory (i.e. a body of knowledge, with its own definitions, results, principles etc., i.e., its own language) that is completely inactive or forgotten by today. ...
user7088941's user avatar
8 votes
3 answers
1k views

Recommendation for learning mathematical statistics and probability

I can easily find my way reading a book on homological algebra or algebraic geometry, but I tried once reading a book on statistics and... I felt dumb really: I simply do not understand the ...
huurd's user avatar
  • 995
11 votes
1 answer
736 views

Books/blogs/websites that have open problems in Algebraic geometry

I got admitted in a PhD program in Europe last year. But due to serious mental health issues , I was deemed unfit by the mathematics department to continue the program. I am from a 3rd world nation ...
2 votes
1 answer
94 views

Fluid dynamics textbook discussing Hele-Shaw flow

In this Wikipedia article, Hele-Shaw flow is discussed in some detail. I'd like to find a textbook that discusses Hele-Shaw flow in greater detail. Thanks
Mathew's user avatar
  • 123
6 votes
1 answer
240 views

Intuitive explanations of the Carlitz-Scoville-Vaughan theorem

Crossposted from MSE: I recently came across Ira Gessel's slides on a theorem he says should "be considered one of the fundamental theorems of enumerative combinatorics." The Carlitz-...
KJL's user avatar
  • 113
8 votes
3 answers
2k views

Textbook suggestions for rigorous fluid dynamics

I am interested in studying fluid dynamics and am searching for a good introductory textbook. I know just the very basics of fluids on the physics side. For mathematical prerequisites, I have ...
CBBAM's user avatar
  • 421
0 votes
2 answers
158 views

Reference request for combinatorial problem related to $\max$ relation

Let $x_{i - j}\in\{1,2,\ldots, N\}$, where $i\in\{1,2,\ldots,N\}$ (is fixed) and $0\leq j\leq i$. Based on such context, I am interested in an explicit formula for the numbers of configurations of $(...
user1234's user avatar
  • 159
5 votes
1 answer
342 views

Book that shows a construction of ZFC with Calculus of Constructions

Is there any book that teaches the basics of Type Theory and Calculus of Inductive Constructions (CIC) and also shows a construction of ZFC (or preferably NBG) in CIC? I only found the paper "...
rfloc's user avatar
  • 463
5 votes
2 answers
2k views

Lang's "Algebra" as a self-study book

I am an undergrad senior math major taking a gap year looking to become an actuary. However, I still want to continue learning pure math. I've been looking for a relatively high level text to self ...
6 votes
0 answers
574 views

How to learn homotopy theory

I studied some basic algebraic topology (homotopy/homology/cohomology groups). When reading about the Dold-Thom theorem, the fancier and more recent sources sooner or later all started to use homotopy ...
Georgonzola's user avatar
1 vote
1 answer
105 views

Curves on $n$-torus analogous to curve implied by diagonal in square for torus

I encountered in my research on dynamical systems a problem, which considers for some $L>0$ on the $C_n=[0,L]^n$ the set $\mathcal{C}_n=\{(x_1,\ldots,x_n)\mid\exists j,k:\,x_{i_j}=x_{i_k}\}$. I am ...
Jens Fischer's user avatar
16 votes
1 answer
476 views

A textbook on foundations of geometry in spirit of Tarski

I am interested in a textbook for studying (and teaching) foundations of geometry in the spirit of Tarski. I know that there is a rather old German book [W. Schwabhäuser, W. Szmielew, A. Tarski, ...
Taras Banakh's user avatar
  • 40.7k
1 vote
1 answer
542 views

Approaching the Riemann-Roch Theorem for algebraic curves

I am using "Algebraic Curves: An Introduction to Algebraic Geometry" by William Fulton as a guidline for approaching the Riemann-Roch Theorem for algebraic curves. I have two questions: ...
J.Spil's user avatar
  • 127
10 votes
1 answer
2k views

Roadmap to understand the Scholze's proof of the local Langlands correspondence for $\text{GL}_n$ over $p$-adic fields

I would like to know which books I should read to understand the paper "The local Langlands correspondence for $\mathrm{GL}_n$ over $p$-adic fields" written by Peter Scholze. I only know ...
user860322's user avatar
2 votes
1 answer
130 views

Mellin transform (of sequences)

Is it possible to define the Mellin transform for sequences of real numbers or even for tuples? Is there any book treating this argument? Any idea or suggestion will be greatly appreciated Since the ...
MathG's user avatar
  • 131
4 votes
2 answers
254 views

Request for references in computational complex analysis

We know complex analysis is one of the most important branches of mathematics connecting myriad areas. It is replete with profound results and theorems and theorems. However, a good number of the ...
AgnostMystic's user avatar
0 votes
1 answer
69 views

Reference request: Left $R/k$-modules [closed]

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 ...
The Student's user avatar
2 votes
0 answers
762 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 ...
Nate River's user avatar
  • 4,802
3 votes
2 answers
369 views

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 ...
AgnostMystic's user avatar
2 votes
0 answers
514 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 ...
Nate River's user avatar
  • 4,802
7 votes
0 answers
193 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 ...
Martín S's user avatar
  • 421
3 votes
0 answers
111 views

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 ...
user1234's user avatar
  • 159
2 votes
0 answers
1k 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 ...
risefrominfinite's user avatar
6 votes
0 answers
194 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 ...
Martín S's user avatar
  • 421
38 votes
13 answers
5k 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
249 views

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 ...
l7ll7's user avatar
  • 131
2 votes
0 answers
995 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 ...
Tommaso Rossi's user avatar
2 votes
0 answers
152 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 ...
tommy1996q's user avatar
5 votes
0 answers
208 views

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 ...
Johnny T.'s user avatar
  • 3,537
2 votes
0 answers
409 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.
XL _At_Here_There's user avatar
4 votes
1 answer
1k 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 ...
1 vote
0 answers
307 views

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 ...
Nate River's user avatar
  • 4,802
0 votes
1 answer
50 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 ...
statwoman's user avatar
  • 109
8 votes
3 answers
1k 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
214 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!
rianko's user avatar
  • 31
0 votes
1 answer
633 views

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 ...
statwoman's user avatar
  • 109
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
1 vote
0 answers
121 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 ...
user3414674's user avatar
16 votes
8 answers
4k 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 ...
BERTI2020's user avatar
  • 169
8 votes
2 answers
553 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 ...
rianko's user avatar
  • 81
11 votes
9 answers
4k 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. ...
10 votes
4 answers
976 views

An introductory text on expanders

I am looking for a book that covers expander graphs rigorously. Preferably a book aimed at beginners.
mahdi meisami's user avatar
2 votes
0 answers
137 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 ...
Philippe Gaucher's user avatar

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