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.
387
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(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.
...
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8
votes
3
answers
683
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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 ...
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11
votes
1
answer
587
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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
68
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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
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5
votes
1
answer
199
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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-...
- 103
7
votes
3
answers
774
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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 ...
- 327
0
votes
2
answers
140
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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 $(...
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0
votes
0
answers
73
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Recurrence relation involving the $\max$ function (reference request): $p_{n + 1} = p_{n} + \max\{r_{p_{n} - 1} - 1, r_{p_{n}}\}$
Consider two sequences $(p_{n})_{n\in\mathbb{N}}$ and $(r_{n})_{n\in\mathbb{N}}$ such that they satisfy the following recurrence relation:
\begin{align*}
p_{n + 1} = p_{n} + \max\{r_{p_{n} - 1} - 1, ...
- 161
5
votes
1
answer
287
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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 "...
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5
votes
1
answer
1k
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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
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0
answers
386
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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 ...
- 163
1
vote
1
answer
94
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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 ...
- 73
14
votes
0
answers
300
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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, ...
- 39.6k
1
vote
1
answer
409
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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:
...
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9
votes
1
answer
1k
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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 ...
- 101
2
votes
1
answer
111
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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 ...
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4
votes
2
answers
229
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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 ...
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0
votes
1
answer
66
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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 ...
2
votes
0
answers
562
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 ...
- 3,414
3
votes
2
answers
313
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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
376
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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 ...
- 3,414
7
votes
0
answers
184
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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
104
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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 ...
- 161
1
vote
0
answers
811
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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 ...
- 111
6
votes
0
answers
188
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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 ...
- 421
38
votes
13
answers
4k
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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
227
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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 ...
- 131
2
votes
0
answers
757
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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 ...
- 441
2
votes
0
answers
132
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"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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4
votes
0
answers
185
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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 ...
- 3,497
2
votes
0
answers
297
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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.
- 2,848
4
votes
1
answer
777
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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
200
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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 ...
- 3,414
0
votes
1
answer
48
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
1k
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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
203
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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
499
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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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25
votes
1
answer
2k
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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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2
votes
0
answers
255
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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) ...
- 3,414
1
vote
0
answers
119
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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 ...
- 21
16
votes
8
answers
4k
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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
532
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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 ...
- 81
11
votes
9
answers
4k
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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
856
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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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2
votes
0
answers
124
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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 ...
- 3,667
0
votes
0
answers
219
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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 ...
- 573
1
vote
2
answers
250
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 ...
- 135
132
votes
22
answers
9k
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
78
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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)...
- 239
1
vote
1
answer
136
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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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