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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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 ...
11 votes
0 answers
2k views

Recommendation textbooks on D-module

I am going to take part in a seminar on D-modules and applications, the textbooks that will be used are : D-modules, Perverse Sheaves, and Representation Theory, A Primer of Algebraic D-Modules ...
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 ...
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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
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7 votes
0 answers
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Books on von Neumann algebras

I am interested in non-commutative $L^p$ spaces. I have a very basic background on von Neumann algebras. But all the papers appearing now a days really requires very deep knowledge of von Neumann ...
Mathbuff's user avatar
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6 votes
0 answers
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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 ...
Georgonzola's user avatar
6 votes
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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
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6 votes
0 answers
217 views

Survey on homological stability

Background: homological stability is the phenomenon that for many natural families of groups $G_0 \to G_1 \to G_2 \to \dots$, the group homology $H_i(G_n)$ stabilizes for $n \gg i$. This is e.g. the ...
Najib Idrissi's user avatar
6 votes
0 answers
1k views

Are French, original editions of Grothendieck's EGA&SGA out of sales?

I have been desperately searching for the hardcopies of Grothendieck's EGA and SGA trilogy, but I could not find available sales except for some used books at Amazon with ridiculously expensive prices....
MathWanderer's user avatar
6 votes
0 answers
774 views

Grothendieck problem

Could you suggest me a book or a link where I can find some information about the Grothendieck problem about differential equations? The Grothendieck problem that I am reffering to is the following: ...
Mary Star's user avatar
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Reference for the Banach Manifold structure of $C^k(M,N)$

I'm completely new to the subject of banach manifolds and I'm looking for a reference of the following: Let $M$,$N$ be smooth (=$C^\infty$) finite-dimensional compact manifolds. Consider the set $C^...
uro's user avatar
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5 votes
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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 ...
Johnny T.'s user avatar
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5 votes
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Geometry of schemes by Eisenbud and Harris

I have some background of algebraic geometry. I am now trying to study schemes from book Geometry of schemes by Eisenbud and Harris. I was checking recommendations for books on algebraic geometry ...
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4 votes
0 answers
182 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 ...
A beginner mathmatician's user avatar
4 votes
0 answers
419 views

Textbooks in differential geometry that treat $C^k$ manifolds

I am looking for textbooks in differential geometry that treat $C^k$ manifolds right from the start. Ideally, the textbook should maintain this general point of view through all chapters and ...
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4 votes
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Commutative algebra books representing the edge of research

Recently I have come across the books Combinatorial Commutative Algebra by Miller and Sturmfels along with Combinatorics and Commutative Algebra by Stanley. I will soon own a copy of each. I also ...
Rex Butler's user avatar
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
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3 votes
0 answers
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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 ...
Dominique Unruh's user avatar
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 ...
James Baxter's user avatar
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3 votes
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Resource request: Moyal $\star$-product based calculations

I already asked two questions about the Moyal $\star$-product here and here but I think I'll have a lot more similar questions, so I'm wondering if anyone can help me with finding some good resources. ...
lel's user avatar
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2 votes
0 answers
763 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
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
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
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
2 votes
0 answers
410 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
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
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 ...
user43263's user avatar
  • 667
2 votes
0 answers
704 views

Textbooks on Algorithmic Number Theory

I am looking for a good textbook suitable for graduate or advanced undergraduate students who want to explore algorithmic number theory. Specifically, algorithms for primality testing, and factoring ...
Chebolu's user avatar
  • 575
2 votes
0 answers
169 views

Are there any recommended texts that cover Turing Tilings?

I have read the original paper by Wang, as well as a paper by Boas [1996] entitled 'the Convenience of Tilings', but wanted to know if there were any other texts that people could recommend that ...
user15756's user avatar
1 vote
0 answers
308 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
1 vote
0 answers
137 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.
Tio Miserias's user avatar
1 vote
0 answers
98 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 ...
spaceman's user avatar
  • 575
1 vote
0 answers
250 views

Copylefted introduction to topology

Is there a textbook in topology with a copyleft license? $$ $$
Anton Petrunin's user avatar
1 vote
0 answers
320 views

Reference for PDE problem book

What I need is a source of solved exercises, problems in Partial Differential Equations; to be hard enough (olympiad style) and in areas like Calderon-Zygmund theory and applications, Paley-Littlewood ...
Eddy's user avatar
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1 vote
0 answers
104 views

Basic results for chi square processes

I could not find any introductory material with basic results regarding chi-square processes. Their definition from The Supremum of Chi-Square Processes is as a sum of $d$ squares of independent ...
Uri Cohen's user avatar
  • 363
1 vote
0 answers
201 views

What is the MP pseudoinverse's role in statistical learning and Self-Organizing Maps?

During a discussion in our lab last month, a professor mentioned to me that the behavior of Self-Organizing Maps can be described in terms of repeated applications of the Moore-Penrose psuedoinverse, ...
SigmaX's user avatar
  • 113
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
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0 answers
236 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 ...
Hvjurthuk's user avatar
  • 573
0 votes
0 answers
83 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)...
Infinity_hunter's user avatar
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.
Hermi's user avatar
  • 274
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0 answers
488 views

Linear Representations of the Groups

Does anyone know a good book on Linear Representations of the finite Groups which does not assumes a lot of background. Book which will be good to study for computer science and will cover all( at ...
user10118's user avatar