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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6
votes
1answer
432 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 ...
3
votes
1answer
160 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. ...
0
votes
0answers
46 views

Mathematical construction: ADM formulation in general relativity

I'm doing my undergraduate thesis and now I'm looking for references that presents ADM Formulation in general relativity mathematically. I studied the basics of general relativity theory by O'Neill ...
6
votes
3answers
610 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
85 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
117 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 ...
7
votes
1answer
121 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, ...
4
votes
1answer
99 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 ...
17
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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
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0answers
109 views

Introductory text on amenability

I am looking for a book that covers amenability rigorously. Preferably a book aimed at beginners.
2
votes
1answer
68 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
905 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 ...
0
votes
0answers
17 views

Star quivers and directed Star graphs

I found the definition of $(s,t)$-star in [1], the definition of star quiver in [2]. I want, if possible a reference that point different definitions of star graphs and star quivers and is this ...
3
votes
2answers
680 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 ...
14
votes
1answer
515 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
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0answers
75 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
508 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
133 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
285 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
498 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
267 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
316 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
243 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
1k 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
671 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 ...
2
votes
0answers
223 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 ...
5
votes
2answers
576 views

Reference request: Oldest books on algebraic curves with unsolved exercises?

Per the title, what are some of the oldest books on algebraic curves out there with unsolved exercises? Maybe there are some hidden gems from before the 20th century out there.
4
votes
2answers
466 views

Background needed to understand modern research on knot homology theories

I am a student of mathematics, and have some background in Algebraic Topology (Hatcher, Bott-Tu, Milnor-Stasheff), Differential Geometry (Lee, Kobayashi-Nomizu), Riemannian Geometry (Do Carmo), ...
8
votes
1answer
276 views

Reference request about “internal language of categories”

I've tried to become familiar with the so-called "internal language of a category" for the last months. However, I'm still not confident enough when, for instance, I find a subobject (of a given ...
0
votes
0answers
94 views

Prerequisites for Hempel's 3 manifolds?

What are the prerequisites for Hempel's 3 manifolds book? I've heard you need a good amount of PL topology. I have read Jennifer Schulten's book and found it accessible, but I've heard Hempel is tough....
6
votes
1answer
445 views

Textbook recommendation: Metric Geometry

I’m currently reading Burago, Burago, Ivanov’s book A Course in Metric Geometry. I’m really enjoying it so far - what would be a good continuation to the book once I’m done?
7
votes
1answer
237 views

Reference request: Introduction to Finsler manifolds from the metric geometry point of view (possibly from the Busemann's approach)

This question is a cross post from Math.SE. I have requested the migration of the question, but unfortunately it is not possible after two months of posting. I also have found this related question, ...
3
votes
0answers
114 views

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 ...
2
votes
0answers
332 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 ...
5
votes
1answer
605 views

Quantum Field Theory: completing the “A Bridge between Mathematicians and Physicists” series

I decided to read the series "A Bridge between Mathematicians and Physicists" written by Eberhard Zeidler. But when I read the preface of the first book I realized that at first this series should be ...
4
votes
2answers
3k views

What is a really good book for complex variables? [closed]

I'm an engineering student but I self-study pure mathematics. I am looking for a Complex Variables Introduction book (to study before complex analysis). I have the Brown and Churchill book but I was ...
1
vote
0answers
211 views

Functional Analysis book with graphical descriptions [closed]

I am looking for some book about functional analysis that has also graphical descriptions and images of the important concepts. Anyone knows some book like this?
5
votes
1answer
230 views

Textbook recommendations: Weakly almost periodic functions

I am currently studying Ergodic Theory from Glasner’s book - in it, weakly almost periodic functions play a large role, as well as general “means” and unitary representations of groups on Hilbert ...
7
votes
0answers
153 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 ...
22
votes
8answers
3k views

Good introductory book to type theory?

I don't know anything about type theory and I would like to learn it. I'm interested to know how we can found mathematics on it. So, I would be interested by any text about type theory whose angle ...
4
votes
3answers
477 views

Problem based representation theory book

I am trying to find books similar in the spirit of Ram Murty's Problems in Analytic Number theory or Murty Esmonde's Problems in Algebraic number theory in the field of Representation Theory (of ...
3
votes
1answer
136 views

Origin of the relations of Leavitt path algebras

I know the formal definition of Leavitt path algebras, but I want know why the relations defining Leavitt Path Algebras are defined in that way? what is special of this relations? My real hidden ...
3
votes
1answer
533 views

Regarding learning Algebraic Topology [closed]

Recently, I read a little portion of homotopy theory from Bredon's 'Topology and Geometry' and found that I like it enough to want to continue reading material in Algebraic Topology. A little ...
4
votes
1answer
330 views

Reference request: Oldest (non-analytic) geometry books with (unsolved) exercises?

Per the title, what are some of the oldest (non-analytic) geometry books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there.
4
votes
2answers
513 views

Reference request: Oldest complex analysis books with (unsolved) exercises?

Per the title, what are some of the oldest complex analysis books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there. I am aware of the ...
5
votes
3answers
589 views

Reference request: Dynamical systems

I’m currently reading Brin and Stuck’s Introduction to Dynamical Systems, and I think I like the field a lot so far. I haven’t finished it quite yet, but what are some other good textbooks I can read ...
117
votes
21answers
17k views

Good “casual” advanced math books

I'm curious if there are any good math books out there that take a "casual approach" to higher level topics. I'm very interested in advanced math, but have lost the time as of late to study textbooks ...
6
votes
0answers
165 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 ...
10
votes
2answers
365 views

Textbook recommendation request: Exercises to supplement Evans and Gariepy

While a great book about measure theory and real analysis in $\mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it ...

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