This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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5
votes
1answer
45 views

Reference about the surgery of Ricci flow

I roughly read the Topping's LECTURES ON THE RICCI FLOW. Seemly, there is not introduction about surgery. Seemly,it is enough to deal singularity by blow up. Then, for knowing surgery I read the ...
9
votes
3answers
1k views

Erdős-Straus conjecture

I'm reading a lot about the Erdős-Straus Conjecture (ESC), a conjecture that states that for every natural number $p \geq 2$, there exists a set of natural numbers $a, b, c$ , such that the following ...
7
votes
1answer
166 views

Have these (extremely simple) classes of algebraic structures been considered in the literature? If so, what are they called?

Questions. Have the following kinds algebraic structures been considered in the abstract algebra literature etc.? If so, what are they really called? (I have used made-up terminology for the sake of ...
2
votes
0answers
21 views

Introduction to morse theory with applications to optimization

I am wondering if there are any easy-to-read introduction materials on morse theory (especially with applications to nonconvex optimization) for people with non-math background.
13
votes
3answers
323 views

Where has this common generalization of nets and filters been written down?

It is well-known that there are two different ways to generalize the theory of convergence of sequences to arbitrary topological spaces: nets and filters. They are of course essentially equivalent, ...
6
votes
1answer
2k views

Basic facts about ultrafilters and convergence of a sequence along an ultrafilter

Could you help, please. I need the information about the ultrafilters, namely, any ideas how one can see that they exist and a proof of the fact that for any ultrafilter every sequence on a compact ...
2
votes
3answers
244 views

Have historians responded to Raju's critique?

C. K. Raju has made some outrageous criticisms of the traditional take on Euclid in particular and Western history in general. Yes he has a book published on the subject with an apparently respectable ...
3
votes
3answers
133 views

Where to read about sheaves?

I'm working through Mumford's Red Book, and after introducing the definition of a sheaf, he says "Sheaves are almost standard nowadays, and we will not develop their properties in detail." So I guess ...
0
votes
0answers
17 views

where can i learn more about primitive recursive arithmetic (PRA)?

The references on the wiki page are articles in journals, which are not easily accessible. I can find the first reference (by Skolem) online... but it is in German. I would expect this to be in a ...
4
votes
2answers
37 views

Ring of algebraic integers as lattice points in the complex plane

Let, $i=\sqrt{-1}$ and $\omega = e^{\frac{2\pi i}{3}}$. I know that we can represent the ring of integers $\mathbb{Z}[i]$ and $\mathbb{Z}[\omega]$ as square and triangular lattice on complex plane ...
0
votes
0answers
27 views

Elementary literature on Group theoretic Power Diophantine Equation

I am looking for an elementary books/pdf notes on group theory related to Power Diophantine Equation. I have read elementary group theory. Please advise some books/pdf notes. Also, it would be ...
0
votes
1answer
96 views

Number of urns containing a ball of each color: is there a probability distribution describing this?

There are $B$ urns. There are $n$ red balls and $n$ white balls with $n\leq B$. Each ball is independently put into each urn with equal probability. An urn can get at most one ball with the same color ...
1
vote
0answers
30 views

Further references on number theory paper.

Courtesy of the wonderful Canadian Mathematical Society which allows free access to their back issues, I discovered a paper written in 1959 in the Canadian Mathematical Bulletin. The paper answers the ...
2
votes
2answers
65 views

Reference: Mahlo cardinals remain Mahlo in L

The following is stated on Wikipedia for Mahlo cardinals. Unfortunately, it's not sourced. Where can I find details? I wasn't able to google any articles dealing with Mahlo cardinals in $L$. Since ...
6
votes
5answers
249 views

List of theorems named after non-human animals [closed]

I think it would be entertaining if we could come up with a list of theorems named after non-human animals (so excluding names like "Gauss's lemma" and the like). So far, I have only encountered two, ...
32
votes
2answers
503 views

Haar Measure of a Topological Ring

A topological ring is a (not necessarily unital) ring $(R,+,\cdot)$ equipped with a topology $\mathcal{T}$ such that, with respect to $\mathcal{T}$, both $(R,+)$ is a topological group and $\cdot:R\...
1
vote
0answers
32 views

Number-Theory Books to read before studying Analytic Number Theory

S.E friends, Due to my genuine interest to Goldbach's conjecture, I decided to self-study the subject of additive number theory on this upcoming Fall. Before jumping to such fascinating field of ...
1
vote
2answers
54 views

Fibered categories, introduction or notes

I would like to learn about fibered categories, I know basic category theory, but not algebraic geometry. Is there a text, or lecture notes, which motivate the definitions from fields other than ...
30
votes
6answers
9k views

Rudin or Apostol

I have an option to choose between the two books Mathematical Analysis by Tom Apostol and Principles of Mathematical Analysis by Walter Rudin as I was gifted Rudin by a friend and ended up buying the ...
2
votes
1answer
58 views

Existence of closed level sets on a surface for some field

Consider an infinite 3D space with only 2 things in it: wind and a solid object. Wind evidently blows around this solid object over its rigid surface. Bascially we are trying to set up a pure field. ...
10
votes
4answers
157 views

Concerning Groups having the property that intersection of any two non-trivial subgroups is non-trivial

The group of rational numbers $(\mathbb Q,+)$ has an interesting property , that the intersection of any two non-trivial subgroups of this group is non-trivial . Let us call this property the " non-...
0
votes
0answers
18 views

About functions with its codomain being the power set of its domain

Can you recommend me some articles or textbooks about functions whose codomain is the power set of its domain (i.e. a function $f:M \to 2^M $ where $M$ is a non-empty set)? In fact, I want to know ...
0
votes
1answer
19 views

Spectral radius of block-skew-hermitian matrix equals norm of block

$$\rho\left(\left[\begin{matrix}0 & A \\ -A^{\dagger} & 0\end{matrix}\right]\right)=\|A\|$$ where $\rho(\cdot)$ is the spectral radius, $\|\cdot\|$ is the induced 2-norm. Question: I am ...
3
votes
3answers
185 views

How does Ulam's argument about large cardinals work?

I am looking for either a reference, a proof, or a suitable proof sketch that can explain Ulam's original argument about measure theory and measurable cardinals. Here is the result I am looking for: ...
2
votes
0answers
31 views

Determining a function is harmonic from mean value property for just three(?) radii.

This theorem is well-known (maybe it can be called Morera's theorem): A continuous function satisfying the mean value property on balls is harmonic. I was recently surprised to hear in a talk ...
2
votes
3answers
226 views

Analytical mechanics book

On my PHD I have to learn the following subject: Analysis on manifolds and Analytical mechanics. But my book is really not good to read; it is too hard. So I need some book that explains to me ...
1
vote
1answer
175 views

Intuitive functional analysis book

I would like a functional analysis book like Terence Tao's Real Analysis and Measure Theory book, full of intuition. I am ...
1
vote
1answer
166 views

Representation Theory Symmetric Group Book?

I'm looking for a nice book that discusses the representation theory of the symmetric group. My background is an introductory class in representation theory.
0
votes
2answers
111 views

Good book on Lebesgue Theory [duplicate]

I am a graduate student and I need a suggestion for a good book in Lebesgue Measure Theory with good exercises and if its possibly with hints or solutions. Thank you.
55
votes
19answers
17k views

Good Book On Combinatorics

What is your recommendation for an in-depth introductory combinatoric book? A book that doesn't just tell you about the multiplication principle, but rather shows the whole logic behind the questions ...
5
votes
4answers
533 views

Graph Theory for Dummies Book [duplicate]

Does anyone have a good book on Graph Theory that will introduce me to some of the basic concepts without being so filled with terminology that it's hard to read? I have taken an introductory course (...
2
votes
3answers
96 views

Help finding specific book

I'm studying Engineering and I'm in my second year, studying Multivariable Calculus, but my University is kind of hard teaching me fresh calculus with topology and analysis, and is kind of hard, so I ...
6
votes
0answers
83 views

Advanced stochastic process book

I am looking for the book about advanced stochastic process . It may cover the following content: Stochastic matrices. Ex: $A(k)$, where $k$ is the time index. Stochastic process in space (...
9
votes
6answers
2k views

Distribution theory book

I'm looking for a good book on distribution theory (in the Schwartz sense), I have the basic knowledge as given in Grafakos' Classical Fourier Analysis, but I want to know more about it. Is the ...
11
votes
6answers
1k views

Tensor Book Recommendation Request

Requirements Tensors Intuitive + Practical Reason for Tensor Introduction Current Knowledge Course Notes Abstract + Theoretical
2
votes
1answer
113 views

What branch/field of mathematics is this? [closed]

I do not want solutions, I just want the field/branch of mathematics that these problems deal with, and possibly a good online source or two to learn it. Problems :- 1:- 2:- 3:- 4:- ...
3
votes
1answer
70 views

Is statistical physics background desirable for probability theory?

I am talking about higher probability viz. Brownian Motion, Ergodic Theory, Concentration, Percolation, Random Graphs, Random Matrix, etc. Going through books, I find that somehow or the other, many ...
2
votes
1answer
42 views

To distinguish among the various subsets of $M_n(\Bbb R)$

I am having problem in doing a certain type of problems relating to matrices: To distinguish among the various subsets of $M_n(\Bbb R)$ such as symmetric, diagonal, diagonalizable, upper triangular, ...
0
votes
2answers
135 views

Physics Book Recommendation Request

General Requirements Physics for Mathematicians Philosophy + Foundations Mathematical Derivation of Theories I want to know if there is a physics book for mathematicians. I attempted to read some ...
0
votes
3answers
188 views

Complex book suggestions

I take complex analysis course. And my instructor use -Bak and Newman's complex analysis book, Springer. This book explains complex analysis too rapidly and superficially. Please give me book ...
1
vote
2answers
138 views

Good book introducing Inconics

General Requirements Book Conic Sections Triange Geometry Inconics of Triangle Ideal Topics Projective properties arising from inconics like collinearity/concurrency relationships Other basic ...
0
votes
1answer
41 views

solve a specific word problem in free groups

Let $F_2=\langle a, b\rangle$ be the non-abelian free group with two generators and $e$ is the neutral element in $F_2$. Given $g\in F_2, k\geq 2$ an integer. I want to know how to solve the word ...
1
vote
3answers
260 views

Introductory Algebra Book Suggestions

General Requirements The algebra book must be no more than 400-500 pages in length and should contain end-of-lesson/chapter exercises. Required Topics linear equations linear inequalities ...
1
vote
1answer
64 views

Can someone suggest books on mathematics and problem solving which nurtures the reader? [closed]

Can someone suggest books on mathematics and problem solving which nurtures the reader like Alexander Soifer's books? Thanks in advance
3
votes
0answers
63 views

Which books or subjects would you recommend for undergrads for grad school? [closed]

I am an undergraduate mathematics student in my third year. Most undergrad programs don't completely prepare you for grad school. I know Ph.D. students are telling me that there is a lot of crucial ...
0
votes
0answers
25 views

Sylow tower theorem involving supersolvable groups

I just want to find out if anyone has a reference to the result that states that if $G$ is a finite supersolvable group then it has a normal Sylow subgroup.
1
vote
0answers
26 views

Book search on statistics

I am searching a book that Analysis of Failure and Survival Data (Chapman & Hall/CRC Texts in Statistical Science) by Peter Smith. Its link is here. I tried to buy it from Amazon, but it is out ...
3
votes
4answers
464 views

Abstract Algebra Book Request

I am looking for a good undergraduate level book on Abstract Algebra. By a 'good book' I mean a book which gives equal importance to both, rigor and the historical perspective of the subject. For ...
1
vote
0answers
26 views

Exercises with solutions for mathematical statistics

I'm currently studying the statistics part of the book Georgii: Stochastics, contents are here (chapters 7 - 12). Sadly, there are no solutions for the exercises given in this book. Do you know a ...
1
vote
1answer
72 views

Linear Algebra Textbook

I'm looking for a textbook on Linear Algebra and I seem to have narrowed down the list to: Linear Algebra by Hoffman and Kunze; and Linear Algebra by Friedberg, Insel and Spence. I'm not ...