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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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
186 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
32 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
228 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
176 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
167 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
112 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
535 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
84 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 (...
10
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
261 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
66 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
28 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
73 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 ...
7
votes
1answer
150 views

On groups with presentations $ \langle a,b,c|a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=(abc)^s=1\rangle $…

$$ \langle a,b,c|a^2=b^2=c^2=(ab)^p=(bc)^q=(ca)^r=1\rangle =\Delta(p,q,r) $$ This is a presentation of a triangle group $\Delta(p,q,r)$, a special kind of Coxeter group. What about the following ...
0
votes
1answer
25 views

Reference for results p-adic integers Z_p as abelian group

I have two facts I want to use in my thesis about $\mathbb{Z}_p$. To be precise: automorphism group is $\mathbb{Z}_p \times \mathbb{Z}/(p-1)\mathbb{Z}$, except for 2, and that any subgroup with finite ...
1
vote
2answers
32 views

Where should I begin the study of fixed point theory, especially of multi-valued maps?

How should one begin one's study of fixed point theory, especially of multi-valued maps? What background --- in topology, analysis, functional analysis, algebra, and set theory --- should one have? ...
2
votes
0answers
42 views

Generalisation of the Poincaré Lemma

Let $\Omega \subset \mathbb{R}^3$ be an open but not simply connected domain and let $v \: \colon \Omega \to \mathbb{R}^3$ be a continuously differentiable vector field. Assume that $\textrm{curl} \, ...
4
votes
0answers
100 views

Almost-Linear Sequence of Positive Integers Excluding a Near-Quadratic Integer Sequence

I remember that I have seen a similar problem to this one here: The set of natural numbers that don't belong to a set (which is a duplicate of $m$ doesn't come in the sequence $a_n=[n+\sqrt{n}+...
2
votes
1answer
80 views

Good, relatively short math textbooks? [closed]

Recently I've been trying to decide on some fun math summer reading on some areas of math which I have less experience with. I'm an undergrad studying mathematics with a focus in actuarial science, ...
2
votes
0answers
28 views

Is a possible use of a Mill's constant the encapsulation/encryption of messages?

I wonder if the way that Mill's constant is defined could provide a good data encapsulation and encryption method if instead of encapsulating primes, for instance a simple ASCII message is ...
2
votes
1answer
36 views

Lines in a metric space - a metric space?

In a metric space, a point $x$ is between points $u$ and $v$ if $d(u,v)=d(u,x)+d(x,v)$. The line determined by points u and v consists of $u$, $v$ and all points $x$ such that one of $x,u,v$ is ...
4
votes
0answers
96 views

Cup/cap product: sheaf cohomology vs singular cohomology

Is anyone aware of a good resource which deals with how the cup/cap products of sheaf cohomology classes are a generalization of those in singular cohomology? I would say that I already understand the ...
1
vote
0answers
26 views

Constructing a Collection of Sets Satisfying Certain Intersecting Properties

I am trying to solve the following problem. We would like to construct $\{A_1, \ldots, A_n\}$, where $n$ is even, and each $A_i \subseteq [m]$, with $|A_i| = k$ and $m = \text{poly}(n)$. Now, I would ...
3
votes
0answers
46 views

Possibly new solution to equal-mass three-body problem; refinement required

(Since I didn't know which authorities to contact, I thought I'd post this here.) While messing around in this Wolfram Demonstrations applet, I found a suspicious pattern, in which I could see ...
1
vote
0answers
21 views

Is this (open) neighborhood graph of a graph a known concept?

Let $G$ be a graph, and for a vertex $v \in V(G)$ let $N(v) = \{ u \mid uv \in E(G) \}$ be the open neighborhood of $v$, i.e., the set of adjacent vertices not including $v$ itself. Let $N'(G)$ be ...
0
votes
0answers
9 views

Contraction clique number of certain Turan graphs

What can we say about the size of the largest clique that is a minor of the complete $r$-partite graph with all vertex classes of size $n$?
0
votes
0answers
18 views

Lattice theory textbooks that do not mention diagrams?

Many lattice theory texts extol the virtue of diagrams (which are also "formalized" as a concept for finite sets). However, I am curious to know of texts which do not mention diagrams (or mention them ...
1
vote
0answers
26 views

Brownian motion hitting probability of boundary and going outside

I was solving an exercise which asks the reader to calculate the probability that a Brownian particle $B(t) = (B_1(t),...,B_n(t))$ starting at the origin in $\mathbb{R}^n$ will strike the surface of a ...
-1
votes
1answer
14 views

Reference request for a theorem of Schlessinger

I am reading The unbearable lightness of deformation theory by Balázs Szendröi (sorry, the umlaut should be a kind of double accent, but I have no idea about how to do it with my keyboard). At page 9 ...
3
votes
1answer
65 views

ZF and the Existence of Finitely additive measure on $\mathcal{P}(\mathbb{R})$

My understanding is that Solovay (1970)'s relative consistency shows that if ZFC+I has a model then ZF+DC has a model in which every subset of the reals is Lebesgue measurable (and hence $\sigma$-...
4
votes
0answers
96 views

How are weakly universal Turing machines actually defined?

For what I know, the definition of a universal Turing machine is something along the lines of the following (of course, details might vary from source to source): A Turing machine $M$ is called ...
4
votes
0answers
175 views

Differentiation under the integral sign when derivative exists only almost everywhere

Regarding the Theorem 3 from here (or pdf ver.). Let $X$ be an open subset of $\mathbb{R}$, and $\Omega$ be a measure space. Suppose that a function $f\colon X\times\Omega\to \mathbb{R}$ ...
3
votes
3answers
87 views

Differential Geometry for General Relativity

I'm going to start self-studying General Relativity from Sean Caroll's Spacetime and Geometry: An Introduction to General Relativity. I'd like to have a textbook on Differential Geometry/Calculus on ...
0
votes
0answers
32 views

Reference for monodromy theorem in SVC

I am looking for a reference for the Monodromy Theorem in several complex variables. I found plenty in the case of one variable, and some other versions who are purely topological and concerned with ...
0
votes
0answers
28 views

Beginning master's student with gaps - References for Riemann Surfaces

I currently have Jost (as well as a few other texts), and have been working through it - I am a master's student who is trying to prepare for thesis work in closely related areas. However, it is far ...