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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16
votes
6answers
1k views

group theory for non-mathematicians

A very smart non-mathematician friend is looking to learn about groups, and I was wondering if people might have suggestions (this is NOT a duplicate of this question, since a textbook is not what I ...
0
votes
0answers
11 views

Elliptic equation with discontinuity

I'm considering the boundary value problem \begin{equation} u''(x)+u(x)=f(x) \; \mbox{on}\; \Omega=(-1,0)\cup (0,1) \end{equation} with boundary conditions $u_x(-1)=u_x(1)=0$ and ...
0
votes
1answer
16 views

Book recommendations for introductory Bayesian statistics?

Anyone here have some recommendations for a good book introducing the reader to Bayesian statistics? Let me mention my background. My undergraduate majors were in Actuarial Science and Statistics, ...
0
votes
0answers
14 views

Studying Polynomials using abstract mathematics

What abstract mathematics topics, like Galois theory, ring theory, field theory, etc, and what specific topics can one study to understand polynomials. The history of investigations into Polynomial ...
2
votes
0answers
31 views

Comparing Patrick Billingsley's Aniversary Edition to previous editions, and to Robert B. Ash's book.

I'm reading some of the reviews at amazon to the Anniversary edition of Billingsley's 'Probability and Measure', and several users state that the book is riddled with new typos, and plain errors, ...
0
votes
1answer
19 views

Limits and Puiseux series expansions

This is a follow-up to my infinite sum question. I'm now faced with calculating: $$\lim_{n\to\infty} \left( 5n+3 \right) \left( 1 - \sum_{k=0}^n \frac{(\frac{3}{6})_k}{(\frac{13}{6})_k}\right)$$ ...
2
votes
1answer
46 views

Set equipped with some operation which is such that it is not known is it a group and is of some importance in mathematics

Well, I know of some examples of groups which are trivial enough and of some which maybe are not so trivial. It could be the case that we could construct some operation on some set which is such that ...
12
votes
5answers
896 views

Real analysis for a non-mathematician.

I'm currently in an engineering program, so most of my mathematical education has been applied in nature (multivariable calculus, ODEs, PDEs, probability). The only real "theory"-based courses I've ...
5
votes
1answer
41 views

Chern character in odd K-theory

I'm familiar with the definition of Chern character for a vector bundle. This leads to the definition of Chern character for $K$ theory (even theory) with values in even cohomology (the definition ...
6
votes
0answers
45 views

Elliptic regularity on the Hypercube

Assume $$ Lu=f\quad \text{in } [0,1]^d\\ u=0 \quad\text{ on } \partial[0,1]^d $$ for some strongly-elliptic operator $L$, and $f\in H^k$$, k\geq -1$. Do we have $u\in H^{k+2}$? I can only find the ...
0
votes
0answers
46 views

Boolean function analysis on random graphs?

Random graphs have some properties that are determined in some random way such as edge probabilities in the interval $[0,1]$. Ryan O'Donnell's book "Analysis of Boolean Functions" (2014) has analysis ...
1
vote
1answer
24 views

Constructing the asymptotes of a hyperbola by compass and straightedge.

Is it possible to construct the asymptotes of a hyperbola by compass and straightedge? And if so, how to construct them? I have no idea how to approach the first question. It seems it should be ...
1
vote
0answers
26 views

Gap probability for i.i.d. random variables

Given a set $\{X_1,\ldots,X_N\}$ of real i.i.d. random variables, drawn from a common parent pdf $p_X(x)$, what is the probability that, given one random variable taking value in $(t-dt,t)$, there are ...
3
votes
1answer
30 views

Can't Remember a Book about Binomial Sums and Hypergeometry

Some time ago I had come across a website which had the online version of a book about techniques dealing with the solution of sums involving binomial coefficients, and something with the word ...
2
votes
0answers
30 views

Up-to-date Matrix Cookbook

My copy of the Matrix cookbook is dated November 15, 2012, and is the newest copy I've been able to find. Identities may not change overtime, but the approach to an error-free presentation can be ...
2
votes
0answers
40 views

Elements of $C(K)^{**}$, do they have a name?

Let $K$ be a compact (Hausdorff) space, and let $C(K)$ be the Banach algebra of contunous functions on $K$ (with the usual $\sup$-norm). The enveloping von Neumann algebra of $C(K)$ is its second dual ...
2
votes
1answer
24 views

Reference request for stochastic processes on manifolds

I'm looking for some references on stochastic processes on manifolds. The more introductory the better. Thanks.
2
votes
1answer
26 views

The significance of CW-complexes in homotopy theory

I try to understand the significance of CW-complexes in homotopy theory, in particular with respect to the classical models structure on $\mathbf{Top}$. Why do we chose Serre cofibrations for the ...
0
votes
0answers
16 views

Reference request: monotone and strongly monotone with respect to derivatives

Recall, let $H$ be a real Hilbert space. A mapping $F:H \rightarrow H$ is said to be monotone if $$ \langle F(u)-F(v), u-v\rangle\geq 0, \quad \forall u,v\in H; $$ strongly monotone if there exists ...
0
votes
0answers
33 views

Reference request: planar Cayley graphs

In 1896, Maschke classified all finite groups that admit a planar Cayley graph. The paper is here: http://www.jstor.org/stable/pdf/2369680.pdf I've been trying to digest this paper, but I'm finding ...
2
votes
1answer
33 views

Module over an infinite dimensional algebra

I have two question related to infinite dimensional algebra I have been seen a lot of example about Module over a finite dimensional $k-$algebra, but I could not find a literature about Module ...
1
vote
1answer
47 views

Every $\mathcal{C}^1$ manifold can be made smooth?

I heard of a theorem saying that each $\mathcal{C}^k$-manifold with $k\geq 1$ can be made into a smooth manifold, i.e. $\mathcal{C}^{\infty}$ (by restriction of the atlas). However, I cannot find ...
6
votes
1answer
110 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
0answers
29 views

Do you know which book this is?

A professor wrote that there is a book that takes a historical approach to mathematical logic: There is a book I’d think you’d enjoy, that takes a historical approach. Can’t remember what it’s ...
3
votes
3answers
65 views

Looking for strictly increasing integer sequences whose gaps between consecutive elements are “pseudorandom”

I am doing some tests with strictly increasing integer sequences whose gaps between consecutive elements show a "pseudorandom" behavior, meaning "pseudorandom" that the gaps do not grow up ...
1
vote
0answers
9 views

Covering vertices of a graph by cycles (not necessarily disjoint)

As title says, I want to find $k$ cycles of a graph $G$ such that each vertex appears at least once in a cycle. Let's count a single vertex as a cycle. To be more specific, I'd like to have some ...
2
votes
1answer
208 views

Tutorials for Sprague-Grundy Theorem/Nimbers?

Help needed in understanding S-Grundy Number , any good tutorial. I am trying to solve Mathalon Problem 146 S-Grundy Game (dead link).
0
votes
1answer
19 views

$C(A)$ is $\|\cdot\|_2$-dense in $\ell_2(A)$

Let $A \neq \varnothing$ and $\cal {F}$$(A) = \{F \subset A \mid F$ is finite$\}$. Define $\ell_2 (A) =L^2(A, 2^A, \mu_C)$, with $\mu_C$ the counting measure. Let $C(A) = \{f: A \to \Bbb C, \exists ...
2
votes
1answer
42 views

Taylor series for $(x^n + x^m + 1)^s$

Using the trinomial theorem one gets that $$ [x^t](x^n + x^m + 1)^s = \sum_{\substack{i + j + k = s\\mi + nj = t}}{s \choose i,j,k}. $$ I was wondering if one could point out to me a reference (I'm ...
1
vote
0answers
29 views

Is $|z_1|^2 - |z_2|^2 = 1$ a conic section?

In complex analysis of one variable, I'm aware that $$||z-a|-|z-b||= 2c$$ is the equation of a hyperbola with foci $a,b$ such that $a, b, c \in \mathbb{C}$. Now if we move up in dimension, i.e. we ...
0
votes
0answers
9 views

Explain following Congruences in elementry way

While studding David M Burton I am felling difficulties with Linear Congruence is there any another way expertise this area (online resources). And how can I show that $21x \equiv 49\ (mod\ 10)$ can ...
13
votes
4answers
388 views

Examples of adding a constant to integration by parts.

The formula for integration by parts is given by $$ \int uv'=uv-\int u'v $$ As most of you know. The result is invariant if we use$v=v+c$, instead of $v$ where $c$ is some arbitary constant. $$ ...
0
votes
0answers
19 views

Recommend 2nd logic and discrete math books?

I passed all the required undergraduate math for the computer science program at my university. It didn't include a course in complex analysis and the advanced required courses were about discrete ...
0
votes
3answers
45 views

Reference request: integration of *one*-forms along curves on a differentiable manifold.

Could somebody please direct me to a book/lecture notes with an introduction to integration of one-forms along curves in a differentiable/Riemannian manifold -- preferably leaning more towards ...
2
votes
0answers
28 views

Is there a formula for the number of proper k-colorings of a graph $G$ up to isomorphism?

In Richard Stanley's Algebraic Combinatorics book, he gives a formula for the inequivalent colorings of a set $X$ up to action by some permutation group $G$, namely: $$ \frac{1}{|G|}\sum_{\pi \in G} ...
2
votes
0answers
27 views

Arithmetic in a dihedral extension

Let $\;$L = $\Bbb Q$[$\sqrt[4]{2}$, i ]$\;$ which is a dihedral extension of the rationals. There are three quadratic and five quartic intermediate fields between L and $\Bbb Q$. The following ...
29
votes
2answers
454 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 ...
0
votes
1answer
20 views

Regularity of solution to an elliptic PDE

Let $R$ be the shifted open unit cube \begin{equation} \Big(-\frac{1}{2}, \frac{1}{2} \Big)^3 \subset \mathbb{R}^3, \end{equation} and let $k \in \mathbb{C}$ be a constant with $\textrm{Re}(k) ...
0
votes
0answers
25 views

Difficulty during self-studying unique set proofs

I have been following Velleman's How to prove it and working through it on my own. I am working full time now so I can only study after work without any other help. It's been going fairly ok until I ...
0
votes
1answer
30 views

Extending fast growing functions to the reals “naturally”

There are a lot of incredibly fast growing functions defined on the natural numbers. Typical examples start with tetration, further hyper operators, Ackermann, and then there is monsters like the ...
44
votes
25answers
3k views

What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?

I am struggling to pick out books when it comes to self studying math beyond Calculus. My situation is as follows. I have taken all math courses at my school (up to Calc BC and AP Stats) and I have ...
2
votes
2answers
72 views

Path - Geometry [closed]

I am currently completing the end of a Bachelor degree in pure mathematics. I would like to work on an interesting project (by myself) this summer in the field of spectral geometry. Does someone could ...
1
vote
1answer
64 views

Proving ZFC is consistent

I've heard from a friend that we can actually prove the consistency of ZFC if we assume at least one inaccessible cardinal exists. How is this carried out, precisely? Googling doesn't help and my ...
2
votes
1answer
49 views

Reference for category of Lie algebras?

Are there any references which deal with categorical aspects of Lie algebras? I'm looking for constructions like kernels, products, coproducts (limits and colimits in general) etc. My goal is to ...
2
votes
1answer
30 views

“Faint” continuity

Definition: A function $f:\mathbb{R}\to \mathbb{R}$ is called faintly continuous in $x$ if there are two series $x_n < x < y_n$ with $\lim_{x_n \to x} f(x_n) = \lim_{y_n \to x} f(y_n) = f(x)$. ...
2
votes
1answer
89 views

Can somebody suggest me a book on linear algebra including these topics?

I want to cover the following topics of linear agebra: Dual and Double Dual spaces Transpose of linear operator Rational and Jordon forms Triangulisation and Diagonalisation Cyclic Decomposition ...
0
votes
0answers
28 views

Rank of curvature operator under Ricci flow.

I think under Ricci flow ,the rank of curvature operator does not change by +1 or -1, it will directly change to full rank or zero rank . I want to write it as term paper, but I don't know whether ...
2
votes
0answers
44 views

Optimal positioning of tokens on a unit disk

Suppose we have $N$ tokens, labeled $x_1,x_2,\ldots,x_n,\ldots,x_N$. Our goal is to place these tokens optimally (defined below) on a unit disk. Formally (and please let us know if our notation is ...
0
votes
0answers
15 views

Table of Product Representations of Functions?

Does anyone know where I could find a (preferably free, online) table with infinite product expansions of basic functions (e.g. trig functions, logarithms, special functions)? Specifically ...
-3
votes
1answer
34 views

Refrence for order topology

Can anyone give reference for order topology which covers order topology in detail with many examples other than munkered