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.

learn more… | top users | synonyms (3)

-1
votes
0answers
34 views

English version of the paper - L’algèbre de Fourier d’un groupe localement compact [on hold]

Help regarding finding the English translation of the paper below required: Pierre Eymard. L’algèbre de Fourier d’un groupe localement compact. Bull. Soc. Math. France, 92:181–236, 1964
0
votes
0answers
10 views

What are some modern books on Markov Chains with plenty of good exercises?

I would like to know what books people currently like in Markov Chains (with syllabus comprising discrete MC, stationary distributions, etc.), that contain many good exercises. Some such book on ...
3
votes
1answer
26 views

Is $\mathsf{nCob}$ bicomplete?

Let $\mathsf{nCob}$ be the category of $n$-cobordisms, whose objects are $(n-1)$-dimensional closed manifolds and morphisms are bordisms. Is this category bicomplete, or even finitely bicomplete? ...
0
votes
2answers
51 views

A weaker than “zero derivative” condition implies that a function is constant?

Let $f:(a,b)\to R$ be a continuous function such that $\limsup\limits_{n\to \infty}\frac{f(x_n)-f(x_0)}{|x_n-x_0|}\leq 0$ for every $x_0\in(a,b)$ and sequence $x_n$ converging to $x_0$ such that ...
1
vote
1answer
16 views

$S_n$ as a Coxeter group? (with Matsumoto's theorem)

I need to find a book in which basic $S_n$ theory is covered, mainly the part about Bruhat order, length of an element $w \in S_n$ and invariance modulo braid relations of the expressions ...
1
vote
0answers
6 views

Number of translated cubes covering a given hypercube in $\mathbb{R}^n$

Let $\Omega \subset \mathbb{R}^n$ be open and bounded, and let $Q \subset \Omega$ be a hypercube. Furthermore, denote by $D$ the $n$-dimensional unit cube $(0,1)^n$. Let $k \in \mathbb{N}$ be big, ...
2
votes
2answers
30 views

Is there an alternative approach to the definition of prime numbers based on the definition of the natural logarithm?

Is there an alternative approach to the definition of prime numbers based on the definition of the natural logarithm? These are my thoughts about it, the questions are at the end: Basically when a ...
1
vote
0answers
9 views

On the existence of magic squares of every order different from $2$

I was reading about magic squares and suppose that we speak here only of the magic squares that have in itself numbers from $1$ to $n^2$. It is easy to see that we cannot have $2$x$2$ magic square ...
1
vote
1answer
18 views

Online course for numerical methods/analysis of PDEs

Could anybody recommend an online course for implementing numerical methods to solve PDEs which can supplement reading? This is with a view to writing an implementation to solve the Monge-Ampere ...
0
votes
0answers
15 views

Linking circles inside an immersed surface

A smooth embedding $f : D \to \mathbb{R}^3$ can be isotoped to a canonical inclusion $D \hookrightarrow \mathbb{R}^3$. (This is part of a proof that only the unknot has the disk as a Seifert surface.) ...
1
vote
1answer
53 views

What kinds of transformations preserve network topology?

I have been reading a number of "network science" papers where the authors perform transformations on networks that seem to preserve the topology of those networks. By "topology", I mean a collection ...
0
votes
1answer
35 views

linear algebra in infinite dimension

I look for an advanced linear algebra (A complete book but wich deals indiferently with infinite/finite vector space). To give an idea i expect a book that (for exemple) would prove the existence of a ...
2
votes
1answer
50 views

Euler and Bernoulli Polynomial Identity Proof

Given that the Euler Polynomials $E_n(z)$ are defined in terms of the generating function $$\frac{2e^{xz}}{e^x+1}=\sum_{n=0}^\infty E_n(z)\frac{x^n}{n!}$$ and that the Bernoulli Polynomials $B_n(z)$ ...
3
votes
1answer
61 views

$\Bbb R,\Bbb C,\Bbb H$ are the only complete normed division rings

Does anyone have a proof or reference for this often-quoted fact? How complicated is the proof? If $K$ is a complete normed division ring, then $K$ is isomorphic to the real numbers, complex ...
1
vote
0answers
19 views

references for abstract harmonic analysis

I am currently studying a basic course in abstract harmonic analysis. I do have a good background in abstract algebra and functional analysis but I have not done a course in Fourier analysis. Is it ...
6
votes
0answers
61 views

Confusion with Courant: Which of his two calculus books is THE one?

Since I've worked my way through Spivak's Calculus book, I thought I'd give Courant's allegedly fantastic exposition of the subject a go as well. However, I've run into a problem. People in ...
1
vote
1answer
30 views

Determinant of a tuple of vectors: is this a thing? If so, where can I learn more?

Let $k \leq n$ denote a pair of fixed but arbitrary natural numbers. Definition 0. Write $\varphi$ for the unique $\mathbb{R}$-linear function $$\Lambda^k\mathbb{R}^n \rightarrow \mathbb{R}$$ such ...
0
votes
0answers
23 views

Functional Equation of Probability Distributions

Suppose you have a real random variable $X$ that has probability distribution $f_X$ meaning $$ P(\alpha \le X \le \beta) = \int_{\alpha}^{\beta} f_X(x) \ dx $$ Now assume $\Phi(f_X)$ is also a ...
1
vote
0answers
32 views

What simple topological properties of conic sections can be explored?

In the framework of my science fair project I am working on conic sections in different metric spaces. What simple topological properties/operations and so can I explore on them? Edit: To clarify, ...
0
votes
0answers
6 views

Illustration of the search for the right proportion that symbolizes the golden ratio.

My teacher asked us to illustrate, using a scientific poster the search for the right proportion that symbolizes the golden ratio. The problem statement is the following: What about today that ...
1
vote
0answers
24 views

Looking for Severi varieties.

Let $K$ be an algebraically closed field of characteristic $0$, and let $\mathbb{O}$ be the Cayley algebra over $K$. Let $$ \mathfrak{J}_{3}=\{A\in\mathcal{M}_{3}(\mathbb{O}):A\text{ is Hermitian}\}, ...
3
votes
1answer
48 views

Probability theory with the hyperreals?

Forgive the undoubted ignorance of this question. I am out of my element both in probability and in nonstandard analysis. A mathematically curious layperson friend recently had a conversation with me ...
0
votes
0answers
9 views

Normalizer problem for finite Metabelian Groups with abelian sylow 2-subgroup

I am studying Normalizer problem (which states that given an integral group ring $\Bbb{Z}G$, $N_{\cal{U}}(G)=G\frak{z}$ where $\frak{z}$ denotes centre of $\cal{U}$ = $\cal{U}$$(\Bbb{Z}G))$ and I came ...
0
votes
0answers
28 views

Learning outcomes of reading textbooks [on hold]

So I've densely mined this site for the scholarly materials I need most. And have prudently written many of them down, so I can sort them if I see fit. But, are the books always the preferred method ...
4
votes
2answers
78 views

recommend math books [on hold]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number ...
0
votes
0answers
14 views

Source for Space-Time Fourier transform theory

I need to do research on Space-Time Fourier transforms (specifically applications within EM theory). Since the resources for learning this digitally seem to be limited (by my very advanced Google ...
3
votes
3answers
58 views

A good companion to Axler's “Linear Algebra Done Right”?

Seeing as Axler is very reluctant to talk about determinants and generally avoids computations and playing around with algebra, I'd like to get a book that will serve as a companion to Axler's ...
0
votes
0answers
25 views

Pell's Equation sources

I am researching about Pell's equation and wanted to ask what the best resources are for it? So far I have Stopple's book and Hardy's book.
0
votes
0answers
47 views

Reference request for a very particular problem solving skill

I want to start with an apology for a very verbose description of my question but if there is a way to cut it down, please let know and I will do so right away. I have been trying to get better at ...
1
vote
1answer
32 views

Where can I find a proof of the Presentation for Semidirect Products?

I have seen it claimed online that: Given two groups $G = \langle X \mid R \rangle$ and $H = \langle Y \mid S \rangle$ with some action $\theta \colon H \to \text{Aut}(G)$, then $$ G\rtimes_\phi ...
4
votes
1answer
46 views

References for information theoretic statistical tools

Strange statistical concepts like spaces of probability distributions, "metrics" like Fisher information or relative entropy, and convergence with respect to these quantities are necessitated in my ...
37
votes
6answers
2k views

Proving the existence of a proof without actually giving a proof

In some areas of mathematics it is everyday practice to prove the existence of things by entirely non-constructive arguments that say nothing about the object in question other than it exists, e.g. ...
7
votes
1answer
70 views

Are weakly étale ring homomorphisms of finite presentation étale?

Following [Stacks, 092A], say a ring homomorphism $A \to B$ is weakly étale if both $A \to B$ and $B \otimes_A B \to B$ are flat. Question. Are weakly étale ring ...
1
vote
1answer
63 views

The eigenvalues of $AB$ and of $BA$ are identical for all square $A$ and $B$ …a different approach

The eigenvalues of $AB$ and of $BA$ are identical for all square $A$ and $B$. I have done the proof in a easy way… If $ABv = λv$, then $B Aw = λw$, where $w = B v$. Thus, as long as $w \neq 0$, it is ...
1
vote
2answers
26 views

reference request Schur Zassenhaus Theorem

I am looking for a reference for the Schur Zassenhaus Theorem, saying that any normal Hall subgroup admits a complement. An on-line search show that it is supposed to be in "The theory of groups" by ...
-2
votes
1answer
49 views

How good is Naive Set Theory by Halmos? [on hold]

I happened to run into this book in an old shop and got it for like half a dollar. Has anyone read this book? Is it worth the time? (Please don't respond things like "every math book is worth the ...
0
votes
0answers
14 views

Material on Koszul complex

I have tried a lot of books to understand Koszul complex but eventually failed. I have tried Eisenbud's book, Weibel's homological algebra, but I just can not how to construct Koszul complex by tensor ...
1
vote
0answers
18 views

Infinite series, continued fractions, nested radicals and such - is there a general recursive algorithm theory?

The nature of infinity and irrational numbers (among other things) always gave me trouble. But recently I learned to think about infinite sequences in terms of recursive algorithms and their time ...
0
votes
1answer
29 views

Partitioning a convex object without cutting existing convex subsets

$C$ is a convex object in the plane. $D_1,\dots,D_n$ are pairwise-disjoint convex subsets of $C$ such that $D_1\cup\dots\cup D_n \subsetneq C$, like this: Is it always possible to partition $C$ to ...
2
votes
0answers
15 views

A sufficient condition for factorization in a complete local ring

I think something like the following statement is true, but I don't recall a reference. Suppose $f(x,y)\in k[[x,y]]$ is power series with no constant or linear terms. Then, if the quadratic terms ...
1
vote
0answers
44 views

Estimates for the Dedekind number $M(9)$

The Dedekind number $M(n)$ is the number of antichains in the partial order of subsets of $\{1,\dotsc,n\}$. It is only known for $0 \leq n \leq 8$. Question. What are some known upper and lower ...
0
votes
1answer
46 views

Using derivatives to get some trigonometric identities

Is there a way of using derivatives to get some trigonometric identities in a straight-forward fashion? I use to forget them, so that would help me a lot... For example, since when we get the ...
2
votes
1answer
56 views

Why is even codimension necessary to apply excision for the Euler characteristic?

In this answer on MathOverflow, it is claimed that $$\chi(X/Z)=\chi(X)-\chi(Z)$$ holds for complex subvarieties $Z$ only because $Z$ has even codimension. It is implied that for $Z$ with odd ...
4
votes
1answer
65 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 ...
1
vote
3answers
118 views

Book on foundational reasoning of standard arithmetics “curriculum”

I am interested in a book that is about arithmetics but the presentation is not just the known to all formulas but the foundational logic behind it. The closest example I can think about is the way ...
10
votes
0answers
87 views

Category Theory Zoo

There are a few very useful websites when it comes to either finding a specific object with certain properties (and maybe lacking other properties) or finding out which properties a certain object ...
3
votes
0answers
83 views

Name for categories with a certain property on coproducts

Is there a name for categories with the following property: The category has zero morphisms, coproducts, and for each family $(X_i)_{i \in I}$ of objects the natural map $$\hom(Y,\bigoplus_{i \in I} ...
0
votes
0answers
29 views

“Peak lemma” and explicit monotone subsequence

Looking at the proof of Bolzano–Weierstrass theorem, it found an interesting lemma (called the peak lemma here) : Every sequence $(x_n)_{n\in \mathbb{N}}\in \mathbb{R}^\mathbb{N}$ has a monotone ...
0
votes
1answer
18 views

Asymptotic bounds on sum of primes

Let $p_i$ denote the $i$th prime number, and let $p_k\#$ denote the $k$th primorial, $p_k\# \overset{\textrm{def}}= \prod_{i \le k} p_i$. I am interested in asymptotic upper bounds for the ...
1
vote
1answer
30 views

Is the braid category biclosed and bicomplete?

Let $\mathcal{B}$ be the braid category, as in Categories for the Working Mathematician §XI.4 p.262 (objects are natural numbers and morphisms are the braids $n\to n$). Then this can be given a ...