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 views

Several options using Black-Scholes equation(s)

Could someone provide me some information about the modelling of several options at the same time by using Black-Scholes (probably coupled) equations? Any reference to papers and/or books shall be ...
2
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0answers
21 views

How to read Spectral Theory of Graphs

My background is a course is Linear Algebra -Hoffman,Kunze Graph Theory-Clark. I am reading Spectral Theory of Graphs. My professor has asked me to start from the book Spectra of Graphs by ...
0
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0answers
13 views

Good introductory book in geometric probability

I recently came across the proof of the Buffon theorem and I was fascinated by geometric probability. Could someone indicate me a good introductory book? Maybe with many exercises?
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0answers
3 views

Counting subgraphs of bounded extremal degrees

Let $m\leq n-1$. Is there a closed expression counting the subgraphs of minimum degree $\geq m$ (resp. maximum degree $\geq m$) on $n$ labelled vertices?
0
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1answer
49 views

Regarding Apostol's theory of integration

I have some questions regarding the theory of integration as discussed in Tom Apostol's Calculus. Integration is defined using step functions. My question is, is this definition he presents equivalent ...
3
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2answers
36 views

Proofs of Liouville Theorem

Are there proofs of Liouville theorem (bounded functions holomorphic in $\mathbb{C}$ are constants) without using the Cauchy theorem?
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0answers
5 views

References: Manifold with boundary, corners, and stratified manifolds

I would like to know some references on: Manifolds with boundary and corners Stratified manifolds I am looking for introductory texts, possibly with some physical insights. Thank you
4
votes
1answer
98 views

Why is “$\pi^2= g $” where $g$ is the gravitational constant?

Some months ago a professor of mine showed us a 'proof' of why $g\approx 9.8 ~\text{m}/\text{s}^2$ (the gravitational acceleration at the surface of the Earth) is 'equal' to $\pi^2\approx9.86\dots$ ...
3
votes
1answer
17 views

How to see that the prime gaps functions isn't monotonic?

Let $g(n)$ be the distance between the $n$th prime and the next. By elementary means we can see that $g(n)$ is not eventually constant and that $g(n)$ is not strictly monotonic. Further we know that ...
0
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1answer
40 views

Math for a computer engineering graduate course [on hold]

I'm going to take a master's course in Computer Engineering. Now I've not taken a CS course in my undergrad, hence my knowledge in some of the core areas of CS like algorithms are limited. I'm quite ...
4
votes
1answer
44 views

How to put my knowledge of probability and statistics to practice

Background: I am a masters student in stochastic analysis. My course is very theoretical, which in general is fine by me, it is what I enjoy the most. From the more data-friendly subjects, I have (or ...
-1
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0answers
36 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
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0answers
15 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
31 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
60 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
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1answer
20 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
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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
34 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
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0answers
10 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
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1answer
22 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 ...
1
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0answers
18 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
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1answer
60 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
41 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
53 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
64 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 ...
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0answers
20 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
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0answers
66 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
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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 ...
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0answers
24 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 ...
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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
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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
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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
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1answer
51 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
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0answers
10 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
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0answers
29 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
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2answers
80 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
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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
59 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
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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
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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
33 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
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1answer
48 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 ...
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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
2answers
82 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
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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 ...
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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
51 views

How good is Naive Set Theory by Halmos? [closed]

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
19 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
30 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 ...