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 views

Hilbert's double series theorem $\sum_{n,m}\frac{a_n b_m}{m+n}$ and its generalizations.

Let $l_p$ be the space of all complex sequences $x=\{x_n\}$ equipped with the finite norm $\|x\|_p=\left(\sum_n |x_n|^p\right)^{1/p}$. Hilbert's double series theorem states that $$\sum_{n,m}\frac{a_n ...
2
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0answers
5 views

Nice embedding of the permutohedron of order $n$ in ${\mathbb R}^{n-1}$

The permutohedron $P_n$ of order $n$ ($n\geqslant 2$) is the convex hull of the points $P_\pi=(\pi(1),\dots,\pi(n))$ where $\pi$ ranges over all permutations of $\{1,2,\dots,n\}$. Obviously, since ...
2
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1answer
25 views

Affine Transformations: Book to Study over the Summer

I've briefly heard of affine transformations in both linear algebra and calculus and I'd like to find a good book on the subject to study over the summer. So what's a good undergrad-level book on ...
3
votes
1answer
32 views

What is a good reference for rigorous Electromagnetism and Electrodynamics?

Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for ...
1
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0answers
8 views

calculator for p-adic valuation and absolute value

Does anyone know a website where I can enter a prime base and a rational and get the p-adic valuation and the p-adic absolute value? For sure I know how to do it by hand but I want to check my results ...
4
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1answer
89 views

Where is Cauchy's wrong proof?

Allegedly, Cauchy mistakingly "proved" that pointwise convergence of continuous functions is continuous. I saw this somewhere in a book, and it is also in wikipedia: Uniform convergence. In his ...
0
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1answer
30 views

Which discrete mathematics book do you think is better between Epp's and Rosen's for a clueless self-learner?

I am a programmer, and I want to become a machine learning researcher and a good software engineer. I dabbled with calculus, linear algebra, and real analysis for a few months when I was enrolled in a ...
2
votes
1answer
13 views

About fractional Sobolev space

I'm reading a paper used Sobolev space $H^s(\Omega)$ , I only know the definition of these space when $\Omega=R^n$ which used Fourier Transform, what if $\Omega$ is a bounded open set? And I also ...
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0answers
24 views

What are some genuine ways to define the derivative of a fractal?

Seeing the success of applying measure theory to generalize integration to fractals, I wonder whether or not there is a method to generalize the derivative to a fractal. Most courses start off fractal ...
6
votes
2answers
114 views

If $a=b$ then $a+c=b+c$? [duplicate]

A friend of mine just asked me how to prove that if $a=b$ then $a+c=b+c$, where $a,b$ and $c$ are real numbers, I'm not sure what I should answer. I have a book called introduction to logic and to the ...
4
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3answers
33 views

Largest subset with no arithmetic progression

I am trying to find some weak bounds on the largest subset of a set, such that the subset has the property that it contains no three elements in arithmetic progression. The elements of the original ...
3
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0answers
35 views

Can someone help me find a Mathematical documentary that aired on British television within the past 10 years about Leibniz?

I have been searching for a documentary that aired on British television between around 2006 and 2012 which was centred around the German Mathematician, Gottfried Leibniz. All that I can remember ...
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4answers
81 views

What is the best book for measure theory? [on hold]

What is the best book about measure theory I want the book has a lot of solved exercise I don't want just definitions theorem and examples I want a book has exercise and solved exercise
2
votes
0answers
17 views

What's Griffiths' ampleness in modern language?

When reading Griffiths' paper "Hermitian differential geometry, Chern classes and positive vector bundles", I found his definition of ampleness: Let $X$ be a compact complex manifold, $E\to X$ a ...
0
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0answers
11 views

Ordinary Differential Equations self-study reference request

I know there are a lot of reference requests for differential equations textbooks but none seem to be what I need. I'm looking for a book I can use for self study that isn't overly complicated and ...
0
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0answers
14 views

Bibliographic reference for $\sum_{n\in\mathbb Z}(z-n)^{-k}$

I am currently writing a paper which requires the closed-form expression of \begin{equation} S_k(z)=\sum_{n\in\mathbb Z}\left(z-n\right)^{-k} \end{equation} I believe $S_2$ is extremely classical ...
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2answers
35 views

The class of all functions between classes (NBG)

Is it possible in NBG (von Neumann-Bernays-Gödel set theory) to construct the class of all functions $X \to Y$ between two (proper) classes $X,Y$? I guess that this does not work. In the special case ...
11
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7answers
991 views

Is an empty parenthesis a valid mathematical expression? [on hold]

Is using an empty parenthesis valid? For example, $15+()=15$. What is the meaning if it is valid? I need an academic reference to validate this.
11
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0answers
30 views

Analogue of Dirichlet $L$-function for $\mathbb{F}_q[T]$.

We consider an analogue of the Dirichlet $L$-function in $\mathbb{F}_q[T]$. Let $g \in \mathbb{F}_q[T]$, $g \neq 0$, let $\chi: (\mathbb{F}_q[T]/(g))^\times \to \mathbb{C}^\times$ be a homomorphism, ...
0
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0answers
26 views

thorough proof of Mayer-Vietoris implies Excision

Where could I find a very complete proof of how the Mayer-Vietoris sequence implies the Excision theorem? I've read a few proofs, but they always leave out the details! Thank you!
1
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1answer
29 views

Intersection of Eigenvectors and Multivariable Calculus

This isn't really a problem but more of a reference/example question: do eigenvalues and eigenvectors ever show up in multivariable calculus? The two seem very unrelated to me. Specific examples would ...
4
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0answers
10 views

Where was it originally proved that $K$-finite automorphic forms are of uniform moderate growth?

I'm providing an overview of some classical results about automorphic forms in one section of a paper I'm working on, and I've realized I don't have a good reference for the following. Let $k$ denote ...
0
votes
1answer
21 views

Extending a diffeomorphism outside a compact set

I believe that the following statement is true: Let $U,V\subset \mathbb{R}^n$ be open sets, $K\subset U$ compact, and $\gamma:U\to V$ a diffeomorphism. Then there is a diffeomorphism ...
0
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1answer
13 views

What is a good source for learning Control Theory

I need to start learning and understanding Control Theory for my research. Does anyone know good resources for doing this.
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1answer
145 views

Who are the big names in Mathematics nowadays? [on hold]

The questions I pose are: Who are the big names in mathematics now? What branch do they study, what big problems are they looking at? I know of Wiles and Perelman (and I don't even know if those are ...
1
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4answers
57 views

How to come up with proofs of these results? Or, are these results true in the first place?

Let $x_n$ and $y_n$ be integer sequences determined by $$x_n + y_n \sqrt{2} = (1+\sqrt{2})^n \ \ \ \mbox{ for } \ n= 1, 2, 3, \ldots. $$ Then how to show that (a) $x_{n+1} = y_{n+1} + y_n$, $\ \ \ ...
1
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1answer
32 views

Positive and negative logical connectives

By inspecting the rules of inference for (intuitionistic) predicate calculus (or, alternatively, thinking about double negation translation), one sees that there is a certain dichotomy between two ...
-1
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0answers
11 views

gradient descent to solve binary non linear optimization problem [on hold]

I am trying to code a solution for an optimization problem that has binary matrix which has to be optimized,since the problem is not convex and has binary variables,i am finding it hard to solve ...
4
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0answers
23 views

Mathematic reasoning in nonEnglish/non Western languages [migrated]

I am teaching in an Eastern Asian environment (precisely, teaching Mathematics using English in Korea, with Asian students) and I figured out that my reasoning is a lot based on my language ...
3
votes
0answers
31 views

Generalizing convexity of sets

Let $X$ be a subset of some Euclidean space. We say that $X$ is convex if for any two points $p$, $q$ in $X$, the line segment joining $p$ and $q$ is also in $X$. But what if we loosen this definition ...
2
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0answers
21 views

Lifting of Commuting Maps of Vector Bundles

Assume that we have a vector bundle $\mathcal{F}$ over $\mathbb{P}^d(\mathbb{C})$ that is generated by global sections. Let $\pi \colon \mathcal{O}^n \to \mathcal{F}$ be the associated map that is ...
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2answers
27 views

book for numerical methods for solving pde

I need to find some masters-level exercises about numerical methods for solving pde. Are there any good references?
2
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1answer
24 views

Integrating over an embedded manifold: Jacobian factor?

Let's say I want to integrate a function $$ f(x,y),\quad x\in\Gamma_1,y\in\Gamma_2 $$ where $\Gamma_1,\Gamma_2$ are both embedded manifolds in $\Bbb{R}^3$. The dimension of $\Gamma_1$ is 1 (a ...
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0answers
14 views

Quick question: Pull back under double cover of tangent space on the projective plane is stable?

Let $f:\mathbb{P}^1\times\mathbb{P}^1\rightarrow\mathbb{P}^2$ be the double cover branched along some conic $C\subset \mathbb{P}^2$. Is $f^*T_{\mathbb{P}^2}(-1)$ $\mu$-stable/semistable? Is there any ...
3
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1answer
19 views

Looking for information about a random graph model

I have the following random graph model, and I am looking for its name and/or any work done concerning it. Given $n$ nodes, $\{v_1,...,v_n\}$, and $n$ timesteps, proceed as follows: On the $k$th ...
3
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0answers
32 views

Potential theory for LCA groups

I was wondering if there is a potential theory for locally compact abelian groups.
1
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1answer
119 views
+500

Fermat's last theorem and $\mathbb{Z}[\xi]$

I heard that one can prove special cases of FLT by using unique factorization in $\mathbb{Z}[\xi]$ (whenever this is possible), where $\xi$ is a primitive $n$-th root of unity. How can one do this in ...
0
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0answers
10 views

What is an inner-outer iteration?

Inner-outer iterations are used in papers, for finding a stationary point of a system or in optimization. It is not clear, what is called an inner-outer loop though? Is it a nested loop where the ...
0
votes
1answer
18 views

What is a good source for learning fourier transformations as an application

I'm an undergraduate physics major and for my research I need to start learning and understanding fourier transformations for my research. Does anyone know good resources for doing this. I don't need ...
1
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0answers
29 views

Finite groups of Mobius Transformations

Let $M_2(\mathbb{C})$ be the group of all Mobius transformations $z\mapsto \frac{az+b}{cz+d}$ from $\mathbb{C}\cup\{ \infty\}$ to itself. Let $PSU(2,\mathbb{C})$ be the group of all Mobius ...
0
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1answer
34 views

Connection between Functional Analysis and Quantum Physics [on hold]

Hi does anyone have an idea of which specific areas of Functional Analysis and Topology have a strong connection with the study of Quantum Mechanics and Quantum Field Theory? Thanks.
0
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0answers
12 views

Reference for set theoretic topology

I would like to self study set-theoretic topology for research purpose. I have background in algebraic topology, complex analysis, real analysis, set theory. May I know what are the texts should I ...
2
votes
2answers
75 views

One-dimensional Noetherian UFD is a PID

I am looking for a reference which has a self-contained (elementary, that is, at the "undergraduate algebra level") proof of the the fact that any one-dimensional Noetherian UFD is a PID. Does anyone ...
2
votes
1answer
52 views

Examples of connections between bounded cohomology and geometric properties of groups

I think that the question is self explanatory. The only example that comes to my mind is the characterization of hyperbolic groups given by Mineyev ("Straightening and bounded cohomology"). There is ...
3
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1answer
30 views

Convex functions up to reparametrization

I would like to know if there is a standard name for functions $f:[0,1]\to\mathbb R$ with the following convexity property: $$ \forall s<t<u\qquad f(t)\leq\max\{f(s),f(u)\}$$ (the fact that ...
1
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1answer
58 views

Where do I best learn informal set theory?

I want to learn math for machine learning, and I want to start with informal set theory. I was reading 'naive set theory' (1960) by halmos, and it didn't seem to contain modern set notations. If ...
2
votes
1answer
23 views

Zeta Function : Identify This Variant of an $L $- Series

This is my first question on Math.SE ; if I am wrong somewhere , please correct me I believe that there are not any mentioned variations of a Zeta function of this form : Where, $ w $ is a ...
1
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2answers
43 views

Arithmatic on modular curves

I had tried to read the first few pages of Glenn Stevens's$\,$ Arithmetic on Modular Curves, but it is somehow extremely unreadable to me, the text format is odd and stating too much facts without ...
1
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0answers
22 views

Are there some theories that explain the connections between differential equations and cellular automaton? [closed]

What connections are there between cellular automaton and partial differential equations?
3
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1answer
31 views

Recommended second textbook for dynamical systems?

I recently finished a course on dynamical systems supplemented by Strogatz's textbook. There are a few parts of the book that we didn't cover (in particular, the material on fractals), but the ...