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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35 views

Good resources to learn Hopf algebras

I am finding it hard to find resources that can educate me in this subject. I have looked up this and I can't find anywhere to start. Any advice?
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1answer
23 views

Literature: Derivations in C*-Algebras

Do you have some nice reference for dynamical systems in C*-algebras (including discussion of their derivations!) like notes, papers, books, etc.?
0
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0answers
39 views

Dedekind(?) representation lemma on posets?

Here's an easy lemma: Any poset $(S, \preceq)$ is order-isomorphic to a subset of the powerset $\mathcal{P}(S)$ ordered by set-inclusion. I seem to recall having seen this attributed to Dedekind. ...
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0answers
24 views

Existence of strong solutions to parabolic p-Laplace equation

Can I find a reference to where the existence of strong solution $u \in L^2(0,T;W^{1,p})$ with $u_t \in L^2(0,T;L^2)$ is proved to the equation $$u_t - \Delta_p u = f$$ $$u(0) = u_0$$ ...
2
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1answer
51 views

suggest a topic about history of mathematics

Can you suggest a topic (the history of mathematics) concerning the evolution of a given concept from a document written in English from varied scientific resources What do you think of the ...
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0answers
27 views

Is $F(x_1,x_2,\dots,x_n)$ where $(x_1,x_2,\dots,x_n)\in \Delta$,a semi-algebraic function?

Given $$F(t_1,t_2,\dots,t_n)=\int\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}dx_1dx_2\dots dx_n$$ where $P_1(x_1,x_2,\dots,x_n), P_2(x_1,x_2,\dots,x_n)$ are polynomials whose coefficients ...
1
vote
1answer
27 views

Is it decidable that any two computable function over reals $ f(x_1,x_2,\dots,x_n)\equiv g(x_1,x_2,\dots,x_n)$

Is it decidable that any two computable function over reals or over sphere of complex $ f(x_1,x_2,\dots,x_n)\equiv g(x_1,x_2,\dots,x_n)$ ?
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2answers
35 views

Is a intersection of chain of non enumerable dense sets non enumerable?

Let $M_1\supset M_2\supset \cdots$ sets such that each $M_k$ is a non enumerable set, all of then open and dense in $S^1$ and such that $Leb(M_k)\to 0$ when $k\to \infty$, where $Leb$ denote the ...
1
vote
1answer
25 views

Does every quasi-affine variety have an open cover of affine dense subsets?

Suppose you have a nonempty, quasi-affine variety $Y$. Does $Y$ always have an open cover of affine dense subsets? I know that every quasi-affine variety has an open cover by quasi-affine varieties ...
1
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0answers
22 views

Reference request: classification of simple Lie groups and simple real Lie algebras

I am trying to understand the classification of simple Lie groups and the theory of highest weights for semisimple Lie groups by first understanding the case for complex Lie algebras, then relating to ...
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2answers
545 views

Locating a paper in Euler's complete works

I'm currently reading Disquisitiones Arithmeticae and I keep seeing references to Euler such as "Comm. acad. Petrop., 8 [1736], 1741, 141". My question: How can I go about locating this paper in ...
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1answer
75 views

A comprehensive book on Applied Mathematics for beginners

The Princeton Companion To Mathematics is described on Wikipedia thus: The book concentrates primarily on modern pure mathematics rather than applied mathematics, although it does also cover both ...
1
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0answers
56 views

Does this lemma have a name or where can I find a proof?

Does the lemma at the bottom of this page have a name? Or could someone give me an idea of where I can find a proof? In case you can't access the link: Lemma $\ \ $ If $g$ is of class ...
3
votes
1answer
39 views

Hypercomputation & Higher Dimensional Variants of Conway's Game of Life

Conway's Game of Life is a simple and important mathematical game with some rules of evolution in a two dimensional space. It appears in many subjects in mathematics, artificial intelligence and ...
4
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1answer
75 views

Question about the Ascoli-Arzelá Theorem proof

Ascoli-Arzelá Thoerem: Let $K$ be a compact space and $M$ be a metric space and $C(K,M)$ be the set of continuous functions from $K$ to $M$. $H \subset C(K,M) $ is relatively compact if and only if ...
0
votes
0answers
11 views

Order of distribution of the zeros of the interference function of periodic oscillations?

Given a finite (or an infinite) number of periodic oscillations of different shapes but even functions, along the abscissa $x∈R$, every such periodic oscialltion may cross on some zero points the ...
0
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0answers
61 views

Powers of simple groups

I have heard about the following result: for each natural number $r\ge 2$ and each finite simple non-abelian group $S$ there exists a number $n=n(r,S)$ such that the power $S^n$ is $r$-generator but ...
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4answers
96 views

math-biography of mathematicians

Some of the mathematicians agree that reading Biography(Or more specifically, math-autobiography, scientific-biography ) gives lot of inspiration for working; and I am one of them. One book which I ...
2
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0answers
47 views

Is there any inconsistent large cardinal axiom which its inconsistency proof is essentially different from proof of Kunen inconsisteny theorem?

There is a long list of large cardinal axioms. Most of them deemed to be consistent with ZFC but there are also some axioms like existence of Reinhardt or $\omega$-huge cardinals which are natural ...
3
votes
3answers
156 views

Discrete Mathematics for someone who has already done Analysis/Algebra?

I graduated with an undergraduate mathematics degree this past May, but I had never taken a Discrete Mathematics course. I took the usual years' worth of Algebra and Analysis. I am interested in a ...
14
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2answers
279 views

What is the most influential work of Grothendieck in mathematics?

Recently Alexander Grothendieck has passed away but his mathematical wave is still alive and passes its growth ages. It is hard to describe the influence of such a great man in mathematics just in few ...
3
votes
1answer
92 views

Best approximation for a normed vector space $X$

I am self-studying functional analysis. As far as I know, a best approximation of $X$ by a closed subspace $C \subseteq X$ exists and is unique if $X$ is a Hilbert space, a uniformly convex Banach ...
1
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1answer
16 views

what is one basic/intermediate regression analysis standard textbook that is math intense

What is one basic/intermediate regression analysis standard textbook that is math intense with proofs/derivations? Also, i need that one to be comprehensive yet the diffculty is suitable for self ...
3
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3answers
97 views

Gathering books on Lorentzian Geometry

I find it very hard to find books on Lorentzian Geometry, more focused on the geometry behind it, instead of books that go for the physics and General Relativity approach. More specifically, I'm ...
2
votes
2answers
234 views

Real numbers as decimals

I'm looking for a book that develops the theory of real numbers in a rigorous way in terms of their decimal expansions. The exposition should be concrete and preferably aimed at mathematically ...
1
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1answer
61 views

Intuitive diagrams for models of non-well founded set theory

Based on our intuition about von-Neuman's rank, there is a standard view to describe a model of ZFC as a large V-shape world. When we remove the Axiom of Foundation (AF) from ZFC and replace it with ...
2
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0answers
32 views

Accessible textbook about basic Fourier analysis in terms of integrals wrt measures

I am looking for a basic and accessible textbook (or set of lecture notes) that discusses basic fourier analysis but in terms of measures and integrals with respect to measures. Not sure if it is done ...
1
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0answers
11 views

Graph invariants for rooted trees

I'm looking for a few graph invariants (that have been studied before) that help distinguish rooted trees. I have a large, real-world collection of these graphs and I'd like to see what has been ...
1
vote
1answer
23 views

Finding free subgroups thanks to Lie algebras

Let $f : F \to G$ be a homomorphism from a free group $F$ to a group $G$. I heard that, in order to verify whether or not $f$ is one-to-one, it is possible to associate a Lie algebra $E_0^*(H)$ to any ...
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5answers
310 views

Examples of Mathematics in Court

In court trials, natural sciences such as physics and biology routinely make an appearance, e.g. when estimating the speed of a vehicle based on impact damage or trying to deduce from the condition of ...
2
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2answers
39 views

History of fixed point theory

I am looking for encyclopedic references for fixed point theory and its applications. What is the best reference for this subject? thank you.
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0answers
30 views

Reference for Spectral theory

I'm studying Bernard Aupetit: A Primer on Spectral Theory but the textbook we are using is a little bit heavy going for me. Is there a "gentler" book to learn about these things? Thank you.
2
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1answer
45 views

Possible values of $\gcd(a+b, a\times b)$

Main Question: Let $N \in \mathbb{N}$. What are the possible values of $\gcd(a+b, a\times b)$ given that $\gcd(a,b) = N$? Fact 0. If $\gcd(a,b) = N$, then $N \leq \gcd(a+b, a\times b) \leq ...
1
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0answers
21 views

Proof that difference equations as asymptotic to their differential analog.

Given a difference equation $a_{n+k}=f(a_n,a_{n+1},\dots,a_{n+k-1})$, we can classify $n=\infty$ as an ordinary, regular singular, or irregular singular point by classifying $x= \infty$ in the ...
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0answers
49 views

Instructive sources for arguing without elements

There is a trend in mathematics towards reasoning without elements if possible (coming from category theory, I presume). I see the appeal and want to learn how to argue avoiding the use of elements, ...
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0answers
15 views

Name for a generalization of Dyck paths, Motzkin paths

A Dyck path is a function $P:[n] \rightarrow \{0,1,2,\ldots\}$ with $P(1) = P(n) = 0$ and $P(i+1) - P(i) \in S$ where $S = \{-1,1\}$. If we use the same definition except change $S$ to $\{-1,0,1\}$ ...
5
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1answer
213 views

Closed-form formula for the $n^{\rm th}$ term of ${1,1,1,1,\ldots, 1}, {2,2,2,2,\ldots, 2},\ldots, {k-1, k-1}, k.$

Let $k$ be a positive integer. Consider a finite sequence $L_k(n)$ given by $$\underbrace{1,1,1,1,\ldots, 1}_{k\text{ terms}}, \underbrace{2,2,2,2,\ldots, 2}_{k-1\text{ terms}},\ldots, ...
3
votes
2answers
143 views

Is there any general method of finding the lower bound of $x$ that satisfy the inequality?

Is there any general method to find a real valued function $f(x)$ such that, $$\dfrac{x}{\ln x -(1+\epsilon)}>\pi(x)>\dfrac{x}{\ln x -(1-\epsilon)}$$ for all $x \geq f(\epsilon)$. The value of ...
2
votes
1answer
69 views

finite simple groups and free groups

It is well known that any group is a homomorphic image of a free group. I want to know more about this theorem when $G$ is a finite simple group. Does there exist any reference to state about it? ...
1
vote
0answers
56 views

Reference for principal bundles and related concepts

I am looking for a good reference for fibre bundles, Ehresmann connections, principal $G$-bundles and principal Ehresmann connections (the $G$-equivariant version of Ehresmann connections). Could ...
2
votes
1answer
57 views

Applications of the Little and Great Theorems of Picard

I have completed the two famous theorems of Picard, presenting their proofs in an graduate course, but I have not managed to discover a good number interesting applications. List of applications ...
0
votes
1answer
53 views

Distance of subgroup to element in Lie groups

Given a (compact, closed) Lie group $G$ and a (closed) subgroup $H$, what is the distance of the identity to $Hg$ (or $gH$), where $g\in G$ and $Hg$ denotes the orbit under left-multiplication? The ...
2
votes
1answer
92 views

Level of Difficulty of an Undergraduate Curriculum

I'm considering joining an University which is renowned for mathematics in my country. The curriculum it offers is as follows : All the courses listed below except the course on Writing of ...
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0answers
18 views

infinite dimensional system of ode

please, in which applications do the following systems arise: $\dot x_k=f_k(t,x_1,x_2,\ldots),\quad k\in\mathbb{N}$? actually where can I find anything about them? The topological spaces of the ...
2
votes
1answer
61 views

Is $L^1(\Omega)$ isomorphic to $l¹$?

I'm trying to understand a statement in the Brezis book, that $L^1(\Omega, \mu)$ is not reflexive. He divides the problem into two parts: one in which $\mu$ is a non atomic measure and another in ...
2
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1answer
50 views

all Sylow subgroups of $GL_n(\mathbb{F}_q)$

Can you give some references to find all Sylow subgroups of $GL_n(\mathbb{F}_q)$? I know that upper triangular matrices with diagonal's 1 is a Sylow $p$-subgroup where $q=p^n$. But how about the other ...
0
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0answers
38 views

When can definite integration be numerically computable?

under what condition,can the integration $$\int_{\Delta}f(x_1,x_2,\dots,x_n)dx_1dx_2\dots dx_n, \text{where } \Delta \text{ is integration domain defined by function},f(x_1,x_2,\dots,x_n) \text{ ...
5
votes
2answers
212 views

Can it be decidable for any polynomials to have the intersecting point?

Give system of polynomials$$P_1(x_1,x_2,\dots,x_n)=0,$$$$\vdots,$$$$P_k(x_1,x_2,\dots,x_n)=0$$ Can it be decidable for thoses polynomials to have the intersecting point ?
1
vote
0answers
17 views

Side and angle relations in a hyperbolic quadrilateral.

Let $PQRS$ be hyperbolic quadrilateral, i.e. a quadrilateral in $\mathbb{H}$ whose sides are hyperbolic geodesic. Let length$(PQ)=l_1$, and length$(PS)=l_2.$ Also $\angle SPQ=\theta_1$, $\angle ...
3
votes
1answer
74 views

Did Gauss find the formula for $1+2+3+\ldots+(n-2)+(n-1)+n$ in elementary school?

I heard Gauss's primary school teacher gave some busy-work to his class: to add all the numbers between 1 and 100 up. Gauss immediately wrote 5050. His teacher was shocked, so she told him to add up ...