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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1answer
7 views

Looking for examples of finite loops and monoids

I am looking for examples of (small) finite loops and monoids that are not groups for demonstrating what happens if you omit some of the group axioms. Does anyone know some ressources for this? I ...
0
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0answers
9 views

Where can I learn more about the “else” operation / “else monoid”?

(The set of natural numbers $\mathbb{N}$ starts at $0$ for me.) Let $X$ denote a set, and define $X_\bot = X \uplus \{\bot\}.$ Let $\mathbf{else}$ denote the binary operation on $X_\bot$ defined as ...
1
vote
0answers
22 views

The Nagell-Ljunngren Equation

I have been trying to find the papers of Nagell and Ljunngren, which deal with the equation $$\frac{x^n - 1}{x - 1} = y^2$$ and solve it completely. Many papers cite these papers, but I haven't found ...
1
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0answers
24 views

Defining Lebesgue measure on a subspace of $\mathbb{R}^n$

Let $\bar{w}_1,.., \bar{w}_k$ be linearly independent vectors in $\mathbb{R}^n$. Let $W$ be the subspace spanned by these $\bar{w}_i$'s. I know how the Lebesgue measure is defined on $\mathbb{R}^n$. ...
0
votes
0answers
13 views

Self contained book on Ricci Flow/Geometric Analysis

Can someone please tell me whether there is any self contained book on Geometric Analysis/Ricci Flow/analytic techniques used in Riemannian Geometry? By self contained I mean it does not assume that ...
0
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1answer
57 views

Linear algebra references for a deeper understanding of quantum mechanics

I'm a graduate student studying quantum mechanics/quantum information and would like to consolidate my understanding of linear algebra. What are some good math books for that purpose?
4
votes
1answer
65 views

No Borel well-order of the reals?

I'm told there is no Borel well-order of the reals (in ZFC). I'm told, in fact, that this is because of Borel determinacy. However, this is usually a vague handwave of the form (a) take the usual ...
3
votes
0answers
26 views

Multiples of some set has density

Nathanson gives a proof in Elementary Methods in Number Theory (Theorem 7.14) that, if a set $S$ of positive integers has $$ \sum_{s\in S}\frac1s<+\infty $$ then the set of positive multiples of ...
0
votes
2answers
37 views

Is there any good software to plot trigonometry graph?

I want to plot trigonometry graph like sine function, cosine function, etc. (degrees, not radians) but I don't find anyway to make it in my computer. I like graph produced by WolframAlpha, but it ...
4
votes
1answer
36 views

Introduction to proofs. [duplicate]

I am not at all familiar with mathematical proof-writing and would like to learn how to create my own proofs. So, I was wondering whether it would be possible for you to recommend me to any book or ...
2
votes
0answers
24 views

Natural action of $\operatorname{Aut}(G)$ on sets of subgroups of $G$ of same order is transitive.

I am looking for the classification of those finite groups whose automorphism group acts transitively on sets of subgroups of same order. Let $G$ be a finite group and $d$ be a divisor of the order ...
0
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0answers
18 views

A physical model for pde

Do you know any mathematical model of a physical process such that it satisfies the following equations ? $$\mathrm{u_t=a(t)u_{xx}},\,\,\,0<x<1,\,\,\,t>0$$ ...
1
vote
1answer
14 views

Non-uniqueness of worst-case (max-min or min-max) optimization

I have a worst-case optimization problem, where i want to maximize the minimum from the uncertainty set (uncertainty is given as an ensemble of 100 realizations, so an ensemble based approach). It is ...
3
votes
1answer
31 views

Reference request for stochastic process

I studied the book, "Probability with the book, Probability, Random Variables and Random Signal Principles" by Peyton Peebles. And I am a little bit familiar with statistical analysis like signal ...
3
votes
3answers
606 views

What is the name of this book?

Anyone knows the name of this book: http://www.maa.org/sites/default/files/pdf/pubs/books/meg/meg_ch12.pdf? I've already tried to find it online and in the maa catalog without success. I need help. ...
1
vote
0answers
18 views

Algebra of matrix valued functions on the sphere

I was watching a video of a lecture by Alain Connes, and at around 8:00 he very briefly mentions a way to think about the algebra of 2x2 matrix functions over the 2-sphere, i.e. the maps from $S^2 ...
0
votes
0answers
16 views

Rentschler's theorem on non-commutative algebras

Rentschler's theorem says that every locally nilpotent derivation of the algebra $A=\mathbb{C}[x,y]$ (i.e., a linear map $\phi$ that satisfies the Leibniz rule and such that for every $p \in A$ ...
0
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0answers
38 views

Seeking Recommendation on Number Theory textbooks [on hold]

S.E advisers, I am a college sophomore with double majors in mathematics and Russian language. I wrote this email to seek a recommendation on good introductory textbooks for number theory. I will ...
1
vote
1answer
60 views

Prerequisite books before Hungerford's Algebra?

Prerequisite books before Hungerford's graduate Algebra? I have an pdf version of the book and feel the Hungerford is overcomplicated after i finish some of the books title with something like first ...
0
votes
1answer
27 views

The multiplicative group of integers modulo n

I need to write an introduction about the history who first showed that the multiplicative group of integers modulo $n$ is cyclic for certain $n$, when they showed it, why it was surprising, etc. ...
-1
votes
0answers
15 views

Defining a stochastic process indexed by angle

I have a random closed curve of the form $(\theta,r_\theta)$, where $\theta\in [0,2\pi]$, is the counter clockwise angle from the x-axis and $r_\theta$ is the radial distance from the origin ...
0
votes
1answer
17 views

Axioms for constructability

When we are doing geometric constructions we assume that the only operations we can perform are We can draw a line between to points. We can draw a circle with one point as the centre and the other ...
1
vote
1answer
92 views

Reference request for the independence of $ \text{Con}(\mathsf{ZFC}) $.

Gödel’s Second Incompleteness Theorem says that if $ \mathsf{ZFC} $ is consistent, then $ \mathsf{ZFC} \nvdash \text{Con}(\mathsf{ZFC}) $, i.e., $ \text{Con}(\mathsf{ZFC}) $ is not provable in $ ...
1
vote
1answer
30 views

If I want to learn mathematical optimization where should I start?

I'm working in the area of transportation engineering, to be specific, mostly involved in management. I read some papers in Transportation research part x, and something like that, and noticed that I ...
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votes
0answers
28 views

Proof theorem of Lie's Algebra [on hold]

I need help with a proof this theorems, anyone could be help? I need a proof this theorems. Corollary of Lie's Theorem: Let $L$ be a solvable subalgebra of $\text{gl}(V)$, $\dim V = n$ (finite). ...
1
vote
0answers
29 views

What is some elementary differential geometry textbook that is self contained and are intermediate level?

What are some intermediate differential geometry textbook that are more advanced than pressley's, Barrett's, Christian's and krezig's books and are self contained but below the level spivak's vol ...
1
vote
1answer
27 views

1-surgery on the figure-eight knot: reference request

As far as I know, 1-surgery on the figure-eight knot gives ($\pm$) the Brieskorn sphere $\Sigma(2,3,7)$. However, is there a citeable source for this? Sometimes Thurston's notes are mentioned, but I ...
0
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0answers
16 views

Required sub-chapters or more materials needed to learn Statistical Inference other than my textbooks

My school is using new curriculum now and chapter "Statistical Inference" appears in my textbooks. Now I'm at second level of senior high school. I have two books, each of them has own sub-chapters ...
1
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0answers
31 views

How much does convolution with a compact C^m kernel increase the order of continuity.

Let $f \in C^n$ and $g \in C^m$, with $g$ compactly supported and integrable. How much does the convolution $f\star g$ of $f$ with $g$ increase the order of continuity? Statement: I think that, under ...
0
votes
1answer
29 views

Convergence of spectrum with multiplicity under norm convergence

This article by Joachim Weidmann claims that, if a sequence $A_n$ of bounded operators in a Hilbert space converges in norm topology, i.e., $\|A_n - A\| \rightarrow 0$, then "isolated eigenvalues ...
2
votes
0answers
31 views

Does this matrix normal form have a name and has it been used?

In a research paper in Theoretical Computer Science, we are using a certain matrix normal form, which I was not able to find in the literature (I have to admit that my Linear Algebra got a bit rusty, ...
2
votes
0answers
12 views

Relationships between affine closures and convex closures

Let $V$ denote a vector space. Then the following concepts make sense: affine subset of $V$ affine closure (affine "hull") of a subset of $V$ Suppose $V$ is in fact a real vector space. Then the ...
1
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0answers
22 views

Prove Grigorchuk group is self similar.

Where I can find a proof of self similarity of Grigorchuk group. I read it somewhere that Grig group follows this interesting property so I read about it but could not find a proof anywhere. It was ...
0
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0answers
39 views

Suggestions(Anything) regarding GRE Math Subject test [duplicate]

I am to appear for GRE Math Subject test probably this year or next year .I have basic knowledge of calculus 1,2,3 ,group theory ,Linear Algebra , Small part of real analysis . I haven't yet studied ...
3
votes
2answers
74 views

How did Rudin conclude his argument there is no “boundary” between convergent and divergent series?

I lost my baby Rudin book on real analysis book but I recall a pair of results in homework exercises that he seemed to indicate that there is no "boundary" between convergent and divergent series of ...
3
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0answers
36 views
+50

Literature request: Method for constructing projective manifolds

Currently (background: I'm preparing to write a thesis in mathematical physics) I'm quite often encountering a certain method for constructing projective manifolds, where the space is specified by ...
2
votes
0answers
35 views

How to prove that the tangent map $T\phi$ into the pullback bundle is smooth?

Assume $\phi: M\rightarrow N$ is smooth. Let $\phi^*(TN)$ be the pullback bundle of $TN$ by $\phi$. Define $T\phi:TM\rightarrow \phi^*(TN)$ as follows: $T\phi(m,v)=(m,d\phi_m(v)) $. We also have the ...
0
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0answers
17 views

Monograph about periodic representations of numbers in non-integer bases

I'm looking for a monograph (book, article, lecture notes, whatever) about the representation of numbers (real or complex) in non-integer bases. I am especially interested in results about algebraic ...
3
votes
2answers
69 views

Non-factorizable graphs in which every edge can be extended to a maximum matching

All graphs in this question are finite, simple, undirected, and unweighted. A graph is said to be factorizable if has a perfect matching, and non-factorizable otherwise. An edge in a graph is said to ...
2
votes
0answers
28 views

Literature about Ultrafilters

I am in the early stages of planning my senior project and was wondering if anybody had some recommendations of literature about the applications of ultrafilters in social choice theory, along with ...
1
vote
1answer
19 views

Fractional Sobolev spaces on closed manifolds

Let $M$ be a closed manifold and $0<s<1$. How is the fractional Sobolev space , $H^s(M)$ defined? In particular if $M$ is a closed smooth simple curve in the place how is $H^{1/2}(M)$ ...
0
votes
0answers
22 views

Reference Request for Complex Analysis (with some specificity regarding Ahlfors and Cartan)

I am a self-studier and am making my second pass through Complex Analysis. I have read the reference request posts many times. Yet perhaps I could get some advice as to the relevant benefits of ...
0
votes
1answer
43 views

Recommendations for textbooks covering these parts of mathematics? [closed]

I would like some recommendations for textbooks that cover these parts of mathematics: Logic, algebra, geometry, and analysis. For example, with regard to algebra, I'm looking for a book that provides ...
0
votes
0answers
29 views

Deformation theory in a paper of Bogomolov and Tschinkel

I am trying to read this paper http://www.math.nyu.edu/~tschinke/papers/yuri/00ajm/ajm.pdf, by Bogomolov and Tschinkel. I had 0 preparation in the theory of deformation of complex structures, but in ...
0
votes
1answer
26 views

linear algebra texts suggestions

I am looking for a textbook about linear algebra. I want one with a pure math/algebraic approach and not one with a geometric or a applied/numerical approach. Do you have any suggestions? Thank you
3
votes
1answer
37 views

Conjectured diagonal Ramsey numbers

While doing some reading on the Wikipedia page for Ramsey numbers, I stumbled upon OEIS sequence A120414, which lists the allegedly conjectured values of the diagonal Ramsey numbers $R(n,n)$. I ...
0
votes
0answers
24 views

Hausdorff measure, volume form, reference

Could you tell me where I can find a reference to the fourth corollary in this encyclopedia? Corollary $4$: Assume that $\Sigma \subset \mathbb{R}^m$ is an $n$-dimensional $C^1$ ...
1
vote
1answer
25 views

Reference to line parametrization

Defining two lines in space, $\mathbb{R}^3$, as: $l_1: \textbf{a}_1+\lambda_1\textbf{b}_1$ $l_2: \textbf{a}_2+\lambda_2\textbf{b}_2$ The line to line intersection condition is: $\textbf{b}_1\cdot ...
0
votes
1answer
88 views

Is it necessary to read point set topology to read differential geometry?

I want a quick insight in differential geometry but it is hard to start directly although i have done courses in calculus and basic algebra .is it necessary to get through point set topology and ...
0
votes
0answers
17 views

Diffusion semigroup generated by Laplacian [closed]

Let $M$ be a complete Riemannian manifold and $\Delta$ denote the Laplacian on it. Also assume that the spectrum of $-\Delta$ lies inside $[a, \infty)$. Let $P_t, t > 0$ denote the diffusion ...