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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9 views

Reference request for conditional and unconditional covariance of n-times integrated Brownian motion

I'm working through an old Diaconis paper on Bayesian numerical analysis, and am currently calculating the details behind his brief comments on using $n$-times integrated Brownian motion as a function ...
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0answers
30 views

A good book to read with Chapter III of Neukirch's “ANT”

The book Algebraic Number Theory from Neukirch is a beautiful book in ANT, but it still have a serious lack in examples and motivation to the concepts. I've already read the first two chapters of the ...
1
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1answer
5 views

Reference request: Topological space of polygonal chains and its properties

I'm interested in approximations of $C^1([a,b])$-functions by polygonal chains: image File:NURBstatic.svg by User:WulfTheSaxon licensed under GNU Free Documentation License A polygonal chain can be ...
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0answers
9 views

Laguerre's theorem on power of a point w.r.t. an algebraic curve

So on Wikipedia article for a power of a point there is a short section about Laguerre's theorem. The problem is, the article has no references, and whenever I'm trying to Google it the only things I ...
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2answers
13 views

PDE Solving: Difference between Similarity Solution and Characteristics?

As far as I understand, both the method of characteristics and similarity solutions allow us to reduce certain partial differential equations to ordinary differential equations which can then be ...
2
votes
1answer
37 views

Is $f(z)=\sum_{k=1}^{\infty}\frac{1}{(k+\frac{1}{k})^{z}}$ somehow related to Riemann's zeta function?

I was looking at this series $$ f(z)=\sum_{k=1}^{\infty}\frac{1}{(k+\frac{1}{k})^{z}} $$ and wondering if it is somehow realted to the Riemann's zeta function $$ ...
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0answers
16 views

How to figure out whether PCA can be performed on a data set or not?

I do have idea on the way PCA works but I do not know how to figure out whether a high dimensional data set is suited for PCA compression. I googled for some algorithms but could find any. Are there ...
0
votes
1answer
10 views

What are existing methods to count colored subgraph frequencies in a large colored directed graph?

I have a directed colored large network or graph. By 'color' I mean that nodes are of different categories. There are some small 3 or 4 node colored directed subgraphs. I need to know how to count ...
2
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0answers
22 views

Perimeters Areas and Volumes

I have to write an article for a school magazine. I thought it is better to choose a simple topic like Perimeter, Area and Volume. I am looking for historical fact and surprising facts about ...
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0answers
35 views

Help: Studying A-Level Mathematics [on hold]

Although I am a latecomer at the age of 21 years of age, I have enrolled in self taught mathematics A-level with "Edexcel" both mathematics & further mathematics. I am in need of help with ...
1
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0answers
6 views

Is the co-limit of a chain of normal subspaces necessarily normal?

Suppose $ X_0 \subset X_1 \subset X_2 \subset \dots$ is a chain of normal subspaces of $X$ such that $X= \cup_{i=1}^{\infty} X_i$. Assume that $X$ has the colimit topology w.r.t. these subspaces. Can ...
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1answer
33 views

Good books about elliptic integralsa, hypergeometric and special functions

Can you please tell me some good books from where I can learn elliptic integrals and special functions like hypergeometric functions?
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0answers
29 views

question about theorem references (who made it, year, etc.) [on hold]

The statement of the theorem that i would like to know some references is this: if we fix two numerical invariant $K^2$ and $\chi$ then there exist a quasi projective moduli space of the canonical ...
1
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1answer
28 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 ...
2
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0answers
28 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 ...
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0answers
34 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 ...
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0answers
25 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 $\mathbb{R}^n$. ...
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0answers
16 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 ...
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1answer
69 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?
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1answer
79 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
31 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 ...
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2answers
38 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
40 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
1answer
31 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 ...
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0answers
22 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
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1answer
25 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
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1answer
36 views

Reference request for stochastic process

I studied the book, "Probability, Random Variables and Random Signal Principles" by Peyton Peebles. And I am a little bit familiar with statistical analysis like signal estimation and detection. In ...
3
votes
3answers
611 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. ...
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0answers
19 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 ...
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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
39 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
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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
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1answer
28 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. ...
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votes
0answers
16 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
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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
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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
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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
29 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
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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
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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 ...
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votes
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 ...
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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
15 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 ...
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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
40 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
37 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 ...