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Questions tagged [reference-request]

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.

0
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1answer
18 views

Jacobian of vec of a matrix into vec of its inverse

Suppose that $X$ is invertible and $n\times n$ and the transformation: $$ \varphi:\operatorname{vec}(X)\mapsto\operatorname{vec}(X^{-1}). $$ For example, with $n=2$ and $X=\begin{pmatrix}a & b \\ ...
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0answers
10 views

Definition of the Fell topology: Completion with respect to a seminorm

I'm reading about the Fell topology and have a question on some preliminary material. My reference is these notes on automorphic representations. Let $G$ be a locally compact Hausdorff, second ...
0
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0answers
32 views

Non-infinitesimal differential operators, do they exist?

I already know they do exist in signal processing, I have built many myself. It is a whole art to do so in any discipline that handles noisy data. But is it possible to find out which ...
0
votes
1answer
19 views

What are good strategies for stable numerical approximations of special functions?

I am trying to write a scientific calculator for a very small microcontroller with no floating point unit. If the standard c math libraries were included the compiled code would be too large to fit on ...
0
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0answers
12 views

Finding kernel of a matrix over char. 0 from solutions in prime char.

Consider the a set of linear equations with coefficients in $\mathbb{Z}$, $Mx=0$, where $M$ is some arbitrary $m\times n$ integer matrix. I want to know if there is a general procedure to find a ...
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0answers
17 views

Theorem which says that the tangent bundle at $1$ of a Lie group is a Lie algebra?

I am looking for the theorem which says that the tangent bundle at $1$ of a Lie group is a Lie algebra, together with its proof. By Theorem 15.27 of my differential geometry book proposes only the ...
0
votes
1answer
33 views

Reference for the “points of continuity of a function is a $G_\delta$ set”.

Let $f: X \to Y$ be a function between metric spaces. I was told that the points of continuity of $f$ are a $G_\delta$ set and the points of discontinuity an $F_\sigma$ set of $X$. Can anyone give me ...
9
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2answers
186 views

How one should treat M.Kline's “Mathematics. The Loss of Certainty”?

Recently the article "Foundations of mathematics" in Russian Wikipedia attracted my attention by lots of strange (and often absurd) declarations, in particular, it is written there that David Hilbert (...
3
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0answers
23 views

Resources for Abelian Equations

I am taking a Galois Theory course using Cox's Galois Theory text book, and we have a required student project. Having read the section on Abelian Equations, section 6.5 page 143, I want to know more ...
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0answers
11 views

Finding or fitting a manifold to a set of points in a euclidean space

The question I'm going to ask is rather a vague one. I try my best to describe the question as best as I can. Because of the generality or maybe vagueness of my question, I'm not looking for an exact ...
0
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0answers
54 views

Does anyone know if there exists a complete solutions manual to Hardy's PURE MATHEMATICS?

Ok, this may be a ridiculous question and if so, you guys will shut it down. But I didn't know where else to ask it-it certainly doesn't belong on Math Overflow. Does anyone know if anyone ever ...
0
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0answers
23 views

Where do I learn latex for math overflow. [migrated]

I am very beginner in writhing math in computer and I want to learn latex to write in math overflow where do I start and how does latex is invoked in math overflow.
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0answers
23 views

Spherical derivative in several variables

This is more of a reference request, really. The spherical derivative of a holomorphic function (in one variable) $f$ is defined by $ f^\# := \frac{|f^{'}|}{1 + |f|^2}. $ Is there a corresponding `...
5
votes
0answers
48 views

Are ordinals greater than $\varepsilon_0$ used outside Ordinal Analysis?

I know of Conway's use of ordinals to exhibit the algebraic closure of $\mathcal{F}_2$. I also read a document about the Cantor Bendixson rank of some family of groups. But I found no applications of ...
0
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0answers
14 views
+50

Bounding the MGF of a non-homogeneous Rademacher chaos of order two

I am trying to bound a quantity of the form $$ \mathbb{E}[ F( \sum_{i,j} a_{ij}\varepsilon_i\varepsilon_j' + \sum_{i,j,k} b_{ijk}\varepsilon_i\varepsilon_j\varepsilon_k'+ \sum_{i,j,k} b_{ijk}\...
2
votes
0answers
37 views

Optimality results for Fitch-style natural deduction proofs

Suppose a student submits a Fitch-style natural deduction proof in propositional or predicate logic. Two natural questions arise (beyond correctness): Is the proof as short as can be? Is the proof as ...
1
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0answers
32 views

Simple extensions of $\mathbb{Z}$ by rational numbers

I'm afraid this question might be considered opinion-based, but I dare. It might be considered opinion-based because it starts from a probably biased observation: In textbooks examples and discussions ...
1
vote
1answer
17 views

Structural Equation Modeling Reference Text

I'm looking for a good introductory book on the theory behind structural equation modeling in the social sciences. I have a solid background in multivariate statistics and in pure mathematics, so ...
0
votes
0answers
80 views

Inverse limits with discontinuous bonding maps

I have been studying inverse limits and the following question came up to mind. Suppose that $X_i = [0,1]$ for every $i \in \mathbb{N}$ and $f^{i+1}_i: X_{i+1} \to X_i$ is a linear piecewise expanding ...
3
votes
3answers
161 views

Recommended Problem books for undergraduate Real Analysis

So I am taking an analysis class in my university and I want a problem book for it. The topics included in the teaching plan are Real Numbers: Introduction to the real number field, supremum, ...
1
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1answer
40 views

Book reference for proof.

A finite group characteristically simple is isomorphic to a direct product of simple groups. Does anyone know of a book that contains this proof? I just need to reference it, but in the books I've ...
2
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0answers
33 views

Maps $f:X\to X$ with $x \geq f(x$)

In order theory, what do we call maps $$f:X\to X \mbox{ with } \forall x\in X:x \geq f(x)$$ (with or without the demand that it is order preserving)? I'm thinking of contraction or something of the ...
1
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0answers
29 views

Books to buy before transferring? [on hold]

I will be transferring to University from a CC in 10 months. Long story short, my remaining classes are non-stem, and I would like to self study math and physics in those 10 months, specially in the ...
1
vote
1answer
31 views

How do I find a closed form of the characteristic function of Gamma distribution?

It’s written in wikipedia that $(1-i \beta t)^{-\alpha}$ is the characteristic function of the Gamma distribution $Gamma(\alpha,\beta)$. I tried to prove this but I failed. So I googled it for a proof,...
1
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0answers
27 views

Authoritative reference of double induction

In my recent work, I have used the following double induction: Let $ P(n,m) $ be a proposition about $n,m\in\mathbb{N}\cup\{0\}$. To show $P(n,m)$ is true for all $n\in\mathbb{N}\cup\{0\}$ and all $m\...
0
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0answers
33 views

What is known about the equation $p^i + q^j = 2^k$?

The equation $p^i + q^j = 2^k$, with $p,q$ odd primes and $i,j > 2$, seems to have no solutions. Does this result/conjecture have a name? What is the intuition behind $p + q = 2^k$ having plenty ...
1
vote
0answers
16 views

Sampling extreme points from Minkowski Sum

I recently stumbled upon the following subproblem: we are given zonotopes $P_1, \dots, P_m$ in $\mathcal{V}$ representation (i.e. we are given the extreme points of each $P_i$). Denote the Minkowski ...
1
vote
1answer
30 views

Degree of images of projective varieties

Let $X\subseteq\mathbb{P}^n\times\mathbb{P}^m$ be a projective variety of dimension $p$ and degree $d$ defined over an algebraically closed field $k$. Let $X'\subseteq \mathbb{P}^n$ be the projection ...
0
votes
1answer
45 views
+50

Reference Request - Lagrange's Approach to Solve Polynomials by Radicals

What is a decent reference that explains Lagrange's attempted approach to solve polynomials by radicals? It is not necessary, but it would be ideal, if it also compares this approach to Galois's ...
1
vote
0answers
79 views

Solving complex integrals? [closed]

I am interested in solving complex conformally invariant integrals, that arise e.g. in 2 dimensional CFTs, of the type $$\int dz_1d\bar z_1dz_2 d\bar z_2\,\prod_{i=1}^2 z_i^{p_{1,i}}\bar z_i^{p_{2,i}}...
1
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0answers
36 views

Equivalent definition of a universal measure zero set.

I am studying Richard Laver's "On the consistency of Borel's conjecture" and i came across this definition and i need a little bit of help with it's equivalent form. X has universal measure zero if ...
0
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0answers
21 views

Plücker relations generate Plücker ideal

I've been reading Maclagan and Sturmfels Introduction to Tropical Geometry, who define the Plücker relations and ideal on p. 61. They state that the Plücker relations generate the Plücker ideal and ...
1
vote
1answer
22 views

Sums and differences of factors

I am looking for a reference containing listing or table of the sums and differences of factors of positive integers; i.e. $\forall \space m_i\ge n_i,\space k=m_in_i$, list every $m_i\pm n_i$ for each ...
0
votes
0answers
6 views

How to use m-thly payable annuities to determine the answer to this problem?

A fund is to be accumulated by twenty semi-annual deposits. The first deposit is due January 1st, 1996. The fund provides 16 quarterly withdrawals of 1700 each. The first is due on October 1 2005. ...
4
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0answers
53 views
+50

Online estimation of drifting discrete probability

I recently come across (in a practical setting) to the following problem. Suppose I receive items from a finite set ,one at a time . At each moment one item is drawn independently from an unknown ...
-1
votes
0answers
15 views

Specific reference for Lebesgue spaces and Banach spaces

I searched on Google by "$L^p$ spaces and Banach spaces" and I found this link, which has exercises very interesting about theses spaces. I would like to know what is the book or the lecture notes ...
-1
votes
0answers
38 views

Thesaurus for algebraic terms [closed]

I got the impression that using different names for the same mathematical concept (synonyms) makes sense when the concept is used in different contexts (to make conceptual correlations clearer). ...
1
vote
0answers
27 views

How to imbed the irrational rotation algebra into AF algebra?

I'am reading Kenneth R.Davidson`s book C*-Algebras by Example. I feel confused by the construction of embedding irrational rotation algebra into associated AF algebra, Is there another book give a ...
2
votes
1answer
57 views

Introductory reference on rationality and irrationality of real numbers

I am looking for a good reference on the proof of the rationality or the irrationality of some real numbers. I think these kinds of problems show a nice variety of proofs and techniques, ranging ...
2
votes
0answers
37 views

Gentle introduction to Hilbert modular forms?

I've been recently wanting to begin learning about Hilbert modular forms, but I haven't found a good set of notes to start from. I know a little bit about modular forms, the modular curve, oldforms, ...
1
vote
1answer
26 views

Seeking for text on the theory of infinite sets

I am looking for some supplementary material on the theory of infinite sets, because I always seem to run into trouble with countability arguments in Analysis and Topology. Any recommendations? I ...
1
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0answers
61 views

Do there exist functions which are differentiable everywhere but analytic nowhere?

Once upon a time, when the earth was still young and innocent I studied one complex variable. In this course I learned that a function can be complex analytic, but that there are far fewer functions ...
0
votes
0answers
32 views

Null homologous loop and orientable surface

I am reading Algebraic Topology: A First Course written by Greenberg and Harper. On page 67 of this book it is stated that Let $\gamma$ be a loop in $X$ regarded as a map $f:S^1\to X$. For $\chi[\...
0
votes
0answers
18 views

Reference of material regarding both simplicial stuff and HoTT

I am currently reading both the HoTT book and "Stuff on quasicategories" by Rezk, and recently I am feeling that some thoughts of them looks similar. Could someone please point out something to let me ...
2
votes
0answers
31 views

consecutive prime gaps and explicit bounds

I am aware of the theorem that $p_{n+1} - p_n \leq n^{0.535}$ which is true for all sufficiently large numbers due to Baker, but if i want to make the implicit for all sufficiently large number to ...
11
votes
1answer
64 views

Mathematical logic material for blind student

A friend of mine (trained in philosophy and history) has recently become interested in mathematical logic. Because he is effectively blind, he has a hard time coping with formalism, as it does not ...
0
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0answers
32 views

Measure-theoretic boundary of a fat Cantor set

Let $C_\lambda\subset [0,1]$ be the fat Cantor set of parameter $\lambda$ (which is constructed as the usual Cantor set, removing at the $n$-th step the middle intervals of length $\lambda / 3^n$). ...
1
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0answers
35 views

Binary coding of Numbers with Minimum Hamming Distance

I am looking for binary encoding of a set of integers that satisfy the following two properties: The number of 1s in the larger numbers is larger. The hamming distance between the encoding of two ...
0
votes
0answers
30 views

Practice with Complex Polynomials

I'm looking for some exercises in manipulating complex polynomials and roots of unity. Problems like this: Alternate Way of Computing Complex Polynomial? Do people know of a good place to find some?
6
votes
1answer
139 views

Complexity of Random Delaunay Triangulation in 3D

My question: Is the number of cells in a three-dimensional Poisson-Delaunay triangulation with $n$ vertices $\mathcal O(n)$ with probability one? which is equivalent to the question Is the ...