This tag is for questions where the poster seeks 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
8 views

Introduction to Toeplitz operators

I just finished my undergraduate education in mathematics, and i'm starting a graduate program, and i get interest for learning to work with Toeplitz operators, but i have no background with ...
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0answers
65 views

Crazy Set Theory Analogies

I think the following analogies are too interesting to be ignored: Union = Least Common Multiple If $G_1,...,G_n$ denote a number of sets of points (either linear or in any number of dimensions), ...
0
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0answers
5 views

What are the classes in A.N. Maslov hierarchy of indexed languages corresponding to Chomsky Hierachy?

As we know,that classes in A.N. Maslov hierarchy of indexed languages of level 2 is in sensitive languages of Chomsky hierarchy. What are the classes in A.N. Maslov hierarchy of indexed languages ...
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0answers
13 views

Where to learn about the Chow scheme and the Hilbert-Chow morphism?

I would like to learn something about the Chow scheme of cycles on an algebraic variety. I am not after an abstract treatment of the moduli problem in full generality, actually I would be happy with a ...
1
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1answer
21 views

Lie ideals of $gl_n(K)$

I am looking for some reference where I can find a detailed study of the Lie ideals of the general linear Lie algebra $gl_n(K)$ with the bracket $[A,B]=AB-BA$, where $K$ is a field (if there are ...
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0answers
9 views

Proof of “Normal approximation to the log-normal distribution” [on hold]

I saw the post about the normal approximation to lognormal (Normal approximation to the log-normal distribution). The proof is shown as well. Yet as I'm looking for the proof in a journal article form ...
3
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1answer
69 views

Has anyone succeeded in formalizing Leibniz notation in such a way that the chain rule and inversion rule “work”?

The notation $\frac{\partial}{\partial x}$ is ubiquitous and totally useful, but also kind of weird. It seems to be doing the following: Bind $x$ Compute the derivative Evaluate at $x$ To ...
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0answers
28 views

Formal Trigonometric Refrence

I'm Using a textbook for mathematic which is produced to learn for normal students. Here I'm giving the link of chapter of trigonometric functions of my textbook : ...
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0answers
12 views

Reference request on numeric semigroups

I watched some talks about numeric semigroups, and thei relation whti algebraic geometry (such as Weierstrass semigroup of a curve), and I'm interested in take a deeper look in this topic, can anyone ...
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0answers
26 views

Codifying ways to think and write about imprecise ideas?

This question will not be about affine spaces; rather those are mentioned here as one of many examples. A vector space has an underlying set and a field of scalars and an operation of linear ...
3
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2answers
63 views

Book for Undergrad Differential Geometry

I am soon going to start learning differential geometry on my own (I'm trying to learn the math behind General Relativity before I take it next year). I got the sense that a good, standard 1st book ...
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0answers
40 views

Banach Fixed Point Theorem. Measurable version.

The Banach fixed point theorem has the following statement THEOREM ( Banach contraction principle). Let $(Y,d)$ be a complete metric space and $F:Y\to Y$ be contractive . Then $F$ has a uniqe ...
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0answers
27 views

Is there a translation to English of this calculus book of Hermite?

I would like to read "Cours de M. Hermite" (1891) ( https://archive.org/details/coursdemhermite00andogoog ) in English. It was translated to Russian as "Шарль Эрмит -- Курс анализа" (1936) but I did ...
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0answers
46 views

Complex structures on Riemann surfaces

Let $M$ be a Riemann surface and $[\alpha] \in H^{0,1}(M; T^{1,0} M) \simeq H^0(M;K^2)$. Considering $\alpha$ as a map $T^{0,1} M \to T^{1,0} M$, the bundle $$ \{v + \alpha(v) \mid v \in T^{0,1} M\} ...
1
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1answer
26 views

Ergodic properties of orthogonal group O(n)

The orthogonal group O(n) is the group of distance-preserving transformations of a Euclidean space of dimension n that preserve a fixed point, where the group operation is given by composing ...
1
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1answer
38 views

Learning Math with Mathematica

Are there any books/online courses that use Mathematica (or other software) to teach mathematical concepts? I find learning more advanced concepts a lot easier when I am exploring the concepts ...
5
votes
1answer
26 views

Asymptotics bound on Jacobi polynomials in the complex plane and for large $n$

Dear mathematicians and theoretical physicists, I am a theoretical physicist and I am bothering to you since I need to know some asymptotic and analytical properties of Jacobi polynomials ...
1
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0answers
34 views

Existence of periodic orthogonal basis in $L^2([0,1])$ which is not trigonometric?

Let $$ \psi(x) := \sin(\pi x). $$ It is well-known that system $\{ \psi(n x) \}_{n \in \mathbb{N}}$ forms an orthogonal basis in $L^2([0,1])$. My question is the following: Are there other examples ...
5
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1answer
63 views

If $f: A\to\mathbb R$ one-to-one but not monotone, there exist $x,y,z\in A$ with $x<y<z$ such that $f(x) < f(y)$ and $f(y) > f(z)$ (wlog)

The following result is part of the folklore, but I'd like to have a standard reference for something that I am writing: If $A \subseteq \mathbb R$ and $f: A \to \mathbb R$ is one-to-one but not ...
2
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0answers
37 views

Hesse's Pencil: Base Points and Resolution of Singularities through Blow-ups

A snippet of the definition given on wikipedia (full link: here) The Hesse pencil is a pencil (one-dimensional family) of cubic plane elliptic curves in the complex projective plane, defined by the ...
0
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1answer
34 views

Pair of functions $F(x)$ (transcendental),$A(x)$ (algebraic) with expanded series of positive integer coefficient linked by derivative

$$F(x)=\sum_0^{\infty}b_k x^k,b_k\in \mathcal{N} \bigcup 0,\exists M \space b_k \leq M^k$$. $$A(x)=\sum_0^{\infty}a_k x^k,a_k\in \mathcal{N} \bigcup 0,\exists M \space a_k \leq L^k$$ where $F(x)$ is ...
3
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1answer
47 views

Re professional mathematicians working on several problems at once. Source needed.

Recently I read a quote from a working mathematician where he pointed out that professionals have to get used to carrying around several unsolved problems at once. Can anyone help me with the source ...
6
votes
1answer
110 views

How do people on MSE find closed-form expressions for integrals, infinite products, etc?

I always wanted to ask this question since when I joined MSE, but because I was afraid of asking too many soft questions I never asked it. I've seen some pretty complicated integrals and infinite ...
1
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0answers
33 views

Where is the most clear and concise exposition of the spectral theorem for self-adjoint operators on Hilbert space?

This question is certainly subjective, which may warrant votes to close. I'm simply looking to find the "best" written exposition of the spectral theorem for possibly unbounded self-adjoint operators ...
2
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0answers
46 views

Any other operators that may convert algebraic function into transcendental ones

As we know, the integral may convert or map a rational function or algebraic function into a transcendental one. Are there any other operators that may convert a rational function or algebraic ...
1
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0answers
20 views

Complex structures on punctured disks.

Let $X$ be a smooth surface diffeomorphic to the punctured unit disk $\{(x,y)\in \mathbb{R}^2 \ | \ 0<x^2+y^2<1\}$ in the plane. It admits a lot of non equivalent complex structures, for example ...
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0answers
33 views

Reference book for Hilbert space

I want to have an intuitive sense of Hilbert space, especially the geometric sense of the inner product, can anyone give me some reference book for that? Since it may be a little vague, I will give an ...
0
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0answers
17 views

Is logistic regression unbiased and efficient?

Seeing how in social sciences the Carmer-Rao lower bound is used as variances of the found parameters it would seem that the parameters are both unbiased and efficient, but what is the proof for this? ...
1
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1answer
64 views

How do you self-study Functional Analysis?

It would be very handy to know about function spaces, distributions and Fourier stuff. It looks like Rudin's Functional Analysis covers these things, but I do not yet have the foundation for it. (see ...
5
votes
1answer
62 views

Basic Notions of Categorification

In this post John Baez defines a categorification of a set $S$ as a map $$ p:\DeclareMathOperator{Decat}{Decat}\Decat(\mathscr C)\to S $$ where $\Decat(\mathscr C)$ is the set of isomorphism classes ...
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0answers
42 views

Self-Contained Books / Series / Lectures for Comprehensive Introduction to College-Level Math for Someone with VERY Poor Math Foundation?

I've long been interested in various math related subjects (technology, philosophy, sciences, computer science, languages, etc.) without really invested time to actually any learn any of them. I ...
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5answers
320 views

Exercises in category theory for a non-working mathematican (undergrad)

I'm trying to learn category theory pretty much on my own (with some help from a professor). My main information source is the good old Categories for the working mathematician by Mac Lane. I find the ...
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0answers
28 views

Quotients of varieties by polynomial relations

Let $V$ be an affine variety in $\mathbb{C}^{n}$, i.e. $V$ is the vanishing set of an ideal $I \subset \mathbb{C}[x_{1}, \dots, x_{n}]$. Furthermore let $g \in \mathbb{C}[x_{1}, \dots, x_{n}]$. ...
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1answer
40 views

Factorization of rational powers of rational numbers

If I am not wrong, rational powers of rational numbers can be factorized in an unique way as product of rational powers of different prime numbers: $10^{1/2} = 2^{1/2} \cdot 5^{1/2}$ $(8/9)^{1/6} = ...
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0answers
25 views

Di Perna-Lions theory for transport equation

Does someone know if some notes on the topic mentioned in the title are available online? I'm reading the paper "Ordinary differential equations, transport theory and Sobolev spaces" by Di Perna and ...
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0answers
24 views
+50

Does the Gagliardo–Nirenberg interpolation inequality hold on compact closed manifolds?

The Gagliardo–Nirenberg interpolation inequality on a bounded domain is of the form $$|D^j u|_{L^p} \leq C_1|D^m u|_{L^r}^\alpha|u|_{L^q}^{1-\alpha} + C_2|u|_{L^s}$$ where are there restrictions on ...
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0answers
32 views

Websites for math tests/quizzes

Next semester I'm taking calculus at college and I was looking for websites that have quizzes/test for things like trigonometry, trig formulas, pre-calculus, calculus readiness, etc. so I can get ...
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0answers
36 views

Finding a lie group structure on $\mathbb R^n\setminus\{0\}$

I want to find all maps $g: \mathbb R^n\setminus \{0\} \rightarrow GL_n(\mathbb R)$ which satisfy the properties $g$ is differentiable and injective $g(g(a)b) = g(a)g(b)$ for all $a,b\in\mathbb ...
2
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1answer
36 views

Origin of Slater's condition

I've been looking all over the internet to answer this question: Slater's condition is a commonly used to certify that strong duality holds in a convex optimization problem. Although used in many ...
3
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0answers
55 views

Expository Papers on Extenders

Extenders are discussed in many set theory text books. Here I am looking for some expository "papers" which are focused on this subject and its connection with forcing and large cardinals. More ...
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0answers
28 views

Maximum number of compressed RLE strings under any given length

Given a random string of length L (for instance, "01100010000101" of length "14"), and knowing that this string is only numerical, how many other strings under the form Y one can achieve by ...
2
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1answer
42 views

Is there something that studies equivalent forms of writing and expression?

Supose we have: $x^2+x$, one could write it as $x(x+1)$ which would be equivalent to the first expression. I guess there might be a finite number of ways of writing expressions such that they are ...
3
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0answers
63 views

Problem solving strategy?

This question has always bothered me, and I've never had a maths coach to guide me along the way and show me what to do next. Nevertheless, I did make top 50 nationally in my national mathematics ...
1
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1answer
38 views

Banach valued sequence spaces $\ell^p(X)$

Let $X$ be a Banach space and $\ell^p(X)$ denote the space of sequences $x_i\in X$ for which the norm $\big(\sum_{i=1}^\infty\|x_i\|^p\big)^\frac1p$ is finite, when $X=\mathbb{R}$ we get the usual ...
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0answers
45 views

Insightful books on differential equations?

What are some recommendations for insightful books on differential equations and difference equations? These books don't need to be in the format of a textbook, and don't need to provide the same ...
3
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1answer
164 views

What is this myth/legend and origin of related ideas?

There is a story I recently heard but the story teller (who read about it someone on the Internet) have forgotten the majority of the story, so there is little I can work on: my search attempts went ...
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2answers
230 views

Is it normal that a pure math student doesn't know vector analysis?

Today I was watching a series of online video lectures about electromagnetism. At some point of the lecture, the professor used this vector calculus identity: $$ ...
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0answers
109 views

“Deep” maths books in certain subjects [closed]

I would like a suggestion on the 'deepest' books in Calculus and analysis (something along the lines of Rudin's) Linear algebra Abstract algebra Geometry (and topology); (even something along the ...
0
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0answers
45 views

problems in finding mathematical reviews journal (MR XXX)

for example, this one: http://www.ams.org/mathscinet-getitem?mr=0215729 the journal has the number like "MR215729 (35 #6564)" I wanna know what does the 35 #6564 means... because for some ...
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0answers
18 views

Existence and Uniqueness of Solutions of PDEs

I have been looking into the Cauchy-Kovalevskaya Theorem where one can "establish the local existence of analytic solutions to a system of PDEs". I wanted to see an application (for example, see ...