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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0
votes
1answer
30 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
votes
1answer
44 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
85 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
vote
0answers
27 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
votes
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
vote
0answers
16 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 ...
0
votes
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
votes
0answers
15 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
vote
1answer
55 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 ...
4
votes
1answer
54 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 ...
0
votes
0answers
35 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 ...
9
votes
5answers
306 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 ...
1
vote
0answers
27 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 $g \in \mathbb{C}[x_{1}, \dots, x_{n}]$. ...
0
votes
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} = ...
1
vote
0answers
24 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 ...
2
votes
0answers
15 views

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 ...
1
vote
0answers
31 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 ...
1
vote
0answers
34 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
votes
1answer
35 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 ...
2
votes
0answers
52 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 ...
-2
votes
0answers
25 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
votes
1answer
40 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
votes
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
vote
1answer
30 views

Banach valued sequence spaces $l^p(X)$

Let $X$ be a Banach space and $l^p(X)$ 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 $l^p$. ...
1
vote
0answers
43 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
votes
1answer
163 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 ...
12
votes
2answers
226 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: $$ ...
0
votes
0answers
103 views

“Deep” maths books in certain subjects [on hold]

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
votes
0answers
42 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 ...
1
vote
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 ...
0
votes
2answers
117 views

Where can I find SOLUTIONS to real analysis problems? [on hold]

I'm specifically interested in problem sets in Real Analysis that have solutions. I have a few books on it, but I'd like to compare my solutions with some given answers in a lot of cases to ensure ...
2
votes
1answer
82 views

Where to learn integration techniques?

Is there any book or any website that let you learn integration techniques? I'm not talking about the standard ones like integration by Parts Substitution (trigonometric) Partial fractions Order ...
0
votes
0answers
42 views
+50

Partial Differential equations and applications- Reference request

I will be taking up a PDEs course next semester and would like to find some good references. The topics covered in the syllabus is given below. Partial differential equations: Conservation laws, ...
2
votes
1answer
33 views

Third Order PDE written as a System of (Linear) First Order PDEs

I need to rewrite the PDE $$f_{y}+ff_{x}+f_{xxx}=0,$$ where $f=f(x,y)$ as a system of first order quasi-linear PDEs. I have no idea how to tackle this problem. Any form of help will be appreciated. ...
0
votes
0answers
10 views

the multidimensional Hilbert transforms or partial Hilbert transforms

The one-dimensional Hilbert transform can be defined by the convolution $Hf:=f*\frac{1}{\pi x}$, or can be given by Fourier multiplier $(Hf)\hat{\,}(\xi)=-i\mathrm{sgn}(\xi)\hat{f}(\xi)$. ...
4
votes
2answers
70 views

Theoretical computer science text for mathematician

I am a high school student, I know some basic programming in java,python and visual basic. I love combinatorics and I have encountered various cases in which I have found some problems are really ...
1
vote
0answers
45 views

Why is it called a primitive root?

I am looking for a paper or reference that explains why primitive roots are called primitive roots. I know what they are but was wondering if there was a reason?
0
votes
0answers
34 views

what are the interesting geometric properties of a regular n-gon? [closed]

I want to know about the interesting geometric properties of a regular n-gon. I know there are lot of results on this subject. I am interest about simple geometric properties which are easy to ...
3
votes
1answer
40 views

Start studying mathematical biology from basics

I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic. I've just got my bachelor's degree in biology (ecology) but scince ...
0
votes
0answers
24 views

Most suitable book after Bergmann Logic Book

I'd like to know what the best book would be to pick up after this one would be. Essentially, it covers basic logical concepts (validity, soundness, consistency) and goes on to sentential and ...
1
vote
1answer
33 views

Where can I find a good set of notes discussing main theorems/ideas surrounding non-orientable surfaces?

I'm currently looking at non-orientable surfaces, but know very little about them. Is there are good set of notes that will teach me the classical results surrounding non-orientable surfaces?
2
votes
0answers
53 views

Reference for simplicity of the principal eigenvalue of the Laplacian

i'm currently searching for a proper reference or proof to see that the first eigenvalue $\lambda \in \mathbb{R}$ of \begin{equation*} - \Delta u = \lambda u \text{ in } \Omega, \\ u \in ...
1
vote
2answers
66 views

Universal quantifiers that are interpreted “almost-everywhere”

Often sentences that are false, are nonetheless "true almost everywhere." Example 0. The integers do not satisfy the cancellation law: $$\forall a\forall xy(ax = ay \rightarrow x=y)$$ This is ...
1
vote
0answers
41 views

Fibers of toric morpisms

Let $f: X(\Delta_1) \to X(\Delta_2)$ be a toric morphism of toric varieties, and let $\sigma \subset \Delta_2$ be a cone, then for any point in the corresponding orbit $x \in O(\sigma)$ the fiber ...
0
votes
0answers
34 views

Proof of the sum of an alternating series similar to the alternating harmonic series [closed]

Hi I know I saw the answer to the following question somewhere online, I think it was stackexchange but I'm not absolutely certain..repeated searching on this website and on google have been ...
5
votes
0answers
28 views

Name for Number of Ancestors/Descendants of Vertex in Directed Acyclic Graph

Let $G = (V, E)$ be a directed acyclic graph. For each vertex $v \in V$, define the ancestors of $v$ to be the set of vertices $u \in V$ such that there exists a directed path from $u$ to $v$. ...
1
vote
0answers
76 views

A Question Regarding Consistent Fragments of Naive (Ideal) Set Theory

It is well known that Naive (to some, otherwise known as Ideal) set theory, that is, the set theory generated by the axioms: (EXT) (x)(x $\in$ A iff x $\in$ B) iff A=B (COMP) ($\exists$y)(x)(x ...
3
votes
0answers
29 views

Parameter-dependent integral: Is the following statement true?

Is the following statement true? If so, could anyone provide a reference? Suppose $f(x, \alpha)$ is continuous on $(a, b) \times \{\alpha_0\}$. If there exists $g(x)$ which is continuous on $(a, b)$, ...
5
votes
0answers
40 views

Representation theorem for Heyting algebras?

A fundamental theorem by Stone asserts that any Boolean algebra is isomorphic to a subalgebra of the archetypical Boolean algebras, that is the power sets of a set $X$ (equipped with intersection, ...
1
vote
0answers
40 views

Homotopy groups of unitary groups

in this paper I found some explicit generators of homotopy groups of unitary groups, for example $\pi_3[SU_2]$: $\begin{bmatrix}z_1\\z_2\end{bmatrix}$$\rightarrow $$\begin{bmatrix}z_1 ...