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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1
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1answer
39 views

Simple Set theory question and reference request

Let $A\cap (C\cup B)=A\cap B$ Can this be simplified to: $C\cup B = B$? How is this correct or wrong? Also please recommend a good Set theory resource! Thank You.
2
votes
1answer
25 views

Quotients of curves

Magma (link) has a lot of functionality for computing quotients of curves by group actions. I am interested to know how one does this in general and I am finding it oddly difficult to find literature ...
0
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0answers
26 views

Category of $\mathcal{L}$-structures

Given a purely relational language $\mathcal{L}$, the set of $\mathcal{L}$-structures forms a category under the definition of homomorphism found here. Call this category ...
-1
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0answers
26 views

Exercise of these topics! [on hold]

I am looking for more exercise to practice on these topic rings modular arithmetic isomorphism homomorphism
1
vote
1answer
40 views

Is there a classification of f.g. infinite abelian-by-finite groups?

Let $G$ be a f.g. infinite abelian-by-finite group, i.e. there exists a f.g. infinite abelian group $N$ which is normal in $G$ and such that the quotient $G/N = Q$ is finite. The problem of ...
0
votes
0answers
32 views

Some notes on $D_n, S_n$ and $A_n$

http://www.stat.uchicago.edu/~lekheng/courses/repth/sol2.pdf In these solutions it refers to See "Some notes on $D_n, S_n$ and $A_n$". Does anyone know where these notes can be found? They sound ...
9
votes
5answers
1k views

I want to learn mathematics to extend myself.

I am a middle school student that is highly fascinated by mathematics and its elegance. However, I have found that to appreciate a lot of mathematics a lot of knowledge is required. Currently, I can ...
-2
votes
0answers
37 views

How do I avoid asking duplicate questions on SE? [on hold]

During the last two and a half years since I became a member of the SE community, it has happened so many times that my questions have been marked as duplicate, especially during the first few months ...
2
votes
0answers
47 views

Good starting point for learning noncommutative geometry?

Currently, I am attempting to learn noncommutative geometry. My interests mostly lie on the boundaries of pure mathematics and theoretical physics, so I am not only interested in the mathematical ...
7
votes
0answers
19 views

Reference Request: Complete Proof of Braikenridge–Maclaurin Theorem

Where can I find a reference to a complete proof of the Braikenridge–Maclaurin theorem, which is stated as: If the three pairs of opposite sides of (an irregular) hexagon meet at three collinear ...
5
votes
3answers
99 views

Real Analysis book with pictures and ideas of proofs

I am taking real analysis course in my graduate class of Maths. My classes will start in 3 months. I have studied real analysis but not very rigorously. Whenever I see theorem I have no idea on how ...
0
votes
3answers
30 views

Looking for good intro book on differential equations

I am looking for a good book to study ordinary differential equations. My background is that I have successfully completed calculus 1 through 3. So this included derivatives and integrals, ...
4
votes
0answers
25 views

Axioms of Newtonian Mechanics

Axiomatically speaking, could Newton's laws be derived (as theorems) from the conservation of momentum and energy -- along with a few suitable definitions of things like an inertia frame and force? ...
4
votes
0answers
30 views

Morley’s Categoricity Theorem for uncountable languages.

Where can I find an accessible exposition of Shelah’s generalization of Morley’s theorem to uncountable languages? (Please, do not answer “Shelah’s Classification Theory”.)
0
votes
1answer
103 views

What is the general skill to solve third order ordinary differential equation? [on hold]

What is the general skill to solve third order ordinary differential equation, and just list the references? Those are with or without trigonometric, logarithms, exponential and with the typical x ...
3
votes
5answers
227 views

Technique for proving four points to be concyclic

While making my way through an exercise, I stalled on question 7: 7. Prove that the points $(9, 6)$, $(4, -4)$, $(1, -2)$, $(0, 0)$ are concyclic. The book does not provide any guidance on how ...
1
vote
0answers
29 views

Hilbert's double series theorem $\sum_{n,m}\frac{a_n b_m}{m+n}$ and its generalizations.

Let $l_p$ be the space of all complex sequences $x=\{x_n\}$ equipped with the finite norm $\|x\|_p=\left(\sum_n |x_n|^p\right)^{1/p}$. Hilbert's double series theorem states that $$\sum_{n,m}\frac{a_n ...
2
votes
0answers
10 views

Nice embedding of the permutohedron of order $n$ in ${\mathbb R}^{n-1}$

The permutohedron $P_n$ of order $n$ ($n\geqslant 2$) is the convex hull of the points $P_\pi=(\pi(1),\dots,\pi(n))$ where $\pi$ ranges over all permutations of $\{1,2,\dots,n\}$. Obviously, since ...
2
votes
1answer
32 views

Affine Transformations: Book to Study over the Summer

I've briefly heard of affine transformations in both linear algebra and calculus and I'd like to find a good book on the subject to study over the summer. So what's a good undergrad-level book on ...
3
votes
1answer
42 views

What is a good reference for rigorous Electromagnetism and Electrodynamics?

Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for ...
1
vote
0answers
8 views

calculator for p-adic valuation and absolute value

Does anyone know a website where I can enter a prime base and a rational and get the p-adic valuation and the p-adic absolute value? For sure I know how to do it by hand but I want to check my results ...
1
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0answers
8 views

reference for regime shifting models

I'm looking for a good introduction to regime shifting models. It would be nice to see things like simple example of regime shifting models, ways to detect a regime shift in data, fitting regime ...
4
votes
1answer
95 views

Where is Cauchy's wrong proof?

Allegedly, Cauchy mistakingly "proved" that pointwise convergence of continuous functions is continuous. I saw this somewhere in a book, and it is also in wikipedia: Uniform convergence. In his ...
0
votes
1answer
32 views

Which discrete mathematics book do you think is better between Epp's and Rosen's for a clueless self-learner?

I am a programmer, and I want to become a machine learning researcher and a good software engineer. I dabbled with calculus, linear algebra, and real analysis for a few months when I was enrolled in a ...
2
votes
1answer
15 views

About fractional Sobolev space

I'm reading a paper used Sobolev space $H^s(\Omega)$ , I only know the definition of these space when $\Omega=R^n$ which used Fourier Transform, what if $\Omega$ is a bounded open set? And I also ...
0
votes
0answers
31 views

What are some genuine ways to define the derivative of a fractal?

Seeing the success of applying measure theory to generalize integration to fractals, I wonder whether or not there is a method to generalize the derivative to a fractal. Most courses start off fractal ...
6
votes
2answers
115 views

If $a=b$ then $a+c=b+c$? [duplicate]

A friend of mine just asked me how to prove that if $a=b$ then $a+c=b+c$, where $a,b$ and $c$ are real numbers, I'm not sure what I should answer. I have a book called introduction to logic and to the ...
4
votes
3answers
35 views

Largest subset with no arithmetic progression

I am trying to find some weak bounds on the largest subset of a set, such that the subset has the property that it contains no three elements in arithmetic progression. The elements of the original ...
3
votes
0answers
36 views

Can someone help me find a Mathematical documentary that aired on British television within the past 10 years about Leibniz?

I have been searching for a documentary that aired on British television between around 2006 and 2012 which was centred around the German Mathematician, Gottfried Leibniz. All that I can remember ...
5
votes
0answers
35 views
+50

What's Griffiths' ampleness in modern language?

When reading Griffiths' paper "Hermitian differential geometry, Chern classes and positive vector bundles", I found his definition of ampleness: Let $X$ be a compact complex manifold, $E\to X$ a ...
0
votes
0answers
13 views

Ordinary Differential Equations self-study reference request

I know there are a lot of reference requests for differential equations textbooks but none seem to be what I need. I'm looking for a book I can use for self study that isn't overly complicated and ...
0
votes
0answers
15 views

Bibliographic reference for $\sum_{n\in\mathbb Z}(z-n)^{-k}$

I am currently writing a paper which requires the closed-form expression of \begin{equation} S_k(z)=\sum_{n\in\mathbb Z}\left(z-n\right)^{-k} \end{equation} I believe $S_2$ is extremely classical ...
1
vote
2answers
39 views

The class of all functions between classes (NBG)

Is it possible in NBG (von Neumann-Bernays-Gödel set theory) to construct the class of all functions $X \to Y$ between two (proper) classes $X,Y$? I guess that this does not work. In the special case ...
11
votes
7answers
1k views

Is an empty parenthesis a valid mathematical expression? [on hold]

Is using an empty parenthesis valid? For example, $15+()=15$. What is the meaning if it is valid? I need an academic reference to validate this.
11
votes
0answers
40 views

Analogue of Dirichlet $L$-function for $\mathbb{F}_q[T]$.

We consider an analogue of the Dirichlet $L$-function in $\mathbb{F}_q[T]$. Let $g \in \mathbb{F}_q[T]$, $g \neq 0$, let $\chi: (\mathbb{F}_q[T]/(g))^\times \to \mathbb{C}^\times$ be a homomorphism, ...
0
votes
0answers
28 views

thorough proof of Mayer-Vietoris implies Excision

Where could I find a very complete proof of how the Mayer-Vietoris sequence implies the Excision theorem? I've read a few proofs, but they always leave out the details! Thank you!
1
vote
1answer
31 views

Intersection of Eigenvectors and Multivariable Calculus

This isn't really a problem but more of a reference/example question: do eigenvalues and eigenvectors ever show up in multivariable calculus? The two seem very unrelated to me. Specific examples would ...
4
votes
0answers
14 views

Where was it originally proved that $K$-finite automorphic forms are of uniform moderate growth?

I'm providing an overview of some classical results about automorphic forms in one section of a paper I'm working on, and I've realized I don't have a good reference for the following. Let $k$ denote ...
1
vote
1answer
27 views

Extending a diffeomorphism outside a compact set

I believe that the following statement is true: Let $U,V\subset \mathbb{R}^n$ be open sets, $K\subset U$ compact, and $\gamma:U\to V$ a diffeomorphism. Then there is a diffeomorphism ...
0
votes
1answer
13 views

What is a good source for learning Control Theory

I need to start learning and understanding Control Theory for my research. Does anyone know good resources for doing this.
-1
votes
1answer
148 views

Who are the big names in Mathematics nowadays? [on hold]

The questions I pose are: Who are the big names in mathematics now? What branch do they study, what big problems are they looking at? I know of Wiles and Perelman (and I don't even know if those are ...
0
votes
4answers
61 views

How to come up with proofs of these results? Or, are these results true in the first place?

Let $x_n$ and $y_n$ be integer sequences determined by $$x_n + y_n \sqrt{2} = (1+\sqrt{2})^n \ \ \ \mbox{ for } \ n= 1, 2, 3, \ldots. $$ Then how to show that (a) $x_{n+1} = y_{n+1} + y_n$, $\ \ \ ...
1
vote
1answer
33 views

Positive and negative logical connectives

By inspecting the rules of inference for (intuitionistic) predicate calculus (or, alternatively, thinking about double negation translation), one sees that there is a certain dichotomy between two ...
-1
votes
0answers
11 views

gradient descent to solve binary non linear optimization problem [closed]

I am trying to code a solution for an optimization problem that has binary matrix which has to be optimized,since the problem is not convex and has binary variables,i am finding it hard to solve ...
4
votes
0answers
23 views

Mathematic reasoning in nonEnglish/non Western languages [migrated]

I am teaching in an Eastern Asian environment (precisely, teaching Mathematics using English in Korea, with Asian students) and I figured out that my reasoning is a lot based on my language ...
3
votes
0answers
33 views

Generalizing convexity of sets

Let $X$ be a subset of some Euclidean space. We say that $X$ is convex if for any two points $p$, $q$ in $X$, the line segment joining $p$ and $q$ is also in $X$. But what if we loosen this definition ...
2
votes
0answers
25 views

Lifting of Commuting Maps of Vector Bundles

Assume that we have a vector bundle $\mathcal{F}$ over $\mathbb{P}^d(\mathbb{C})$ that is generated by global sections. Let $\pi \colon \mathcal{O}^n \to \mathcal{F}$ be the associated map that is ...
1
vote
2answers
28 views

book for numerical methods for solving pde

I need to find some masters-level exercises about numerical methods for solving pde. Are there any good references?
2
votes
1answer
24 views

Integrating over an embedded manifold: Jacobian factor?

Let's say I want to integrate a function $$ f(x,y),\quad x\in\Gamma_1,y\in\Gamma_2 $$ where $\Gamma_1,\Gamma_2$ are both embedded manifolds in $\Bbb{R}^3$. The dimension of $\Gamma_1$ is 1 (a ...
0
votes
0answers
14 views

Quick question: Pull back under double cover of tangent space on the projective plane is stable?

Let $f:\mathbb{P}^1\times\mathbb{P}^1\rightarrow\mathbb{P}^2$ be the double cover branched along some conic $C\subset \mathbb{P}^2$. Is $f^*T_{\mathbb{P}^2}(-1)$ $\mu$-stable/semistable? Is there any ...