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.

learn more… | top users | synonyms (3)

4
votes
2answers
99 views

Do two closed subsets of $[0, 1]$ with measure $\frac{1}{2}$ intersect?

Let $A$ and $B$ be two closed subsets of $[0,1]$, each with a length of $1/2$. Is it always true that $A\cap B\neq \emptyset$? My intuition is yes, because: Either they intersect in their interior; ...
0
votes
0answers
6 views

Recommended gentle introductory reading for computational complexity

I recently read this paper by Scott Aaronson titled: 'Why Philosophers Should Care About Computational Complexity'. I came across it via a link in Hacker News As somebody with a general interest in ...
3
votes
0answers
25 views

How to fill my mathematical gaps?

To do the story short, I became interested in mathematics in a serious way like two years ago, I'm currently in graduate school, but the problem is that my mathematical background is not as good as ...
2
votes
1answer
34 views

Find a rigorous reference that prove the following integration by parts formula in higher dimension?

My professor in the real analysis class had state the following in class but forgot to put the reference of this formula in the power point slide. The formula for integration by parts can be ...
0
votes
1answer
13 views

Reference books or websites for N-body motion problems?

I am looking for references about multibody problems? I would prefer to find a completed example. Also, is it possible to solve these problems without a program i.e., by hand?
0
votes
0answers
13 views

Is there an english edition of Jorge Sotomayor's book on differential equations?

I am currently using "Lições de equações diferenciais ordinárias", in portuguese, by Jorge Sotomayor. However portuguese is not my best language by a long shot, and I struggle a little. Does anyone ...
0
votes
0answers
26 views

Overview of nonlinear analysis, ODE and PDE, dynamical systems, and mathematical physics and their relationships

(Apologies in advance for my naive question.) The fields of (i) nonlinear analysis, (ii) ODE and PDE, (iii) dynamical systems, and (iv) mathematical physics are very huge, fertile, and, in a ...
1
vote
0answers
31 views

Composition of polynomials over finite fields

Consider the set of polynomials of degree at most $n$ over a finite field $k_q$ with $q$ elements where $q$ is prime: $$ P_{n,q} = \left\{ x + c_2 x^2 + \cdots + c_n x^n:\ c_i \in k_q \right\}. $$ It ...
2
votes
1answer
114 views

Which mathematical topics should an applied math major know to be employable in industry? [on hold]

Question I'm a junior majoring in applied math computation at UCLA, and I was wondering what exactly constitutes a viable mathematics education? That is, what kinds of mathematical topics should an ...
1
vote
1answer
21 views

Proof of Riesz-Fisher Theorem

Can someone provide a proof or a source containing a proof of the version of the Riesz-Fisher Theorem provided here: ...
4
votes
0answers
20 views

Behavior of the giant component of an Erdos-Renyi graph near p = 1/n

what is the behavior of an Erdos-Renyi random graph with p = (1 + f(n))/n with $f(n)=o(1)$? If $f(n)=0$ then it has size about $n^{2/3}$, but what if the probability is perturbed slightly, say with ...
0
votes
1answer
8 views

Derivation of continued fraction for the incomplete beta function?

Where can I find a derivation for this continued fraction representation of the incomplete beta function: http://dlmf.nist.gov/8.17#v? I would like to have a reference to the papers where this ...
0
votes
0answers
18 views

Finding Holand-Bell formulas

Could anyone help me please to find out Holand-Bell formulas and their true author preferably (not Holand and Bell:) ) These formulas refer to finite element methods, I guess
1
vote
0answers
36 views

Preparing to start bachelor in Mathematics [on hold]

In a couple of months I'll go to university to start my bachelor in Mathematics. Since the level of math in my high school is really low, I want to prepare myself as good as possible. The courses ...
1
vote
0answers
9 views

Reference Request for Penalty Method for Optimal Control?

Is there a good book or review article to read about the methods like penalty method, method of duality and method of relaxation in problems of calculus of variations and their relations to optimal ...
3
votes
1answer
52 views

Algebraic independence via the Jacobian

I have seen being mentioned that algebraic independence of polynomials can be tested by the so called Jacobian Criterion (Apparently one takes the Jacobian matrix of these polynomials and inspects the ...
0
votes
1answer
26 views

Can anyone recommend good books on (transformation of) random variables and distributions?

I'm currently self-studying and I'm looking for books focusing on random variables and their transformations, which possibly contain examples like the one in this question. I'm also interested in ...
2
votes
0answers
97 views
+50

What are all types of elementary second order ordinary differential equation that can not be expressed in closed form?

Can we define all types of elementary second order ordinary differential equation that can not be expressed in closed form as opposed to the one that we can solve? In differential algebra, ...
4
votes
0answers
29 views

Prove that the Weierstrass-type function is nowhere differentiable

Given $0<\alpha\leq1$. Show that the function $$f(x)=\sum_{j=1}^\infty 2^{-j\alpha}\sin(2^jx)$$ is nowhere differentiable. I have solved the case $x=0$. Taking $t_l=2^{-l-1}\pi$, then ...
4
votes
0answers
64 views

Request for counter examples in group theory

I am looking for books, papers, or even webpages, that have collected many counter examples in group theory (which, I guess, are just examples in group theory). I am particularly interested in ...
0
votes
0answers
32 views

Reference to study moduli spaces

I would like to know about references where the problem of finding the infinitesimal deformations of a given geometric structure, and obtaining the corresponding (elliptic?) complex parametrizing the ...
-1
votes
0answers
34 views

Fixed point theorem in ordered space

Can someone provide a proof or a source containing a proof of the following theorem Theorem: Let $D$ be a subset of the cone $K$ of partially ordered space $E,$ $F:D\rightarrow E$ be nondecreasing. ...
3
votes
0answers
45 views

Looking for a rigorous treatment of improper multiple Riemann integrals

I'm studying undergraduate-level differential and integral calculus and have recently come across the topic of improper Riemann integrals. I'm familiar with the concept for single-variable functions, ...
0
votes
3answers
70 views

Books with insight [on hold]

In physics , Feynman's Lectures stand as masterful piece ,I think that's because the author tries not to hide anything from you, and is very careful as not to make any false presumptions on what you ...
0
votes
0answers
12 views

Lobatto quadrature for $3$ and $4$ knots [on hold]

Determine Lobatto quadrature formulas with $3$ knots, and with $4$ knots. Where can I find it?
1
vote
1answer
48 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
31 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 ...
-1
votes
0answers
37 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
votes
0answers
26 views

Exercise of these topics! [closed]

I am looking for more exercise to practice on these topic rings modular arithmetic isomorphism homomorphism
1
vote
1answer
76 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
41 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 ...
12
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
39 views

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

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
56 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
24 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
122 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
35 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
33 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
32 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
105 views

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

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
239 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
11 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
35 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
49 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
1answer
14 views

Online calculator for $ p $-adic valuations and absolute values.

Does anyone know a website where I can enter a prime base and a rational and then 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 ...
1
vote
0answers
9 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
101 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
16 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 ...