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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15 views

Is the plane homogeneous over the circle?

Let $\mathbf{C}$ denote a concrete category. I had the following idea: call an object $Y$ of $\mathbf{C}$ homogeneous over an object $X$ of $\mathbf{C}$ iff for all embeddings $f_0,f_1 : X \rightarrow ...
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1answer
19 views

Solvability of $a_{1}^{2} = a_{2}^{n} + a_{3}^{n} + a_{4}^{n}$ when $n \geq 5$ is prime?

Aware of a Darmon-Merel theorem that asserts that if $n \geq 5$ is prime then the equation $a_{1}^{2} = a_{2}^{n} + a_{3}^{n}$ has no solution in relatively prime integers $a_{1}, a_{2}, a_{3},$ I ...
0
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1answer
23 views

Seeking Recommendation on Pre-Calculus Textbooks! [on hold]

S.E. advisers, I wrote this email because I am seeking a recommendation on selecting the pre-calculus textbooks. I have been studying the real analysis and number theory, and I felt that I need to ...
1
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0answers
25 views

Making sense of the expression $\lim_{x \rightarrow k^+}f(x)$ using filters, and a reference request.

I don't know much filter convergence, so this is addressed to those who do. Let $f : \mathbb{R} \rightarrow \mathbb{R}$ denote a function. In elementary real analysis, we often write: $$\lim_{x ...
2
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1answer
23 views

Question about characteristic polynomial of the Frobenius endomorphism on elliptic curves.

I have another possibly trivial question about elliptic curves. A lot of papers I've seen state that the characteristic polynomial of the Frobenius endomorphism of an elliptic curve over a finite ...
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2answers
51 views

Examples of names for mathematical objects/results with proper nouns

If this question is duplicate, then I apologize. A recent conversation between a few graduate students led to the question of whether there are any mathematical objects or results with proper nouns ...
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0answers
12 views

Logic problems : references

I'm looking for problems from mathematical contests about logic (similar to the problem PMWC Problem T5).
29
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2answers
680 views

Meaning of the identity $\det(A+B)+\text{tr}(AB) = \det(A)+\det(B) + \text{tr}(A)\text{tr}(B)$ (in dimension $2$)

Throughout, $A$ and $B$ denote $n \times n$ matrices over $\mathbb{C}$. Everyone knows that the determinant is multiplicative, and the trace is additive (actually linear). \begin{align*} \det(AB) = ...
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2answers
21 views

Compute variance of logistic distribution

Consider a random variable $X$ with normalized logistic distribution( so that its pdf is $\frac{e^{-x}}{(1+e^{-x})^2}$). It is well known that its variance $V$ equals $\frac{\pi^2}{3}$ but I couldn't ...
1
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1answer
24 views

Reference for the theory of analytic functions

Question: Are there any good references for a theory on analytic functions? Lagrange attempted to develop analysis from this vantage point. Are there any texts that take a similar approach but, ...
1
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1answer
21 views

Given a non-ideal hyperbolic triangle and the Euclidean comparison triangle with equal side lengths, are the interiors of the two bi-Lipschitz?

Fix three finite real numbers $p,q,r > 0$. Up to isometry, there is a unique 2-simplex $\Delta$ in the Euclidean plane bounded by a geodesic triangle with these three reals $p,q,r$ as side-lengths. ...
2
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1answer
32 views

Books about braid theory

I'm looking for books that talk about braid theory, in the sense of braid groups mostly, and not too advanced, if possible. With material understandable for an undergraduate. Thanks for any ...
1
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1answer
109 views

Famous Problems the Experts Could not Solve [on hold]

After Yitang Zhang stunned the mathematics world by establishing the first finite bound on gaps between prime numbers, it got me thinking about the following question: $\underline{\text{Question}}:$ ...
2
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1answer
50 views

Themes in Mathematics [on hold]

My professors have alerted me to some themes throughout the subject. One that I've found useful is "abstraction and generalization": when studying rings, for instance, I initially saw nothing but a ...
1
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0answers
14 views

Prerequisites to reading *Convergence of Probability Measures* by Patrick Billingsley.

I want to improve myself in asymptotic theory regarding the realm of probability. I tried reading Convergence of Probability Measures by Patrick Billingsley but right off the bat the De ...
7
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2answers
173 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
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0answers
12 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
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0answers
44 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
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1answer
45 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
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0answers
24 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? Instead of planet in ...
0
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0answers
14 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 ...
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0answers
59 views
+50

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 ...
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0answers
36 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
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1answer
120 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
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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
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0answers
21 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
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1answer
12 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
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0answers
20 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
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0answers
38 views

Preparing to start bachelor in Mathematics [closed]

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
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0answers
11 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
53 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
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1answer
29 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
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0answers
115 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
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0answers
35 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
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0answers
69 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
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0answers
34 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 ...
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0answers
35 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
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0answers
56 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
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3answers
71 views

Books with insight [closed]

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 ...
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0answers
12 views

Lobatto quadrature for $3$ and $4$ knots [closed]

Determine Lobatto quadrature formulas with $3$ knots, and with $4$ knots. Where can I find it?
1
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1answer
50 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
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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 ...
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0answers
38 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 ...
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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
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1answer
107 views

Is there a classification of f.g. abelian-by-finite groups? [EDITED]

Let $G$ be a f.g. abelian-by-finite group, i.e. there exists a f.g. abelian group $N$ which is normal in $G$ and such that the quotient $G/N = Q$ is finite. The problem of classifying all such $G$, ...
0
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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 ...
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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 ...
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0answers
40 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
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0answers
58 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 ...
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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 ...