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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Reference request: history of analytic geometry

I am searching a book in the domain of the history of math, that describes the historical origins of analytic geometry, starting from Descartes (?), and that describes also its development (e.g. the ...
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1answer
51 views

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

As a natural extension of the question titled Solvability of $a_{1}^{2} = a_{2}^{n} + a_{3}^{n} + a_{4}^{n}$ when $n \geq 5$ is prime?, I wonder if the equation $$2a_{1}^{2} = a_{2}^{n} + a_{3}^{n} + ...
2
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0answers
23 views

Can someone tell me a book of linear algebra where polynomials are treated widely and closely?

Does anyone know a linear algebra textbook where polynomials are treated in the concept of an algebra and series, i know there is an appendix at Friedberg 4-th ed L.Algebra but there is no algebra ...
2
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2answers
35 views

Change of variables for heat equation

How to make a change of variables to turn the equation $$\frac{\partial{u}}{\partial{t}}=D\frac{\partial^2{u}}{\partial{x}^2}+cu$$ back to the heat equation? Where can I read about change of ...
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0answers
15 views

Toeplitz algebra approach to proving Bott periodicity in operator algebra K-theory

I am aware of the Toeplitz algebra approach to proving Bott periodicity in C*-algebra K-theory. I would like to ask whether this approach can be adapted to prove it for general Banach algebras, and ...
2
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1answer
35 views

Reference for Affine Spaces

I recently started reading Arnold's Mathematical Methods of Classical Mechanics (Second Edition). On pg. 4 Arnold writes: Affine $n$-dimensional space $A^n$ is distinguished from $\mathbb R^n$ in ...
2
votes
1answer
40 views

Proofs of the Riesz–Markov–Kakutani representation theorem

Let $X$ be a compact Hausdorff space, $C(X)$ the set of all real continuous functions on $X$, and $\mathcal{B}$ be the Baire $\sigma$-algebra of $X$, which is the $\sigma$-algebra generated by the ...
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0answers
5 views

How do i get to know if my question has been commented or answered cuz im new here [migrated]

Im new here and i dont know how things work here and dont have any knowledge about commenting or answering questions .Pls help
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1answer
81 views

Existence of the Brownian Motion using the Kolmogorov extension theorem

Kolmogorov extension theorem: Let $T$ denote some interval (thought of as "time"), and let $n \in \mathbb{N}.$ For each $k \in \mathbb{N}$ and finite sequence of times $t_{1}, \dots, t_{k} \in T$, ...
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0answers
6 views

References about action of groups on Variety

Let $X$ a set (or in my case an algebraic complex variety). I need references about the properties of Group acting on $X$. (for example i would like to find what property must have the action of the ...
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0answers
14 views

Matrix Properties Reference

A lot of proofs I come across (working on stability of numerical methods) apply some property of a particular type of matrix. This includes, for example, the fact that the $L_{2}$ norm of a normal ...
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2answers
57 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 ...
3
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1answer
111 views

Reference request: (categorical) commutative algebra text

I'd like a text that puts commutative algebra in a categorical framework. I'm wondering if anybody has any recommendations.
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1answer
47 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 ...
3
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1answer
36 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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0answers
14 views

Logic problems : references

I'm looking for problems from mathematical contests about logic (similar to the problem PMWC Problem T5).
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2answers
784 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
25 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 ...
2
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2answers
33 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
25 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. ...
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2answers
70 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 ...
2
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1answer
127 views

Famous Problems the Experts Could not Solve [closed]

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
56 views

Themes in Mathematics [closed]

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
17 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 ...
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2answers
211 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; ...
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0answers
15 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 ...
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1answer
184 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
51 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 ...
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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 ...
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0answers
17 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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157 views
+100

Overview of nonlinear analysis, differential equations (ODE and PDE), dynamical systems, and mathematical physics, and their relationships

The fields of (i) nonlinear analysis, (ii) ODE and PDE, (iii) dynamical systems, and (iv) mathematical physics are very huge, fertile, and, in a sense, unorganized (see Open problems in ...
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0answers
41 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 ...
3
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1answer
142 views

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

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 ...
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1answer
23 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: ...
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0answers
25 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 ...
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1answer
14 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 ...
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0answers
23 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
14 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
59 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
30 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
150 views

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
36 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
84 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 ...
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0answers
36 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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votes
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
60 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, ...
1
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1answer
51 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.
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1answer
35 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
39 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 ...
3
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0answers
44 views

When does the quotient metric is equivalent to the quotient topology?

Suppose that we have an equivalence relation $\sim$ in a topological metrizable space $(X,d).$ Then we can endow $X/\sim$ with the quotient topolgy. Also, under certains circunstances, there exists a ...