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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22 views

Required sub-chapters or more materials needed to learn Statistical Inference other than my textbooks

My school is using new curriculum now and chapter "Statistical Inference" appears in my textbooks. Now I'm at second level of senior high school. I have two books, each of them has own sub-chapters. ...
2
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2answers
81 views

Algebra Text Recommendations [closed]

I am looking for any recommendations or suggestions for a good book covering an introduction to the following; Relation , sets and functions, divisibility theory and modular arithmetic , groups, ...
1
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1answer
63 views

The following is a necessary condition for a number to be prime, from its digit expansion. Has it been referred somewhere?

Concerning a numbers’ digits we know some necessary conditions on them for the number to be prime, besides the last digit having to be odd (except for prime 2). For example in decimal representation ...
1
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0answers
10 views

All riemannian isometries between open subsets of $\mathbb{R}^n$ are affine

I heard that there is a theorem of Liouville (Something like "Liouville's rigidity theorem") which states the following: Every Riemannian isometry between open subset of $\mathbb{R}^n$ is affine. ...
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2answers
495 views

Is there an opposite to the Squeeze theorem?

I'm familiar with the squeeze theorem (AKA Two Policemen and a Drunk---no matter how wobbly, the drunk will reach the same destination as the policemen). Is there is an opposite theorem that tugs or ...
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1answer
722 views

The most active fields of mathematics?

Which fields of mathematics are the most active at this time -- by number of papers published, grant money, people working in them or by any other measure? Any trends in this regard?
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0answers
64 views

Comments on Eilenberg and Steenrod's “Foundations of algebraic topology” and other similar books for recomendation

The biggest obstacle for me to learn geometry and topology is the haziness of textbooks. I took algebraic topology last semester and the textbook we used in class was Rotman's "An introduction to ...
0
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0answers
32 views

Can someone please suggest an easy book for complex analysis?

Can someone please suggest an easy book for complex analysis? By an easy book I mean to say that the book should give the proofs of the important theorems like Cauchy ,Morera etc in an elegant ...
3
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3answers
90 views

For a prime $p\ge 17$ is $\dfrac{p^2-1}{24}$ ever a prime?

It was indicated in the comments of this MO question that if $p\ge5$ is a prime then $24|p^2-1$. Indeed $p=6k\pm1$ and $p^2-1=36k^2\pm12k+1-1=12k(3k\pm1)$ and exactly one of $k$ and $3k\pm1$ is even. ...
2
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0answers
33 views

Is there a measure theoretic version of Stokes's theorem?

Is there a way to generalize Stokes's theorem on manifolds to general measure spaces? This idea came from trying to generalize the fundamental theorem of calculus to general function/infinite ...
3
votes
1answer
45 views

Could all iterates of $s(n)=2n+1$ be composite for some starting $n$?

Let $s(n)=2n+1$ and $\sigma(n)=\{n,s(n),s^2(n),s^3(n),\ldots\}$, where $s^3$ denotes functions composition, $s^3(n)=s(s(s(n)))$. For example $\sigma(11)=\{11,23,47,95,\ldots\}$. As another example ...
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2answers
103 views

Functional equation $f'(x)=cf(x+1)$ has a solution if and only if $c\leq 1/e$

In Contests in Higher Mathematics: Miklos Schweitzer Competitions, 1962-1991 by Gabor J Szekely, problem F.57 there is the study of $f~:~[0,\infty)\to (0,\infty)$ such that: $\exists c>0, \forall ...
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0answers
52 views

When can/can't one switch limits? [closed]

Is there some nice article where I can find isolated some concrete theorems and counterexamples on when can one switch the order of two integrals, differentiate under the integral sign, differentiate ...
1
vote
1answer
27 views

Applications of differential equations.

I'm trying to explain to a friend the power of differential equations in modelling math stuff. Does anyone have some really engaging/"juicy" examples? I looked at this question and found some good ...
2
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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 ...
4
votes
1answer
3k views

Probability of finding at least k consecutive heads in N coin tosses?

There are quite a few topics on this question already but I couldn't find a well-explained solution. Please point me towards some relevant literature or theory to analyze this problem. $K$ ...
5
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0answers
29 views

When a given family of curves are geodesics of some affine connection?

Let $M$ be a two-dimensional manifold and let $\mathcal C$ be a family of smooth paths on $M$. How to understand whether this family is actually a family of (possibly reparametrized) geodesics of some ...
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2answers
73 views

How do theorems arise?

I am reading complex analysis where I have come across Maximum Modulus Principle which states that if an analytic function $f$ assumes its maximum in a point of the domain $S$ then $f$ is constant ...
2
votes
1answer
21 views

Reference request: infinite-dimensional manifolds

The following books develop various aspects of the theory of infinite-dimensional manifolds: Lang, Fundamentals of Differential Geometry. Kriegl & Michor, The Convenient Setting of Global ...
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0answers
46 views

Mathematical structures with name reffering to a country

I am looking for a list of mathematical structures (not theorems) that refer to a country or nationality. I only know of Polish spaces and Polish groups. Does anyone have other examples? Note: many ...
2
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1answer
39 views

When is shear useful?

I'd never heard of the shear of a vector field until reading this article. Shear is the symmetric, tracefree part of the gradient of a vector field. If you were to decompose the gradient of a vector ...
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0answers
17 views

Derivatives and integrals of polynomials of two variables

Suppose I have a real-valued two dimensional polynomial $p(x,y)$ of order d. The partial derivatives inherit a nice structure, in particular knowing $\partial p/\partial x$ tells you $p$ up to the ...
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3answers
177 views

Do group rings appear outside of representation theory?

I am particularly concerned with finite groups. I have seen group rings used in the fundamentals of representation theory as the dual notion to representations. I haven't ever seen them anywhere ...
1
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0answers
26 views

Best book to understand representation theory.

I have tried to read representation and character theory from a few books but none of them was working for me, like Lieback and Serre. I want to understand representation and character to use them and ...
1
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0answers
9 views

Good resources for learning to recognize word problems in statistics?

I've got a number of books and resources for statistics theory, but I've always had problems with the approaches needed in answering questions, specifically for probability theory where counting ...
12
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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 ...
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1answer
214 views

Crazy Set Theory Analogies

I think the following analogies are too interesting to be ignored: Union = Least Common Multiple If $G_1,...,G_n$ denote a number of sets of points (either linear or in any number of dimensions), ...
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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0answers
23 views

Book Recommendation - Exercise book for Calculus / Analysis I

I am looking for exercise books that provides problems and exercises that together cover those topics: convergence of sequences, series etc. limit points etc. continuous functions derivatives, ...
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0answers
29 views

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 ...
2
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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} + ...
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 ...
3
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1answer
59 views

Differential Delay Equations

What are some good introductory references for differential delay equations? I am especially interested in coupled systems of differential delay equations.
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
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1answer
93 views

good books on measures and integration theory in infinite-dimensional spaces

I am looking for good books on measures and integration in infinite-dimensional spaces, covering generalizations of Wiener measure and their properties.
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 ...
7
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1answer
7k views

Best Book For Differential Equations?

I know this is a subjective question, but I need some opinions on a very good book for learning differential equations. Ideally it should have a variety of problems with worked solutions and be ...
12
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2answers
585 views

On prime factors of $n^2+1$

It is a well-known conjecture that there are infinitely many primes of the form $n^2+1$. However, there are weaker results that one can prove. For example, There are infinitely many positive ...
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4answers
3k views

Primes of the form $n^2+1$ - hard?

I met a student that is trying to prove for fun that there are infinitely many primes of the form $n^2+1$. I tried to tell him it's a hard problem, but I lack references. Is there a paper/book ...
2
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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
1
vote
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 ...
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6answers
4k views

Companions to Rudin?

I'm starting to read Baby Rudin (Principles of mathematical analysis) now and I wonder whether you know of any companions to it. Another supplementary book would do too. I tried Silvia's notes, but I ...
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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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vote
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 ...
0
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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 ...
2
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1answer
53 views

Natural action of $\operatorname{Aut}(G)$ on sets of subgroups of $G$ of same order is transitive.

I am looking for the classification of those finite groups whose automorphism group acts transitively on sets of subgroups of same order. Let $G$ be a finite group and $d$ be a divisor of the order ...
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8answers
914 views

Undergraduate Research Thesis

1. General background information ★ At my university [whose name I will omit] the following practices are customary: ● During their third year of study, students have approximately $4$ ...
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, ...
2
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2answers
321 views

How come mathematics is applicable to the real world?

Often in mathematics one constructs a set of some sort, let's name it $A$. We've constructed it in an abstract way, so, a priori, structural aspects of $A$ are yet unknown to us, until we prove them. ...