This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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8 views

Introduction to Reidemeister--Schreier Method

I am learning Reidemeister--Schreier method, a method determining explicitly presentations for subgroups of a given group. Can anyone recommend some introductory material, preferably those with ...
3
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0answers
25 views

What resources (books, videos, etc) to help develop math thinking skills?

I am a applied mathematics major and have taken basic undergraduate coursework up to multi-variable calculus, ordinary differential equations, and elementary linear algebra. I am currently taking ...
0
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0answers
25 views

What are some good question and answer websites for math?

I already know about Math Stack Exchange. I would like to know where else on the web one can ask and answer questions about mathematics at the university level. Websites need not be in English, but ...
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0answers
46 views

John Wallis put down by authors [on hold]

"In what was perhaps the one real stroke of genius in Wallis 's long mathematical eareer" they said. See? Ungrateful. They should praise, not patronize.
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0answers
15 views

Sample datasets with known outliers for IQR, Q-test and Z-test [on hold]

Is anyone aware of a source for sample data sets with known outliers? I've been looking around for years but haven't come up with a solution, short of creating my own limited database. Sets with ...
5
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0answers
51 views

Legitimate papers refuting the significance of the golden ratio in art?

I'm not sure this is the right place to ask about this, but is there any legitimate peer-reviewed paper refuting the significance of the golden ratio in art? I can find numerous websites and blogs ...
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6answers
2k views

Very *mathematical* general physics book

I am searching for a book to study physics. So far, I've been suggested Resnick, Halliday, Krane, Physics, but it doesn't seem to be very suited for a math major. Can you suggest some more ...
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votes
1answer
16 views

Reference for proof of Kaloujnine-Krasner

The theorem of Kaloujnine-Krasner says Given two groups $D$ and $Q$, the wreath product $D \wr Q$ contains an isomorphic copy of every extension of $D$ by $Q$. I am looking for an English ...
3
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1answer
38 views

Show that Polynomials Are Complete on the Real Line

Consider the Hilbert Space of weighted-square-integrable functions f(x): $$ \begin{equation} \int_{-\infty}^{\infty}\frac{f(x)^2}{e^{x}+e^{-x}}dx<\infty. \end{equation} $$ Note this integral is ...
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1answer
66 views

Thinking and writing about mathematical structures in a way that is rigorous and precise.

Working inside a particular mathematical structure, I have no trouble giving rigorous definitions, nor deciding whether or not a definition is rigorous. For example, working inside $\mathbb{Z}$: ...
2
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2answers
53 views

Exercise books in functional analysis

I'm studying functional analysis and I was wondering if there are some exercise books (that is, books with solved problems and exercises) The books I'm searching for should be: full of hard, ...
0
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0answers
44 views

Exercise books in abstract algebra and number theory

I'm studying Herstein's Topics in algebra and Hardy&Wright's An introduction to the theory of numbers, and I was wondering if there are some exercise books (that is, books with solved problems and ...
0
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1answer
28 views

Exercise books in linear algebra and geometry

I'm studying Brannan's Geometry and Lang's Introduction to Linear Algebra and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as ...
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3answers
162 views

Exercise books in analysis

I'm studying Rudin's Principles of mathematical analysis and I was wondering if there are some exercise books (that is, books with solved problems and exercises) that I can use as a companion to ...
1
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0answers
28 views

Finite characteristic splitting fields of low degree polynomials

Let $f(x) \in \mathbb{Z}[x]$ be a polynomial. Let $f_p(x) \in \mathbb{Z}_p[x]$ denote the polynomial $f \bmod{p}$ (where $p$ is a prime). We say $p$ is good for $f$ if $f_p(x)$ splits (into linear ...
2
votes
1answer
39 views

Books that use fancy probabilistic/combinatorial/graph theoretical/physical/geometrical methods to solve problems from other branches of mathematics

I am searching for some books that describe useful interesting probabilistic/combinatorial/graph theoretical/physical/geometrical methods to solve problems for other branches of mathematics, for ...
2
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0answers
27 views

Textbook for Partial Differential Equations with a viewpoint towards Geometry.

Though similar questions have been asked at Good 1st PDE book for self study and Good reference texts for introduction to partial differential equation? but none of them really answer my query, so I ...
0
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1answer
17 views

Set family closed under symmetric difference

I have been looking for information on (finite) set families $\mathcal F$ such that if $X,Y \in \mathcal F$ then $X \,\triangle \,Y \in \mathcal F$. Are these kind of families (possibly with extra ...
0
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0answers
12 views

Any time series book have provide mathematical derivation or proofs of formula and its application [on hold]

Any time series book have provide mathematical derivation or proofs of formula and its application? I saw most of book only provide definition and computation but not anything i asked above.
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0answers
11 views

Comparison of non-order based voting methods (reference request)

There is plenty written on the relative merits of various voting systems where the voters submit ordered lists of preferences. However, there are several reasonable voting systems not using such a ...
3
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0answers
49 views

Number of lines needed to pass through every region of a map

The webpage http://what-if.xkcd.com/113 explores the fewest number of lines needed so that every state in the US has at least one line going through it. (actuallly great circles on a sphere) Can you ...
3
votes
1answer
42 views

Matrix Lie algebras

I gave an answer to Is there a group between $SO(2,\mathbb{R})$ and $SL(2,\mathbb{R})$? which was not popular. Meanwhile, i found myself at a loss when wishing to explain why a matrix Lie group had, ...
4
votes
1answer
76 views

Novel approaches to linear algebra and geometry

I'll be studying Brannan's Geometry and Lang's Introduction to Linear Algebra for one university course. I would like to know if you can you suggest some books that offer a unique perspective on the ...
0
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0answers
37 views

Run time for factoring a random $n$-digit number

The question, vaguely stated, is the following: Given a random composite integer with $n$ digits, how much time should one expect to spend finding the prime factorization of $n$? Note here that ...
2
votes
1answer
34 views

Identities for differential forms and vectorfields (reference request)

Recently I found the slides of a talk of J. E. Marsden, (Differential Forms and Stokes' Theorem). These slides introduce the required objects and summarize the basics of the corresponding theory. In ...
0
votes
1answer
26 views

Is there a conventional symbol for the set of radical expressions?

There is already a question about the name of such a set: Name for numbers expressible as radicals My question is related. The rational complex numbers might be denoted ℚ(i), and the algebraic ...
5
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4answers
123 views

Novel approaches to calculus problems

Can you suggest a book that offers "simpler" (compared to the standard solution) geometrical (or anyway non-standard) approaches and solutions to many calculus problems? For example, something along ...
0
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0answers
8 views

A refernce about Cartan matrix

There exist an approach to "Cartan Matrix" in Carter's book "Finite groups of Lie type, conjugacy classes an complex characters" p.23, which seems be different to other definitions of Cartan matrix I ...
2
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1answer
50 views

Software for math sketching

Usually when you're writing in LaTeX you want some pretty illustrations. Right now for geometry figures I use GeoGebra, which is easy enough; but I usually see better figures on other papers. Plus, ...
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0answers
50 views

Problem with Functional analysis course [on hold]

I'm having trouble with understanding my Functional analysis course. I have been reading "introductory Functional analysis with applications" by Kreyszig and I've been trying to solve the exercises ...
0
votes
1answer
52 views

Relation between ideals in Noetherian domains.

Suppose that we have a Noetherian domain $R$ and two ideals $I$ and $J$ of $R.$ Now consider the minimal (or irredundant) primary decompositions $I=\bigcap\limits_{i=1}^r Q_i$ and ...
2
votes
1answer
58 views

The spectral theory of unbounded operators

I would like to learn about the spectral theory of unbounded operators. I'm looking for a lucid, rigorous, self-contained and basic exposition of this topic that assumes no more than the material ...
2
votes
1answer
26 views

Concise description of Lebesgue measure in $\mathbb{R}^{n}$

I would like to confirm that the following is an acceptable description of the Lebesgue measure in $\mathbb{R}^{n}$. The outer Lebesgue measure $E \subset \mathbb{R}^{n}$: $$\lambda^{*}(E) = ...
2
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1answer
67 views

Good economics textbooks.

I would like a suggestion for the most mathematically fun/interesting mathematical economics textbook, preferably using abstract math. I want to prove theorems to complete my economics minor. I have ...
0
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1answer
28 views

powers of a unitary matrix that approximate the identity

It seems to me that the following must be well-known. Anybody know a reference for it? Let $U$ be a $d \times d$ unitary matrix. For any $\epsilon > 0$ there exists some positive integer $m$ such ...
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0answers
11 views

Central automorphisms act transitively on Krull-Schmidt decompositions

I'm looking for a modern reference to the subject line, preferably one that doesn't use Ore's generalizations to modular lattices. To clarify terminology... Suppose we have a group $G$ satisfying ...
3
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0answers
28 views

Irrational roots of unity?

Is it possible to take irrational roots of unity? For example, say I wanted to solve $f(x)=(x+1)^{\sqrt{2}}=1$. I found that one solution is the obvious $x=0$, and another one can be written nicely as ...
1
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1answer
20 views

Books for Tensor Algebra used in Physics?

I'm taking a dual Math,Physics undergraduate course.I want to study GR and a few parts of relativistic Quantum Mechanics.I've a decent amount of knowledge in linear algebra. Though we have tensor ...
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0answers
9 views

difference equations/inequalities in two variables without constant coefficients

I have a linear inhomogeneous difference inequality with variable coefficients. I was wondering if there are any general methods available for solving it. The case where the inequality is replaced by ...
1
vote
1answer
27 views

Central limits without replacement in a finite population.

"Everybody knows" that there are lots of variations on the theme of the central limit theorem. The most frequently seen form seems to be this: Suppose $X_1,X_2,X_3,\ldots$ are i.i.d. random variables ...
0
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1answer
36 views

Practice Examples of Proofs by Induction, Direct/Indirect Method

I'm learning about proofs in school, quite a few different sorts (but not geometry ones), but the teacher is teaching by slides mainly, not books. The main ones are proof by ...
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0answers
13 views

Heinrich Hertz on Mathematical Equations

What is the quote from Heinrich Hertz on how he could never exhaust the meaning behind a mathematical equation? (It's not mentioned in the Hertz quotations here.)
1
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0answers
38 views

Klein's absolute invariant and eta-quotients

Could anyone please provide a reference for $(13)$, $(14)$, $(17)$, $(18)$, $(21)$, $(22)$, which are stated on MathWorld without proper citation? Thank you in advance. Edit: It appears that $(13)$, ...
0
votes
1answer
44 views

A formula for polynomial derivative

Does the following elementary result have a name (or a reference to)? Given a field $K$, and a polynomial $P(x) \in K[x]$, divide the polynomial $P(x) - P(y)$ by $(x - y)$ in $K[x][y]$: $P(x) - P(y) ...
2
votes
1answer
35 views

When orthogonal polynomials form an Hilbert basis?

Let $\mu$ be a probability measure on $\mathbb R$, and consider the sequence of orthonormal polynomials in $L^2(\mu)$. These polynomials are constructed by applying Gram-Schmidt to the sequence ...
0
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0answers
52 views

Notes about the ring of $p$-adic integers $\Bbb Z_p$

I'm studing profinte groups. I'm using Wilson's book "Profinite Groups". Here the ring of $p$-adic integers $\Bbb Z_p$ is introduced as inverse limit of rings $\Bbb Z/p^n\Bbb Z$. I'm searching for ...
5
votes
1answer
91 views

Defining truth predicates in set theory

In this blog post J.D.Hamkins shows that KM set theory can define truth predicate for first-order set theory, which means, I believe, that there is a second-order definition of such predicate and KM ...
0
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0answers
29 views

Simplifying square root theorem

My teacher told me about some method to simplify square root which is a part of training for math competitions,I think she told it was Lagrange method but I couldn't find anything such.Anyway other ...
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0answers
16 views

Typo in Caffarelli-Silvestre?

I am reading two papers by Caffarelli and Silvestre, namely Regularity results for fully nonlinear equations by approximation and The Evans-Krylov theorem for nonlocal fully nonlinear equations. From ...
2
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1answer
59 views

William Thurston's 'Knots to Narnia'

http://www.youtube.com/watch?v=IKSrBt2kFD4 Above is the youtube link to the short video called 'Knots to Narnia'. (9 mins) While learning knot theory, I found this interesting video. In the video, ...