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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5
votes
3answers
172 views

Are there “numbers” with infinite number of digits (to the left) and are they useful?

Are there "numbers" with infinite amount of digits (to the left) and are they useful?(not talking about p-adic numbers) By useful I mean used in math (or something) and not a dead end idea. I guess I ...
35
votes
14answers
17k views

Good book for self study of a First Course in Real Analysis

Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introduction ...
4
votes
1answer
114 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
votes
1answer
22 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 ...
0
votes
0answers
60 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
votes
0answers
12 views

equivalence between dispersion relation and pde

I'm seeing a filmed lectures on quantum mechanics and the lecturer stated that thare is an eqivalence between dispersion relation $\omega(k)$ and wave equation. the relation in one direction is of ...
3
votes
0answers
42 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
votes
1answer
69 views

Book on calculus of several variables.

I'm an undergraduate student in mathematics and want to study Calculus of several variables currently this semester which involves the use of analysis, vector spaces and linear transformations. Can ...
0
votes
0answers
33 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 ...
28
votes
10answers
27k views

What is a good book for learning math from the ground up?

I am wondering which books are recommended for learning math from the ground up-- from rather basic math to advanced math (middle school -> graduate school). I am about to finish my masters of ...
3
votes
1answer
42 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 ...
0
votes
1answer
23 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 ...
3
votes
2answers
59 views

Every Banach space is quotient of $\ell_1(I)$

I'm looking for a book containing the proof that for every Banach space E there is an index I so that E is a quotient space of $\ell_1(I)$. If I can't find the book on google books, it would be great ...
5
votes
0answers
65 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 ...
0
votes
1answer
27 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 ...
2
votes
1answer
78 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 $\mathbb{Z}$: ...
3
votes
3answers
188 views

Introduction to Pseudodifferential operators

I'm interested in elementary introduction to pseduodifferential operators and its application to hyperbolic PDE's. I know measure theory, Fourier analysis and some elementary(linear) hyperbolic PDE's ...
3
votes
1answer
51 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, ...
6
votes
3answers
208 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 ...
0
votes
1answer
60 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 ...
1
vote
1answer
82 views

Abstract algebra book suggestion [duplicate]

I have been suggested Artin or Herstein's books. What do you think is more rigorous but at the same time clear and good to read?
1
vote
0answers
36 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 ...
1
vote
2answers
92 views

Book suggestion for probability theory

I need a good rigorous book to learn probability theory. So far, I've been suggested Gnedenko’s Theory of Probability; Shiyayev’s Probability; Feller’s An Introduction to Probability ...
0
votes
1answer
208 views

Solutions to Groups and Symmetry by M.A. Armstrong

I am learning group theory (on my own) using the 'Groups and Symmetry' textbook by MA Armstrong. Does anyone know of a book/website/blog where I can find solutions to the Exercises (so I can check my ...
0
votes
0answers
12 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 ...
2
votes
1answer
35 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 ...
3
votes
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 ...
9
votes
2answers
176 views

Good Reference for Justifying (less well-known fields of) Math?

How do we as mathematicians justify the study of math to students? Or, indeed, how do we justify it to the general public? How do you justify your particular field? I'm particularly interested in ...
0
votes
0answers
67 views

A class of function to study Fourier analysis, which is a subset of BV functions.

In Fourier analysis, while talking about pointwise convergence, we generally start with the class of functions called, BV functions (functions of bounded variation), which have a finite total ...
0
votes
1answer
29 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 ...
2
votes
1answer
65 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 ...
4
votes
0answers
34 views

Is there anywhere some explicit Bruhat decompositions are written down?

Question in title: most places I see Bruhat decompositions treated they're only briefly mentioned and no examples are given. Also, I calculated the following regarding the Bruhat decomposition of ...
0
votes
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 ...
6
votes
1answer
752 views

Difference between Gilbert Strang's “Introduction to Linear Algebra” and his “Linear Algebra and Its Applications”?

Could someone please explain the difference between Gilbert Strang's "Introduction to Linear Algebra" and his "Linear Algebra and Its Applications"? Thank you.
6
votes
2answers
258 views

Rigour vs intuition

Researcher David Tall has written in chapter one of Advanced Mathematical Thinking that ...
2
votes
1answer
73 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 ...
2
votes
1answer
57 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, ...
2
votes
0answers
54 views

Problem with Functional analysis course [closed]

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 ...
6
votes
1answer
394 views

Krivine Machine

Can someone please point out online resources to learn about Krivine Machine? My professor briefly touched it while teaching a course in Computer logic. google did not turn up much except some papers ...
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) = ...
1
vote
1answer
30 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
votes
1answer
29 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 ...
2
votes
2answers
416 views

Expected state of a Markov chain

Let's start with a slightly trivial Markov chain defined as follows: the beginning state is called $1$ and the set of states is $\mathbb{N}$. At each step, when the current state is $n$, the ...
47
votes
23answers
17k views

What is a good complex analysis textbook?

I'm out of college, and trying to learn complex analysis on my own. I took out Ahlfors' text from the library, but I'm finding it difficult. Any textbook recommendations? I'm probably at an ...
1
vote
0answers
13 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
votes
0answers
32 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
vote
1answer
24 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 ...
0
votes
0answers
11 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 ...
0
votes
1answer
163 views

On infinitely many solutions of a nonlinear ODE

I have a problem with showing that a given nonlinear ODE has infinitely many solutions. I would be glad if someone can come up with any examples (and its proof) related to this problem. I would ...
9
votes
1answer
284 views

Type theory as foundations

Does anyone know any good references that describe type theoretical foundations of mathematics? I've read some books e.g. Winskel's The Formal Semantics of Programming Languages and Pierce's Types and ...