Tagged Questions

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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17
votes
5answers
354 views

Big list of serious but fun “unusual” books

I would like to have some suggestions about serious (that is, with good mathematical content) but fun books that cover topics (or propose problems) in "recreational mathematics"; in any other field ...
0
votes
0answers
15 views

Deck transformations and Gromov Hyperbolicity

I would like to ask, once more, for some references in Gromov-hyperbolic spaces. The question is specifically the following: Does someone know any alternative reference, alternative proof, anything, ...
6
votes
0answers
121 views

Isaac Newton did number theory?!

I was reading Whiteside's article called "Newton the Mathemtician", where he says that Newton did Number Theory (e.g. inverstigating which numbers are expressible as a sum of two cubes). If this is ...
8
votes
8answers
436 views

Mathematical breakthroughs [closed]

When I read about mathematical history I hear of breakthroughs. For example, Cartesian geometry, Newton/Leibniz Calculus, and so on. My question is this: What are some recent epoch-making ...
2
votes
1answer
47 views

Computation of adjoint functors (sheafification)

In a (complete) category, limits can be "computed" assuming one knows how to compute products and equalisers. I have seen it mentioned that adjoint functors can be found using certain ...
0
votes
2answers
35 views

References for Linear Algebra needed for Differential Equations and Linear Programming

I am in need of learning the Linear Algebraic theory behind the following Applied disciplines. Could someone please recommend Linear Algebra books for: Differential Equations: Specifically learning ...
3
votes
3answers
83 views

Elementary geometry from a higher perspective

I'm searching for some references that deal with topics from "elementary geometry" analysing them from a "higher" perspective (for example, abstract algebra, linear algebra, and so on).
3
votes
5answers
175 views

Suggestion: good book on probability theory with emphasis on applications to other areas of mathematics and physics

On this website, there are many questions about books on probability theory, but I would like to ask if you can suggest a book (or more than one if necessary) that is: rigorous and accurate ...
3
votes
1answer
75 views

Reference Request to Prepare for Hatcher's “Algebraic Topology”

Hatcher himself has an excellent and always generously free set of notes on point- set topology: http://www.math.cornell.edu/~hatcher/Top/TopNotes.pdf It includes up to quotient spaces. It seems ...
7
votes
3answers
160 views

Books that you think you should have read during your undergraduate years

A quite popular question here is "If you could go back in time and tell yourself to read a specific book at the beginning of your career as a mathematician, which book would it be?" I would like to ...
0
votes
1answer
25 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
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
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 ...
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 ...
20
votes
7answers
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 ...
1
vote
1answer
31 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
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 ...
2
votes
1answer
80 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
68 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
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 ...
2
votes
4answers
149 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 ...
6
votes
3answers
223 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
vote
0answers
38 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 ...
5
votes
4answers
214 views

Books that use 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, not-so-common, (possibly) intuitive and non-standard methods (see note *) for approaching problems and interpreting theorems and ...
3
votes
1answer
77 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
votes
1answer
25 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
votes
0answers
13 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
votes
0answers
53 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
54 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
120 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 ...
2
votes
1answer
39 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
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 ...
11
votes
6answers
358 views

Book with novel approaches to analysis

Now I'm studying Rudin's Principles of mathematical analysis, but I'm searching for a book that offers geometric, physical or otherwise non-standard approaches to topics in analysis. Also, I'm looking ...
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 ...
2
votes
1answer
60 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
55 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 ...
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 ...
2
votes
1answer
67 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
votes
1answer
78 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
votes
1answer
31 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 ...
1
vote
0answers
15 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
33 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
25 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 ...
1
vote
1answer
31 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
0answers
16 views

Generalization of prime and irreducible elements to arbitary magmas

Has anyone ever given a general definition of prime and irreducible elements in arbitrary magmas, that is to say, sets with a single binary operation with no restrictions? I know Walter Noll has given ...
0
votes
1answer
55 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 ...
0
votes
0answers
15 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
vote
0answers
55 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.