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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3
votes
5answers
343 views

Essays on the real line?

Are there any essays on real numbers (in general?). Specifically I want to learn more about: The history of (the system of) numbers; their philosophical significance through history; any good ...
1
vote
0answers
56 views

formulas for exact values of singular values in low dimension?

Are there formulas for the singular values of a real matrix in low dimension, i.e. for a $2 \times 2$ matrix or a $2 \times 3$ matrix? Any comment is welcome.
3
votes
1answer
92 views

Co-ordinate axes: What does the $e$ in ${\hat e}_x$ stand for?

In vector analysis for $\mathbb{R^3}$ we write standard basis vectors in various forms like $\{\hat{x}, \hat{y}, \hat{z} \}$, $\{ \hat{\imath}, \hat{\jmath}, \hat{k}\}$, $\{ {\hat e}_x, {\hat e}_y, {\...
9
votes
2answers
155 views

Literature on general paradox?

I suppose this one teeters on the edge of un-mathematical, but here it goes... I've been on something of a logic binge lately and have (surprise, surprise!) especially been interested in the results ...
5
votes
1answer
283 views

looking for materials on Martin Axiom

Recently, I am learning the Kunen's set theory. Now I will reach the second part of the book, i.e., the important Martin Axiom is introduced here. I found it is a little complex and difficult for a ...
3
votes
2answers
213 views

Determining distribution of $X_t = \int_0^t W_s^2 \mathrm{d} s$

Premise Let $W_t$ be the standard Wiener process, and let $X_t = \int_0^t W_s^2 \mathrm{d} s$. I am interested in determining the distribution of $X_t$. What I did My line of attack has been to ...
4
votes
2answers
2k views

How is a singular continuous measure defined?

On a measurable space, how is a measure being singular continuous relative to another defined? I searched on the internet and in some books to no avail and it mostly appears in a special case - the ...
33
votes
28answers
5k views

Classical texts that should not be missing from any shelf [closed]

It seems to me as if many modern texts are rather streamlined. They are designed not to expect too much from the reader but they often miss the depth of respective classical literature. The purpose ...
1
vote
1answer
163 views

Need reference about quadratic forms on abelian groups.

Let $B$ and $C$ be abelian groups (in additive notation). We call a function $f:B\rightarrow C$ a quadratic form if for all $x,y,z \in B$, the function $f$ satisfies the relation $$f(x+y+z)-f(x+y)-f(...
3
votes
1answer
1k views

Looking for a beginner to advanced maths series

I asked this question previously, but guess I didnt make clear what I am looking for (or something) I am looking for a series of books, like a full set highschool maths curriculum, just to refresh ...
2
votes
2answers
415 views

Primitive roots of odd primes

The following facts about primitive roots of an odd prime seem to be well known. For example, they both appear as exercises in Burton's Elementary Number Theory. Let $p$ be an odd prime. Then: ...
-3
votes
2answers
238 views

Is there any information/research about these extension of the real numbers? [closed]

Some time ago I had the idea of extending the real numbers with a new direction/algebraic sign, similarly how negative numbers extend the positive numbers by adding a new sign. I call this sign §, and ...
2
votes
1answer
210 views

cumulants and infinite divisibility

Where might I find a clear exposition of how to prove that a real-valued probability distribution for which all moments exist is infinitely divisible if and only if all of its cumulants of even order ...
30
votes
3answers
2k views

Original works of great mathematician Évariste Galois

Through this question I wanted to know the original works of Galois. When I was reading Galois theory ( since from last month ) , I have been seeing one common line in every book, whose essence ...
8
votes
4answers
4k views

Difficulties with Chapter 2 in Rudin

I have been reading Rudin (Principles of Mathematical Analysis) on my own now for around a month or so. While I was able to complete the first chapter without any difficulty, I am having problems ...
1
vote
0answers
64 views

reference request

Can anybody help me to find the books on numerical solutions of partial differential equations including examples on irregular geometry (specially books or links on matlab code examples in this case)?
1
vote
1answer
61 views

Anybody got a link for work done on metrics for rational functions?

I was just thinking that as rational functions form an ordered field you could describe analogous version of the absolute value function, but we don't quite have a 'metric' - for example |1/x| < e ...
8
votes
5answers
912 views

I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff

Next week, I'm beginning the 2nd semester of 9th grade in the country's leading Comp Sci High School. (the profile is actually Math-Comp Sci, but this HS focuses more on Comp Sci, whereas other ones ...
7
votes
3answers
446 views

Reference requests: Jitsuro Nagura

I spent some time today looking for any biographical information on Jitsuro Nagura and came up empty-handed. Any suggestions welcome. Also, the Wiki note on the Chebyshev $\psi$ function says that ...
2
votes
3answers
247 views

Intermediate growth rates

Is there any simple function/formula $f(n)$, which eventually dominates every $cn$ for every $c$, and is eventually dominated by $a \cdot n \cdot \ln^k(n)$ for every $a,k \in \mathbb{Z}$, where $\ln^k(...
12
votes
7answers
6k views

Any good Graduate Level linear algebra textbook for practice/problem solving?

I am looking for good graduate linear algebra books that contain practice problems with solutions (which is better) or hints to solve the problems. By the way, two graduate courses I am gonna take are ...
8
votes
5answers
4k views

Need Help: Any good textbook in undergrad multi-variable analysis/calculus?

This semester, I will be taking a senior undergrad course in advanced calculus "real analysis of several variables", and we will be covering topics like: -Differentiability. -Open mapping theorem. -...
1
vote
0answers
93 views

Reference Request: Elementary introduction to holomorphic induction's role in index theory

I am currently working on an index theory senior project which involves Dirac operators, spin modules and holomorphic induction on the representation ring Lie groups. My primary reference is Sternberg'...
1
vote
1answer
92 views

Centralizers in reductive Liegroups = unimodular?

Let $G$ be a real reductive group. Why is the centralizer of an element unimodular? What is a reference?
4
votes
2answers
442 views

Turing's 1939 paper on ordinal logic

I am reading Turing's 1939 paper on ordinal logic ("Systems of Logic Based on Ordinals", A. M. Turing, Proc. London Math. Soc. ser. 2, 45 (1939), #1, 161-228, DOI: 10.1112/plms/s2-45.1.161.) ...
1
vote
1answer
371 views

Properties of generalized limits aka nets

I want to find some article or a book which contains all general properties of nets. Of course some of them similar to properties of sequences with almost the same proofs, but I don't fill the edge, ...
0
votes
3answers
297 views

Cover a line segment randomly with smaller line segments [closed]

Covering a circle randomly with arcs has been well studied in the past (Geometric Probability - Solomon). But the problem when the circle is changed to a line segment doesn't seem to have been ...
9
votes
2answers
721 views

Original source for a quote by Lobachevsky

Lobachevsky is quoted in many places to have once written (said?) "There is no branch of mathematics, no matter how abstract, which may not someday be applied to phenomena of the real world." (In the ...
3
votes
3answers
1k views

Ring theory exercises at the graduate level

Do you know any book or an online source that contains exercises on ring theory? I've solved some exercises of Lang's Algebra and Dummit & Foote's Abstract Algebra but there is a huge gap between ...
1
vote
5answers
399 views

What is a good book about math history?

Which is a good book on math History? I want to give it as a gift to a mathematician.
10
votes
1answer
2k views

Construction of a regular pentagon

In Robert Dixon's Mathographics, a regular pentagon is constructed with straightedge and compass only. It is the pentagon $ABCDE$ pictured below. I am having trouble seeing why the central angles ...
1
vote
0answers
47 views

A resource to browse various function graphs?

I couldn't find what I need from google, so I figured it's time to ask here. Basically I'm looking for something like an online catalogue for all kinds of function graphs. I need a few specific ones ...
6
votes
1answer
441 views

Sum of divisor ratio inequality

Consider the divisors of $n$, $$d_1 = 1, d_2, d_3, ..., d_r=n$$ in ascending order and $r \equiv r(n)$ is the number of divisors of $n$. Is there any expression $f(n) < r(n)$ such that, $$\...
2
votes
0answers
114 views

Lectures of many valued logic

I am looking for a good introduction to this topic... something with lots of examples and models would be nice. I am specially interested by the case where the truth values are open sets in a ...
1
vote
1answer
115 views

counting edges in tesselations of a torus

Tesselate a torus with finitely many simply connected polygons. Do not allow four or more of them to meet at a point. In counting the edges, don't count a "straight line" as just one edge if it's ...
11
votes
3answers
610 views

What is combinatorial homotopy theory?

Edit: After a discussion with t.b. we agreed that this question aims to a different answer from this one, for more information you can read the comment below. Many times I've heard people speaking ...
10
votes
0answers
642 views

“The Galois group of $\pi$ is $\mathbb{Z}$”

Last year, in a talk of Michel Waldschmidt's, I remember hearing a statement along the lines of the title of this question: The Galois group of $\pi$ is $\mathbb{Z}$. In what sense/framework is ...
3
votes
2answers
2k views

What is a good Algebraic topology reference text? [duplicate]

Possible Duplicate: Learning Roadmap for Algebraic Topology The title of the question already says it all but I would like to add that I would really like the book to be about more algebraic ...
2
votes
0answers
430 views

Book Recommendation Needed: Gradient Descent, Euler-Lagrange

On a lecture note I read about Calculus of Variations faculty.uml.edu/cbyrne/cov.pdf the author talks about Euler-Lagrange equation, then continues to say "unfortunately, many times a closed form ...
106
votes
4answers
18k views

Books that every student “needs” to go through

I'm still a student, but the same books keep getting named by my tutors (Rudin, Royden). I've read Baby Rudin and begun Royden though I'm unsure if there are other books that I "should" be working on ...
0
votes
1answer
305 views

Rate of convergence of random variables for weak convergence

Suppose $X_{n}$ be a sequence of random variable that converges to $X$ in distribution. How can we define the rate of convergence? What would be the reference?
0
votes
1answer
89 views

Rate of convergence of double sequences

Suppose $ \{X_{n,m} \}$ be a double sequence of real numbers and suppose $\lim_{n}\lim_{m}X_{n,m}=X$. What is the definition and reference for the rate of convergence of double sequences?
7
votes
1answer
711 views

Any serious work on Lychrel numbers/$196$-Algorithm?

I've been googling around a little lately and have stumbled across the so called Lychrel problem. For a natural number $x$, let $Rx$ denote the number obtained by reversing the base-$10$ digits of $x$ ...
6
votes
4answers
865 views

History of analysis?

Any sites detailing the history of analysis post 1820 (to mid 1900s?) - vis-à-vis Cauchy, Weierstrass, Riemann, Bolzano, ..., Kuratowski, Hilbert? It's something that appears quite interesting and I ...
13
votes
6answers
660 views

Read old articles instead books.

I'd like to know if there is a site, or maybe a collection of books, where I can read old articles in mathematics in order to study topics directly from the source, instead reading books in the field. ...
3
votes
2answers
466 views

Derived functors are Kan extensions

In this short paper by G. Maltsiniotis derived functors are presented as Kan extensions along the localization functor. I began studying derived categories only a couple of months ago, so I'm not at ...
6
votes
2answers
1k views

Introductory book on Topology [duplicate]

Possible Duplicate: choosing a topology text best book for topology? What book would you recommend for an undergraduate wanting to learn the basics of topology? I've come across several books ...
3
votes
3answers
1k views

Graph theory resource for mathematical Olympiads

I would like to learn a bit of Graph theory for mathematical Olympiads.Can anyone please point out a resource from where I can learn it? Here's my background: I have limited knowledge of linear ...
16
votes
3answers
3k views

Best way to learn Algebraic Geometry?

I've been reading the book Commutative Algebra with a view towards Algebraic Geometry. I was wondering is the best way to learn algebraic geometry through commutative algebra? As the book I'm ...
4
votes
1answer
199 views

Is there an overview of several logical systems?

I've heard about many kinds of logic like combinatory logic, relevance logic, higher order logic, paraconsistent logic... but I don't know anything about those logical system except higher order logic....