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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4
votes
1answer
141 views

Is there any mathematician who felt guilty for one of his math discoveries ever?

Quoted from Wikipedia: In 1888 Alfred Nobel's brother Ludvig died while visiting Cannes and a French newspaper erroneously published Alfred's obituary. It condemned him for his invention of ...
2
votes
1answer
50 views

Can somebody explain (and ideally reference) this strange use/version of the Pressing Down Lemma?

In Stevo Todorcevic's "A dichotomy for P-ideals of countable sets" (link, page 261 at the bottom [page 11 in the pdf]), the following confusing situation comes up: (Context: $\mathcal I$ is a P-Ideal ...
0
votes
1answer
37 views

Are there “interesting” examples of complete finite-volume non-compact Riemannian manifolds that are not non-positively curved?

Moreover, it would be good that, if $M$ is such an example, its universal cover $\tilde M$ is "highly" symmetric, i.e. the group G of isometries of $\tilde M$ is "big" (for example, transitive, or a ...
11
votes
1answer
462 views

Looking for an easy lightning introduction to Hilbert spaces and Banach spaces

I'm co-organizing a reading seminar on Higson and Roe's Analytic K-homology. Most participants are graduate students and faculty, but there are a number of undergraduates who might like to ...
1
vote
1answer
42 views

Pressing-Down-Lemma for Jech's notion of stationary sets

So, apparently there is a variant of the Pressing-Down-Lemma (or Fodor's Lemma) for Jech's notion of stationarity, i.e. for sets in $[X]^\lambda$. Does anybody know a citable source for this?
0
votes
0answers
13 views

Gradient inequality in a simpler case

Let $f : \mathbb{R} \to \mathbb{R}$ be a analytic function. There exists $\theta \in (0,1/2]$, $c$, $\sigma$ such that for every $|x-a|\le \sigma$ $$ |f(x) - f(a)|^{1-\theta} \le c |f'(x)|. $$ This ...
2
votes
0answers
38 views

Identities for hypergeometric functions ${}_2F_1$ with z=1/2

Is there a closed form (or approximation) for a hypergeometric function of form: $_2F_1(1,b+c;c;\frac{1}{2}) \quad \text{where} \; b,c \in \mathbb{N}$ ? I researched all identities in ...
0
votes
0answers
26 views

request name of paper of bullet-nose curves by Schoute [closed]

I would like to request name of paper of bullet-nose curves by Schoute to plot this kind of equationhere $$z^2=t(t-i) \Longleftrightarrow x^2+y^2=4x^2y^2 \Longleftrightarrow y=\dfrac{\pm ...
2
votes
0answers
27 views

Continued fraction approximation to a function and its derivative

I am recently working on fitting a model with incomplete beta function. In order to put it into my optimization algorithm, I must find out the derivatives of the incomplete beta function $B_p(x,y)$ ...
3
votes
1answer
56 views

Solving Kepler's second law

Kepler's second law, about equal areas in equal times, is a differential equation: it gives velocity as a function of location. Where are the best expository accounts of the process of solving this ...
1
vote
0answers
44 views

Reference request on a sum-of-determinants identity

Suppose $X_1,X_2,X_3\in\mathbb R^{2\times1}$. Then $$ \det[ X_1,X_2] +\det[X_2,X_3] + \det[X_3,X_1] = \det[X_2-X_1,X_3-X_1]. $$ Where are this identity and higher-dimensional versions and their ...
2
votes
0answers
16 views

double integrals on quantum calculus

I need references or book recommendations to find properties of double integrals on quantum calculus. Especially i need analogue of Fubini's theorem on q-calculus.
0
votes
2answers
24 views

How to prove $x^2=-1$ has a solution in $\mathbb{Q}_p$ iff $p=1\mod 4$

Let $p$ be prime and let $\mathbb{Q}_p$ denote the field of $p$-adic numbers. Is there an elementary way to prove $x^2=-1$ has a solution in $\mathbb{Q}_p$ iff $p=1\mod 4$? I need this result, but I ...
2
votes
1answer
52 views

Group-like structures over the integers and functions on them

The integers with addition build a group $\langle \mathbb{Z},+,0\rangle$. The functions $\operatorname{succ}:\mathbb{Z} \rightarrow \mathbb{Z}$, $\operatorname{pred}:\mathbb{Z} \rightarrow ...
4
votes
1answer
120 views

Is Euler's Introductio in analysin infinitorum suitable for studying analysis today?

I've read the following quote on Wanner's Analysis by Its History: ... our students of mathematics would profit much more from a study of Euler's Introductio in analysin infinitorum, rather than ...
8
votes
1answer
414 views

Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils

I was wondering if mathematics learning process require the use of textbooks. When I was a high school student, I read as a preparation for university, Legendre book on Elements of geometry and ...
0
votes
0answers
17 views

Artin representation of Braid groups

It is a classical result by Emil Artin that the braid group $B_n$ is isomorphic to a subgroup of the automorphism group of free groups $\mathrm{Aut}(F_n)$. I am wondering when and where was this ...
5
votes
1answer
278 views

On the possible values of $\sum\varepsilon_na_n$, where $\varepsilon_n=\pm1$ (i.e., changing signs of the original series)

I have used the following result in an answer on this site. Suppose that $a_n>0$ are positive real numbers such that $\sum\limits_{n=1}^\infty a_n=+\infty$ and $\lim\limits_{n\to\infty} ...
5
votes
3answers
89 views
0
votes
0answers
15 views

Landau's Handbuch der Lehre von der Verteilung der Primzahlen

Landau's Handbuch der Lehre von der Verteilung der Primzahlen is available in German here. I read here that there was a proposal to produce an English translation, which I see was last edited in May ...
3
votes
1answer
82 views

Without AC, it is consistent that there is a function with domain $\mathbb{R}$ whose range has cardinality strictly larger than that of $\mathbb{R}$?

I stumbled across this question earlier, and the top comment on the bottom answer asserts two claims: Without the Axiom of Choice, It is consistent that there exists a function with domain ...
0
votes
1answer
417 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
1answer
23 views

Literature: Derivations in C*-Algebras

Do you have some nice reference for dynamical systems in C*-algebras (including discussion of their derivations!) like notes, papers, books, etc.?
2
votes
0answers
61 views

Deep questions in number theory not accessible by combinatorial results

Number theory and arithmetic geometry were invented to solve many questions about properties of numbers. What are the some of the foundational results or estimates that are accessible to powerful ...
8
votes
10answers
349 views

Real analysis book suggestion

I am searching for a real analysis book (instead of Rudin's) which satisfies the following requirements: clear, motivated (but not chatty), clean exposition in definition-theorem-proof style; ...
2
votes
1answer
59 views

Original Papers on Singular Homology/Cohomology.

I am currently reading Singular Homology Theory and Cohomology on my own mainly from Hatcher's "Algebriac Topology" and "Topology and Geometry" by Bredon. Quite often it happens that it takes a lot of ...
0
votes
1answer
40 views

Reference for a nice formula

In this post, $no identity$ gives a nice formula for the distance of a vector to a subspace: $d^2(p,L)=\frac{G(v_1,\ldots,v_m,p)}{G(v_1,\ldots,v_m)}\tag{1}$ Can anyone give me reference where I can ...
0
votes
3answers
63 views

What are some textbooks on the same level as Ross's “A First Course in Probability”?

Ideally, I would like to have at least six standard probability texts so that I can compare them to each other. Thank You.
6
votes
2answers
413 views

Modified Euler's Totient function for counting constellations in reduced residue systems

I am working on a modified totient function for counting constellations in reduced residue systems for the same range that Euler's totient function is defined over. This post is separated into three ...
15
votes
9answers
2k views

“Honest” introductory real analysis book

I was asked if I could suggest an "honest" introductory real analysis book, where "honest" means: with every single theorem proved (that is, no "left to the reader" or "you can easily see"); with ...
29
votes
14answers
10k views

What are good books to learn graph theory?

What are some of the best books on graph theory, particularly directed towards an upper division undergraduate student who has taken most the standard undergraduate courses? I'm learning graph theory ...
6
votes
1answer
127 views

The distance from the center of a circle, which is tangent to a ellipse $x^2/a^2+y^2/b^2=1$ and two parallel tangent lines of the ellipse is $a+b$

Consider the following problem: Let $E$ be the ellipse $x^2/a^2+y^2/b^2=1$ with $a>b$. Consider two tangent lines on $E$ which are parallel, say, $r$ and $s$. Let $C$ be a circle, which is ...
2
votes
1answer
27 views

Reference for entropy of the binomial distribution?

The Wikipedia page Binomial distribution says that the entropy of the Binomial(n,p) is $\frac{1}{2}\log_2\left(2\pi e n p (1-p)\right) + O\left(\frac{1}{n}\right)$. What is a reference (paper or ...
1
vote
1answer
12 views

Out of plane cross section evolution of surfaces based on local geometry information

With this question I would like to kindly ask for feedback or general pointers to even remotely related works in regards to a challenge I face. Given a smooth surface $S$ $:\mathbb{R}^2\rightarrow ...
-3
votes
1answer
64 views

Discrete Mathematics in KhanAcademy [closed]

Where is a section of discrete mathematics in KhanAcademy? https://www.khanacademy.org/
8
votes
2answers
473 views

Video lectures of algebraic geometry (Hartshorne, Shafarevich, … )

I am a commutative algebra student. I wonder if there is some video lectures of algebraic geometry courses available online for free? I'd like the lectures to cover main topics of the books ...
2
votes
1answer
14 views

Texts on Coxeter groups

I'm looking for an introductory text on Coxeter groups. It can assume undegraduate knowledge of Algebra (Groups up to and including the Sylow theorems in Fraleigh, elementary knowledge of rings, ...
1
vote
3answers
146 views

Frieze groups, wallpaper groups

Can someone suggest a source that proves the classifications of the 7 frieze groups and 17 wallpaper groups in an elegant way?
2
votes
2answers
39 views

Reference request: Introduction to Applied Differential Geometry for Physicists and Engineers

I'm looking for a book on differential geometry or differential topology that is comprehensive and reads at the level of someone with engineering background (i.e. Boyce's ODE, Stewart's Calculus, ...
1
vote
1answer
52 views

Subsets of a monoid closed under left-multiplication by elements of a submonoid

Let $M, T$ be monoids (or, semigroups) with $M \subset T$. Then we can consider subsets $S$ of $T$ that are closed under left-multiplication by something in $M$, i.e. $$ a \in S, m \in M \implies ma ...
0
votes
0answers
20 views

How to search the set of papers whose references contain a given preprint?

I am reading a preprint titled Combinatorial Group Theory In Homotopy Theory I by Fred Cohen (available at Cohen's web page) Now I need to find all papers whose references contain this preprint. Is ...
2
votes
2answers
79 views

Good references on Riemannian Geometry

I'd like a textbook that covers do Carmo's contents (can be more), but that isn't do Carmo. I did not like his writting style. That being said, I particularly like the styles of: Walter Rudin ...
0
votes
1answer
35 views

Books for these topics.

I have an lecturership exam in India and in the syllabus there are few topics under the tags "Calculus of variations" and "Linear integral equations", and if please if someone could tell me which ...
1
vote
1answer
37 views

References for Algebraic number theory

I am doing algebraic number theory first time. I have done all ring theory and field theory. I am interested in algebra , so also pretty much excited about algebraic number theory. I have a month's ...
10
votes
1answer
212 views

Does anyone know about Ramanujan's method of solving the quartic? [closed]

I have read (probably) in Kanigel's book The Man Who Knew Infinity that S. Ramanujan devised his own method of solving the Quartic Equation after he learnt to solve the Cubic Equation. Does anyone ...
0
votes
0answers
28 views

Rreferences for free groups

I have done free groups. I studied it from Rotman two semesters back. But this semester I am doing combinatorial group theory and obviously it starts with free groups. I have to revise Free groups but ...
0
votes
0answers
28 views

Basic question: degree of normal bundle is not self-intersection number

For $C$ a (possibly singular) curve on a nonsingular projective surface $X$, let's define $C^2=deg_C(\mathcal{O}_X(C))$. Why is it not the same as $deg_C(N_{X|C})$ when $C$ is singular? Why do ...
3
votes
5answers
494 views

Recursion theory text, alternative to Soare

I want/need to learn some recursion theory, roughly equivalent to parts A and B of Soare's text. This covers "basic graduate material", up to Post's problem, oracle constructions, and the finite ...
0
votes
0answers
36 views

any online video course for analytic number theory or elementary number theory?

All: I am looking for online video course on analytic number theory for self-study. On Youtube, there are a few seminars, but no complete course for a semester or a year. Can anyone point out if ...
2
votes
1answer
204 views

Examples of Eilenberg-type Swindles

I am compiling a list of 'swindles' in the style of the Eilenberg-Mazur swindle. I've already got some swindles in K-theory, the Mazur Swindle and the proof of the Cantor–Bernstein–Schroeder theorem. ...