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.

learn more… | top users | synonyms (3)

2
votes
1answer
88 views

Can somebody suggest me a book on linear algebra including these topics?

I want to cover the following topics of linear agebra: Dual and Double Dual spaces Transpose of linear operator Rational and Jordon forms Triangulisation and Diagonalisation Cyclic Decomposition ...
2
votes
1answer
58 views

A reference for the equality $|G:H| = \sum_i \dim(V_i)\dim(V_i^H)$

Let $G$ be a finite group and $H$ a subgroup. Let $V_1, \dots , V_r$ be (equivalence class representatives for) the irreducible complex representations of $G$. Let the stabilizer subspace $V_i^H = \{ ...
3
votes
1answer
58 views

Gauss: The study of Euler's works…

I keep coming across this quote by Gauss but I haven't actually been able to locate the original source: “The Study of Euler’s works will remain the best school for the various fields of mathematics ...
4
votes
0answers
25 views

References for actions of infinite-dimensional Banach-Lie groups on infinite-dimensional Banach manifolds

I am starting to study infinite-dimensional manifolds, specifically, Banach manifolds. I found some interesting introductory texts in which the mathematical background is developed with some detail. ...
1
vote
1answer
35 views

Good book for self study of Continued Fractions

Does anyone have a recommendation for a rigorous while readable book to use for the self study of continued fractions? PS - As examples of "rigorous while readable book" for self-learning, A. ...
2
votes
1answer
20 views

Literature on transformed Gaussian matrices

I am considering real $n$-by-$m$ matrices of the following type: $$ M=SM^\prime,\\ M^\prime_{ij} \overset{\text{iid}} \sim N(0,1). $$ Here, $S$ is a fixed $n$-by-$n$ matrix and the entries of ...
0
votes
1answer
23 views

Uniform convergence of the derivative function sequence on compact subsets

Let me make it short here: I believe the following proposition is true, as it is given a "proof" on page 54-55 in Elias Stein and Rami Shakarchi's Complex Analysis (Princeton University Press), which ...
0
votes
0answers
27 views

Looking for an introductory text to complex analysis from a topological viewpoint

After taking topology and real analysis I realized that there's a lot of elementary stuff that can be tackled from both sides, is there any book that deals with introductory complex analysis from the ...
2
votes
1answer
30 views

“Faint” continuity

Definition: A function $f:\mathbb{R}\to \mathbb{R}$ is called faintly continuous in $x$ if there are two series $x_n < x < y_n$ with $\lim_{x_n \to x} f(x_n) = \lim_{y_n \to x} f(y_n) = f(x)$. ...
1
vote
0answers
34 views

Theory of complex integration

I don't know if this is a pedestrian question or not, but here goes. I am working through Ahlfors' complex analysis, which has been a great (and challenging) text to get a grasp of the basics of the ...
7
votes
3answers
220 views

Prove that $\sin n\theta=n\sin \theta-\frac{n(n^2-1)}{3!}\sin^3\theta+\frac{n(n^2-1)(n^2-3^2)}{5!}\sin^5\theta+\cdots$

Prove that $$\sin n\theta=n\sin \theta-\frac{n(n^2-1)}{3!}\sin^3\theta+\frac{n(n^2-1)(n^2-3^2)}{5!}\sin^5\theta+-\cdots$$ If I am not mistaken, this identity was either proven by Newton or ...
11
votes
1answer
94 views

Math for blind people…

What happens if some blind person want to study math? Is there some "braille alphabet" for mathematical symbols? Are there math books, at least for undergraduate students, written for blind people?
1
vote
6answers
76 views

What are some good books on algebraic inequalities?

By algebraic inequalities I mean inequalities like Cauchy's inequality, the AM-GM inequality etc. I need it for the International Mathematics Olympiad (IMO), so I hope I can find some books that ...
1
vote
0answers
43 views

Resources for learning functional programming/Haskell for the mathematically inclined.

I am a math student wanting to learn some functional programming with Haskell. From what I understand, many type theory concepts are analogous, even equivalent, to category theory concepts (e.g. ...
0
votes
0answers
16 views

Can someone recommend a good, concise maths textbook at beginner university level for 3D Geometry (Vectors and Planes) and Pure maths

It's all in the title. A good recommendation would be high appreciated especially for 3D Geo.
-1
votes
0answers
10 views

Introductory references on application of geometry in image processsing

I would like to know more about possible applications of geometry in image processing. Could anyone introduce any expository survey that explains the field in fairly simple words?
0
votes
1answer
6 views

Vertex ideal in graphs?

Vertex ideal originates from lattices here. Is there some relationship to relate it to graphs such as series-parallel graphs?
8
votes
0answers
168 views

Is an étale morphism of algebraic stacks locally quasi-finite?

An étale morphism of schemes is unramified, and an unramified morphism is locally quasi-finite. Does the same hold for étale morphisms of algebraic stacks? Let us recall the definitions, following ...
0
votes
1answer
20 views

Key reference book on toric ideals: normal or not? Which definition to follow?

I want to understand sum of binomials better in terms of ideals such as binomial ideals, normal ideals and so by toric ideals. Examples about toric ideals contain $$\sum x^\alpha+\sum ...
2
votes
2answers
69 views

Path - Geometry [closed]

I am currently completing the end of a Bachelor degree in pure mathematics. I would like to work on an interesting project (by myself) this summer in the field of spectral geometry. Does someone could ...
0
votes
2answers
29 views

Soft Question - book recommendation - Stochastic Processes

My mother language book on stochastic processes is pretty much complete(~500 pages) but would like another one in English, to have in my library. I'm looking for a similar book containing the ...
1
vote
1answer
74 views

Different ways of evaluating $n!$?

I've recently managed to prove the following result and was hoping to know if it already exists? $ \def\lf{\left\lfloor} \def\rf{\right\rfloor}$ $$ \ln(n!) = \sum_{k=1}^{p_k < n}\left( ...
1
vote
1answer
29 views

A combinatorial card-trick

You have $k$ identical decks of cards, with $m$ cards in each deck. You divide each deck to $l$ packs, $m/l$ cards in each pack. You arrange the $l$ packs in a row on the table; so that there is a ...
-1
votes
0answers
28 views

Learning algebraic number theory from Neukirch [duplicate]

Next semester I will be taking a course in Algebraic Number Theory, and the course textbook will be Algebraic Number Theory bu Jurgen Neukirch. As I have not had any such course in the past, I was ...
2
votes
3answers
50 views

Examples of infinite Semi-direct products

I'm looking for some examples of semi-direct products, $G = N \rtimes_\alpha H$ of (infinite) groups. I'm aware of the definitions involved but never really thought through a lot of examples. I would ...
3
votes
2answers
56 views

Enough differences of powers of natural numbers equals a constant

Let $n_k$ be a sequence. We create a new sequence by taking the difference of consecutive terms in $n_k$. So the terms of the new sequence $a_k$ is defined as $a_i=n_{i+1}-n_i$. This is the difference ...
5
votes
2answers
83 views

Good blogs for undergraduate mathematics? [closed]

I search some useful blogs talking about undergraduate and graduate mathematics, like terry tao So any suggestions? Thanks in advanced.
2
votes
0answers
29 views

Are there results for relations between upward and downward closed partitions of some powerset?

I stumbled upon this, given some set $X$ and its powerset $\mathcal{P}(X)$ and some incomparable set $\mathbb{S}\subseteq\mathcal{P}(X)$, i.e. for any $S,S'\in\mathbb{S}$ we have $S\setminus ...
0
votes
0answers
24 views

reference request for advanced geometry book

Can somebody recommend a textbook on a categorical approach to geometry? I know all the basics of differential geometry, and have completed books like Lee's Manifolds and Differential Geometry
1
vote
0answers
39 views

Geometry textbooks from the 1800s

I was reading this paper recently and noticed that the college mathematics curriculum included geometry and trigonometry. It might be a poor assumption, but I'm assuming that geometry (or ...
2
votes
0answers
38 views

Infinite quotient with finitely many torsion elements

I am interested in finding countably infinite group $G$ with the following property. For any normal subgroup $H$ of $G$ with infinite index, the number of torsion elements in the quotient $G/H$ is ...
0
votes
0answers
13 views

Equality constraints into inequalities constraints through elimination

I read here in Section 10.1.2 of this text that a way to eliminate linear equality constraints of the type $$Ax = b$$ in convex optimization problems is to parameterize the related affine space as a ...
58
votes
3answers
593 views

All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$

I would like some reference about this infinitely nested radical expansion for all real numbers between $0$ and $2$. I'll use a shorthand for this expansion, as a string of signs, $+$ or $-$, with ...
1
vote
0answers
36 views

Terminology question about a weaker condition than normal crossings

Let $X$ be an algebraic set (say over $\mathbb C$). From what I understand, we say that $X$ has simple normal crossings if at every point it locally looks like a union of hyperplanes in general ...
0
votes
0answers
33 views

Ideal generated by a set of polynomials $X^{a/b}$ where each monomial having $a$ and not having $b$

Let $$\mathcal R=\mathbb Z_2[x_1,\dots,x_n]/\langle x_1^2-x_1,\dots,x_n^2-x_n\rangle.$$ I want to learn ideal arithmetics to deal with polynomials of the forms such as Consider a set of ...
0
votes
0answers
18 views

Extension of measurable function defined on dense subset.

I'm looking for some books or papers written about the problem below but I don't find them. Problem Let $(a,b)\subset\mathbb{R}$ be an open interval and $I$ be a subset of $(a,b)$ such that $I$ is ...
1
vote
0answers
15 views

Where can I find methods to evaluate products?

I found it was slightly difficult to find resources that discussed methods for evaluating products, like $\Pi_{n=0}^ka_n$ Preferably, I want to start with the basics and move through some readings on ...
6
votes
1answer
105 views

Minimal polynomial of root of unity over quadratic field

Let $p$ be an odd prime and consider the $p$-th cyclotomic field $\mathbb{Q}(\zeta_p)$ and its quadratic subfield $\mathbb{Q}(\sqrt{\pm p})=:K$. I am interested in the minimal polynomial of a root of ...
1
vote
0answers
27 views

Difference between the characteristic function of a sum of independent vectors and a Gaussian

In the book "Sums of Independent Random Variables" by Petrov the following lemma appears in page 109, in preparation to prove the Berry-Esseen inequality Let $X_1,...,X_n$ be independent random ...
0
votes
0answers
5 views

Who proved that the equilibrium problem is equivalent to a monotone inclusion problem?

I'm looking for the original reference where it was proved that given a subset $X$ of a space $E$ and a function $f:E \times E \mapsto \mathbb{R}$, the equilibrium problem of finding $x \in X$ such ...
3
votes
3answers
65 views

Looking for strictly increasing integer sequences whose gaps between consecutive elements are “pseudorandom”

I am doing some tests with strictly increasing integer sequences whose gaps between consecutive elements show a "pseudorandom" behavior, meaning "pseudorandom" that the gaps do not grow up ...
0
votes
1answer
32 views

Combinatorics books that tackle and intermediate level [duplicate]

I have been studying enumerative combinatorics using the book by George Martin: Counting: the art of enumerative combinatorics. I would like to continue learning the subject, but the problem is that I ...
3
votes
0answers
72 views

modularizing category theory

I have made the experience that proofs using category theory often look very elegant and short but when it comes down to verifying the details there is quite a list of commutativities etc. to check. A ...
-1
votes
1answer
59 views

Are zeta functions discussed over finite fields? [closed]

Let $\mathbb{F}$ be a finite field. I wonder if someone discussed the behaviour of the analogous of zeta functions over $\mathbb{F}$? For example, one can easily see that ...
0
votes
0answers
13 views

Reference request: field extensions

This is a standard reference request for field extensions, algebraic extensions, and the like. My class is covering ch13/14 of D&F, and I would appreciate both canonical references and online ...
4
votes
2answers
35 views

Exponential Power Series where Powers are Prime

I am looking for information in regards to a couple particular functions: 1) $P(x)=\sum_{p\in\mathbb{P}}\frac{x^p}{p!}$ 2) $Q(x)=\sum_{p\not\in\mathbb{P}}\frac{x^p}{p!}$ (assuming $0, 1$ are ...
1
vote
1answer
66 views

Where to find about the category theoretic study of manifolds?

I'm looking for a resource about a category theoretic study of manifolds. What do you think is a good start? Hint: Not after very advanced resources. So no worries (indeed, preferred) if it's an ...
0
votes
0answers
17 views

Exercises on the following topics on Markov Chains

We are being taught the following topics in Markov Chains: 1) Markov Chain Monte Carlo: Hard Core model, Counting random q-colourings of a graph 2) Total variation distance for a Simple Symmetric ...
1
vote
0answers
31 views

Is there a standard way of defining a total order between Gaussian primes?

In the case of $\Bbb N$ and $\Bbb Z$ the gap between two consecutive primes could be defined roughly speaking as the absolute value of the (1-dimensional) distance between those mentioned consecutive ...
0
votes
0answers
32 views

Coxeter groups and Reflection groups

What are some of the good books /Journals /Research Papers to study on Coxeter groups? Can someone suggest me a problem to work upon in this area or would a general survey on Coxeter Groups would be ...