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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8
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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
23 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
12 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
584 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
14 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
104 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
64 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 ...
2
votes
0answers
17 views

Have any of the extensions of Frucht's theorem been put to good use in making other connections between group and graph theory?

I am writing a survey paper on the topic of algebraic graph theory for my undergraduate graph theory course, and I am primarily concerned with the connections between group theory and graph theory, so ...
0
votes
0answers
9 views

Generalized Mixed Models and Hilbert Spaces

I recently came across the derivation of the normal equations for linear regression using Hilbert Spaces and projection theorem, and thought it was pretty cool. After doing a lot of googling, it seems ...
-1
votes
0answers
34 views

Does anyone know a good book on $3$ dimensional $\Bbb C$?

I believe someone here had a site with very cool notes on $3$D complex numbers (numbers of the form $X=x+yj+zj^2$, with $j^3=-1$). I wanted to know if there was any literature about this, because ...
1
vote
1answer
31 views

Expository reference on group presentations

I'm looking for expository papers, small books or chapters on the topic of group presentations. I have familiarity with basic abstract algebra (groups, rings, modules, some finite field theory from ...
1
vote
0answers
22 views

Change of scalars and field of fractions

Does someone know a reference in a textbook for the following fact? Let $k \subseteq k'$ be an algebraic field extension and $A$ a $k$-algebra such that the extension of scalars $A \otimes_k k'$ ...
3
votes
1answer
65 views

Reference request: Fibre functor for elliptic curves is pro-representable

I am writing a project on étale fundamental groups of elliptic curves and I want to include a proof of a key theorem: the fibre functor on the category of finite étale covers of an elliptic curve is ...
1
vote
1answer
28 views

Reference request: groups theory and trees

I need to find references to the following two facts (if a second one has a short proof then I can use it instead) 1) Each automorphism of oriented tree has a fixed point or invariant line. 2) Let ...
2
votes
1answer
32 views

Where does the “Zarankiewicz's lemma” from?

In order to prove Turan's Theorem, someone introduced a lemma so called "Zarankiewicz's lemma": If $G$ is a $k$-free graph, then there exists a vertex having degree at most $\displaystyle \lfloor ...
1
vote
0answers
39 views

Reference request to study mathematical modelling

I'm interested in learning mathematical modelling. The course structure is appealing to me and just because of my interest I have already learned complete calculus and differential equations very ...
1
vote
0answers
20 views

Book search on statistics

I am searching a book that Analysis of Failure and Survival Data (Chapman & Hall/CRC Texts in Statistical Science) by Peter Smith. Its link is here. I tried to buy it from Amazon, but it is out ...
0
votes
1answer
16 views

Name of degenerate parameter dependent ODE

I am looking for literature on specific type of degeneracy for odes. Consider the phase space $M= \{ (x_1,x_2)\in \mathbb{R}^2 \}$ and the ode of the general form: \begin{align} \alpha \frac{d ...
0
votes
0answers
29 views

Learning probability via linear algebra?

I've heard that much of probability theory can be thought of in terms of linear algebra (e.g. as this answer explains). Are there any good books that teach probability through a linear algebra ...
1
vote
1answer
34 views

rigorous statistics book recommendations

I am learning statistical inference by myself, I have skim through a few books like Casella Hoggs and I find it omitted lots of details, for example, they didn't introduce the conditional expectation, ...
1
vote
0answers
64 views

Results about Hilbert-Sobolev space with homogeneous boundary condition.

I am currently reading works about numerical method for solving differential equations. The main setting of the work revolves on the space $H^m_0[0,1]$, which is defined by $$ H^m_0[0,1]:=\{f\in ...
2
votes
0answers
50 views

Does the continued fraction for $e^{3/n}$ have a pattern?

Wikipedia has patterns for the simple continued fractions $e^{1/n},e^{2/n}$, which made me wonder whether there is one known for $e^{3/n}?$ (by pattern, I mean that the partial quotients $a_n$ can ...
2
votes
0answers
43 views

Provable Hamiltonian Subclass of Barnette Graphs

Given a bicubic planar graph consisting of faces with degree $4$ and $6$, so called Barnette graphs. We can show that there are exactly six squares. Kundor and I found six types of arrangements of the ...
2
votes
0answers
37 views

Reference request for Galois Theory [duplicate]

I am an undergraduate taking a second semester course in Abstract Algebra. We just got started on Field and Galois theory, and my professor told us that he will teach us Grothendieck's formulation of ...