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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2
votes
1answer
27 views

Rellich-Kondrachov

I read an article about the Rellich-Kondrachov embedding theorem in Sobolev spaces: https://en.wikipedia.org/wiki/Rellich%E2%80%93Kondrachov_theorem. Nevertheless, when I checked the refererence in ...
5
votes
1answer
45 views

Reference about the surgery of Ricci flow

I roughly read the Topping's LECTURES ON THE RICCI FLOW. Seemly, there is not introduction about surgery. Seemly,it is enough to deal singularity by blow up. Then, for knowing surgery I read the ...
0
votes
1answer
44 views

Writing one formal power series as a function of another

Suppose we have a formal power series $x(t)=t+\sum_{k=2}^\infty x_k(t^k/k!)$. In principle, this can be inverted to obtain $g(x)=x+\sum_{k=2}^\infty g_k(x^k/k!)$ such that $x(g(x))=x$. The specific ...
0
votes
1answer
26 views

Curve in a disk

I take a curve $\vec\gamma:[a,b]\longrightarrow \Delta$, where $\Delta \subseteq \mathbb{R}^2$ is the disk of radius $r>0$. If the curve has length $L>0$ does exist an upper bound (in terms of $...
2
votes
3answers
239 views

Have historians responded to Raju's critique?

C. K. Raju has made some outrageous criticisms of the traditional take on Euclid in particular and Western history in general. Yes he has a book published on the subject with an apparently respectable ...
1
vote
2answers
29 views

curl-free vector field on 3-torus

Let $U$ be an open and simply-connected subset of $ \mathbb{R}^3$. Then for every curl-free vector field $v \: \colon U \to \mathbb{R}^3$ there is a potential $\phi \in C^{\infty}(U; \mathbb{R})$ such ...
0
votes
0answers
56 views

Introductory Book on Faltings' Proof of the Mordell Conjecture

I'm currently reading Diamond and Shurman's book a First Course in Modular Forms and I've found it to be a wonderful introduction to the modularity theorem. Is there a similar introductory book for ...
0
votes
0answers
13 views

Reference request on Moduli stacks

I am starting now my self-studies on moduli stacks, and saw some material on internet, but unlike the moduli spaces, I feel that they lack on geometrical meaning. So I would apreciate good references ...
1
vote
1answer
18 views

How to find the invariant forms of a finite group

Let $G\subset GL(n,\mathbb{Z})$. I am looking for an algorithm that finds all symmetric matrices $F$ left invariant by G, ie $$g^TFg=F\quad \forall g\in G.$$ I have found lists of these invariants for ...
0
votes
0answers
11 views

An algorithm to find the general classical solution to a linear gradient system in partial derivatives

I'm looking for a book where the algorithm to construct the general solution for system $$\nabla u(x,y) = \vec a(x,y)\cdot \nabla v(x,y)$$ is given. Could ypu please advice me some source?
0
votes
0answers
17 views

About some good references for self study

I'm willing to start a self study of Hardy spaces, Bergman spaces and Bloch spaces. I would like to know good books on the subject. Since I'm going to study on my own, would be great to find one that ...
2
votes
2answers
69 views

Where to learn the algebra behind the use of differential operators in calculus

Algebra with differential operators is often used as a shortcut in calculus problems. I have previously asked about manipulations such as these: $$\int x^5e^xdx =\frac1Dx^5e^x=e^x\frac{1}{1+D}x^5=e^x(...
1
vote
0answers
52 views

Brownian motion hitting probability and Martin capacity

Consider a Brownian motion $B_t$ in $\mathbb{R}^n, n\geq 3$ and the ball $B(0, r)$ of radius $r$ around the origin. Let $\overline{C}$ be a compact set inside $B(0, r)$ such that $C$ is open in $B(0, ...
-1
votes
0answers
17 views

Transient Brownian motion and stopping time

Let $B(t)$ be a Brownian motion in $\mathbb{R}^n$, or on a compact Riemannian manifold $M$ of dimension $n$, $n \geq 2$. Let us consider the stopped Brownian motion at a deterministic time $T$ (in ...
2
votes
1answer
38 views

Hopf fibration and exact sequence in homotopy

I have encountered the Hopf fibration $S^1\hookrightarrow S^3\twoheadrightarrow S^2$ when studying smooth principal $G$-bundles. Whenever I google the Hopf fibration, I encounter a remark which boils ...
1
vote
0answers
32 views

Reference request for Thom's Transversality Theorem.

I am trying to read the book Introduction to the h-principle by Eliashberg and Mishachev. I am unable to understand the proof of Thom's Transversality theorem in the book. So if anyone can give any ...
1
vote
0answers
33 views

Reference request: how to check whether a set is invariant for a second order dynamical system?

I am looking for some examples where invariant set is proved for second order systems For a example, consider the Van Der Pol equation: $$\dot x_1 = x_2$$ $$\dot x_2 = -x_1 + 0.5(1-x_1^2)x_2$$ In ...
2
votes
2answers
31 views

References for the applications of probability in gambling

The intuition behind many theorems in probability comes from gamblers' games. I would like to know if there are any books or articles which cover some such connections between probability and its ...
1
vote
2answers
32 views

Books on Riemann Surfaces

I am starting a scholarship on geometry and the subject of research is going to be Riemann surfaces (we will focus on compact Riemann surfaces). I am finishing my undergraduate studies so my knowledge ...
2
votes
0answers
26 views

Software for solving first-order logic

Is there any class of software that can help me with the following problem in first order logic: given $\phi$ a formula with a "hole" in it (a subformula which is undetermined) and a particular set of ...
6
votes
2answers
208 views

Future learning for a math graduate in applied mathematics references

As a mathematics graduate with focus on programming we did a whole lot of coding of some mathematical statements (as well as proving them), but yet rarely giving real life examples and applications ...
0
votes
1answer
41 views

Real analysis reference for statistician

I'm a undergraduate statistics student, I think that learn Real Analysis can be useful to me in some points, can anyone suggest a introductory book for self-study ? I'm already multivariate calculus, ...
1
vote
2answers
55 views

Reference request: When is a conic birationally equivalent to the projective line?

I am looking for a reference which contains the proof of the following theorem: "A conic $C$ defined over the field $\mathbb{F}$ is birationally equivalent to $\mathbb{P}^{1}(\mathbb{F})$ if and only ...
3
votes
1answer
34 views

Finite group representation on endomorphism ring

Let $\rho:G\to\mbox{GL}(V)$ be a finite dimensional representation of a finite group $G$. We can assume the base field is $\mathbb{Q}$, but it doesn't really matter. Then we also obtain a ...
2
votes
0answers
50 views

Proof of the Ribet's theorem

My question is very simple : My goal is to read a proof the proof of the epsilon conjecture proven by Ken Ribet (1986) which is an ingredient of the proof of the Fermat Last Theorem (I want the ...
1
vote
0answers
32 views

Congruence numbers

Having read about Stirling numbers of the second kind I am curious. The article says it shows the number of equivalence relations on a set $n$ with $k$ equivalence classes which makes sense to me from ...
1
vote
0answers
18 views

Examples where ostragodsky's method is needed for integrating rational functions

I found out about Ostragodsky's method for integrating rational functions and thought it was pretty cool. However, I have never encountered any examples where it seemed needed (rather than just ...
2
votes
0answers
52 views

How does one read a formula with subscripts and superscripts?

An expression like $\Gamma_{ij}^k$ seems to be pronounced "gamma sub i, j upper k". Is this a generally accepted usage? Question. Is there a quotable source for such usage? Note that $k$ is not a ...
0
votes
0answers
21 views

Combination of certain linear-programming topics new?

I am writing a book on Linear Optimization. Its goal is to present material in a particular form which has not been encountered yet in the literature to the best of my knowledge. I am aiming at the ...
1
vote
0answers
26 views

Return probability of a SRW in an even number of steps

I am looking for some references for the following problem. Consider a graph $G$ and a simple continuous time random walk $(X_t)_{t\geqslant 0}$ on this graph. Consider the family of events $(e_t)...
5
votes
1answer
96 views

Ref. Requst: Space of bounded Lipschitz functions is separable if the domain is separable.

I have been scouring the internet for answers for some time and would therefore appreciate a reference or a proof since i'm not able to produce one myself. Let $(\mathcal{X},d)$ be a metric space, ...
1
vote
1answer
39 views

Fisher information for exponential family: Regularity conditions

for the Fisher-Information to be defined certain regularity conditions have to be fulfilled (like in Lemma 5.3. in Theory of Point Estimation by E.L. Lehmann or on slide 2 here: http://www.stat.nus....
0
votes
0answers
27 views

References request: two-queue, one-server model with pre-emptive queue priority and finite buffers

Sorry of the title is a mouthful. I'm developing a queue model with the following characteristics: Two queues: One contains an infinite number of people (Queue A) while the other (Queue B) is ...
0
votes
0answers
42 views

Good reference for partitions of unity?

I am reading about Sobolev Spaces and regularity theory of PDEs. The partition of unity lemma, as stated in Haim Brezis' Functional Analysis, Sobolev Spaces and Partial Differential Equations, is as ...
2
votes
0answers
32 views

Introduction to flag manifolds

What is a good self-contained introduction to the geometry of complex flag manifolds?
2
votes
2answers
80 views

Introductory Topology Book Recommendation for Economics

Would you please share your 2 cent on book recommendation for introductory topology book to graduate student in Economics. Have exposure to the first half of the yearlong analysis course in the ...
-3
votes
1answer
65 views

Help finding an article [closed]

Hello Recently I have been studying algebra and am in search of the following paper : Kac, V. G. Classification of simple $Z$-graded Lie superalgebras and simple Jordan superalgebras. Comm. Algebra 5 ...
2
votes
1answer
42 views

Uncertainty in a theorem about Sarrus numbers

From https://oeis.org/A001567 there is a theorem of Ray Chandler formulated: An odd composite number $2n + 1$ is in the sequence if and only if multiplicative order of $2\;(\text{mod}(2n+1))$ ...
3
votes
1answer
65 views

proof of Triangle Removal Lemma

Where can I find a proof of the following version of Triangle Removal Lemma (or any version equal to it)? Let $G(V,E)$ be a graph on $n$ vertices such that it contains $\varepsilon n^3$ triangles, ...
1
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0answers
55 views

Calculus of 1 variable [closed]

What are some good web link or pdf link to understand(self study) calculus of variable intuitively?I am a 12 th grade student with some notions of maxima and minima and some other notions in one ...
1
vote
0answers
19 views

Books / lecture series on Homotopy theory

I want to read homotopy theory on my own so I want to know prerequisites, good books and if there is any lectures available which can help me. Links are welcome. Till now I have done point-set ...
2
votes
0answers
61 views

Problem sets on Abstract Algebra

Many times we ask about what books should we read to learn or know more about a math topic (Abstract Algebra, in this case). However, I would like to get a list of the exercises what should we solve ...
1
vote
1answer
99 views

Hailstone collatz max sequence length upper bound of $260.5+x^{.43}$?

Let the Collatz function be defined as if $x$ even $c(x)=x/2$, if $x$ odd then $c(x)=3x+1$ over the naturals. Each operation is defined as a step. For example $3$ goes $(3,10,5,16,8,4,2,1)$ and takes ...
3
votes
1answer
60 views

Unsure on which sources to choose related to Calculus

I tried to get into Spivak's Calculus only to find that I've never been taught the type of Math presented there. First chapters talk about the properties of numbers, then mathematical induction, ...
1
vote
1answer
38 views

I've been working on Spivak and I'm on chapter 7. What are some good books to supplement Spivak for someone beginning to learn pure mathematics.

If I have too much difficulty with a concept/problem, then I'll just press on and solidify my understanding when the concept arises later by going back to it. This seems to be a lucrative method at ...
0
votes
0answers
14 views

Sheaves of Simplicial Rings?

Could someone provide me a reference for a treatment of sheaves of simplicial commutative rings? As in simplicial sheaves with a ring structure.
0
votes
0answers
18 views

Mapping cylinder of chain complexes via $-\otimes \Delta$

An instructor gave me a homework set where the mapping cylinder of a chain map $C_\bullet \xrightarrow{f} D_\bullet$ is defined as $(\Delta^1_\bullet \otimes C_\bullet) \oplus_{C_\bullet} D_\bullet$, ...
1
vote
0answers
61 views

Cardinallity increasing constructions

If we start with $\mathbb{Z}$ we can through localization get $\mathbb{Q}$, but that has the same cardinallity as $\mathbb{Z}$, so it doesn't increase cardinality for infinite sets, which is what I am ...
1
vote
1answer
44 views

Comparison of capacity of sets in $\mathbb{R}^n$

This is mainly in reference to this MSE post. Let $B_r \subset \mathbb{R}^n$ denote the ball of radius $r$ centered at the origin. Consider any set $F \subset B_1$. For all sets $\Omega \subset \...
1
vote
1answer
26 views

minimum distance of a linear codes

My question is about computing the minimum distance (weight) of a linear code. Assume that we have the generating matrix of the code. Then we can easily compute the weights of each row and of course ...