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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22 views

Anyone knows a Good Textbook in Numerical PDES

I am planning on taking a course on numerical PDEs next semester. The course covers the following topics listed below. I am looking for a good book that covers these topics (or at least most of them). ...
2
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3answers
62 views

A mathematically mature introduction to Turing Machines and Computability [reference-request]

In the computer science course for mathematicians held at my university Turing Machines have been presented very briefly. So much so that I didn't quite get why they are relevant to mathematics. I did ...
5
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2answers
87 views

Lang's Linear Algebra: what's next?

I've completed the study of Lang's Linear Algebra ($3^\text{rd}$ edition). To put it simply, I enjoyed the subject a lot and I would like to know "what's next". In other words, I would like to know ...
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1answer
31 views

character theory question [on hold]

Can you offer me some useful books in representation and character theory of finite groups?
0
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0answers
29 views

Bounds on the numbe of groups of degree n [duplicate]

What are the best lower/upper bounds on the number of (non-isomorphic) arbitrary groups of degree n? Thanks!
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0answers
6 views

A treatise on Probabilistic arguments (or even Laplace/Fourier transforms) to solve limits/integrals from basic calculus.

I've seen in some answers in Brilliant.org to some very complicated limits and integrals that uses probabilistic arguments (Let $X$ be a random variable from $[0,1]$... some examples are in those ...
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1answer
34 views

Is there a name for this result in planar geometry?

I found out that the following statement is fairly easy to prove: Let $A$, $B$ and $C$ be thee distinct points in the plane. Let $S_{AB}$ be the circle that has the line segment $AB$ as a ...
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0answers
29 views

Looking for a partial converse of Rolle's theorem

Let $f: [a,b] \to \mathbb R $ be a continuous function differentiable in $(a,b)$ such that $f(b)=0$ and for some $c \in (a,b) , f'(c)=0$ ; then under what additional conditions can we conclude that ...
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0answers
29 views

Some questions about prime divisors and no. of primes

Let for an integer $n \ge 2$ , $\omega (n)$ denote the no. of distinct prime divisors of $n$ and $\pi (n) $ be number of primes not exceeding $n$. Let $a_1,...,a_k$ be integers greater than $1$ and ...
4
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2answers
82 views

Problems whose first solutions had been using Calculus but later was shown to be done by non-Calculus methods

I was wondering about mathematical problems whose first published solutions was obtained by using methods of Calculus but later was shown (or known) to be solvable by using non-Calculus methods. ...
1
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0answers
15 views

Shifting integration variables

I'm not sure how to pose this question precisely, but I'll try. I'm trying to see what happens when you have an integral of the form $\int \mathrm{d}x \,f(x-g(z))$ and you try and write it as $\int ...
2
votes
1answer
55 views

elementary topology exercises reference

Can anyone recommend a good collection of elementary topology exercises? A pdf collection of undergraduate problem sets and homework, or midterm and final exams that I could practice on? Even a ...
2
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1answer
29 views

Proof of Steinitz Theorem

I want a source containing the proof of Steinitz Isomorphism Theorem stating: For any Dedekind domain $R$ and any two nonzero ideals $I$ and $J$ of $R$ we have $I⊕J≅R⊕IJ$. Thanks!
0
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0answers
6 views

What is the formula for the 2-sample Anderson–Darling upper tail test?

There are computationally simple formulas for the Anderson–Darling test between an analytic distribution and an empirical distribution, as well as for the Anderson–Darling upper tail test (again ...
1
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2answers
65 views

Is there a classification of regular maps $\mathbb{P}^1(k)\to\mathbb{A}^1(k)$?

If $\mathbb{P}^1(k)$ and $\mathbb{A}^1(k)$ are the projective line and affine line, respectively, over an algebraically closed field $k$, is there any known classification of the regular maps ...
0
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1answer
59 views

math books of undergraduate/graduate level without formula? [on hold]

Just wondering, is there a math book talks deep into the math ideas (maybe undergraduate or graduate level, so not the pre-algebra content), but comes with no or very few formula?
2
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0answers
31 views

Is there a name for this class of graphs?

Consider the graphs $G=(V,E)$ where there exists a non-empty $S \subseteq V$ such that $G[S]$ is a complete subgraph and every possible edge between $S$ and $V\setminus S$ is present in $G$. ...
1
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1answer
42 views

Base change for Quot-scheme

I am reading the book of Huybrechts and Lehn "The Geometry of Moduli Spaces of Sheaves" with an aim to become a little bit familiar with this topic. Now I am trying to understand what is ...
13
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3answers
276 views

Every invertible linear transformation can be perturbed a bit without destroying invertbility, Neumann series

Let $T: V \to V$ be any linear transformation on a real or complex vector space $V$. Show that there exists $\epsilon_0 > 0$ $($depending on $T$$)$ so that $I + \epsilon T$ is invertible for any ...
0
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0answers
49 views

What is some reason that there are no book bridge the gap of these three books

I am referring to the (beginner's text- Stochastic Calculus by Mircea Grigoriu and Introduction to Stochastic Calculus by klebaner.) and the advanced texts - stochastic differential equation by ...
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1answer
29 views

Reference: Bethe Ansatz Equations

Could someone show me good references to find solutions of the Bethe Ansatz Equations, for simple cases (using algebraic geometry or others interfaces with mathematics)? For example in the case of ...
0
votes
0answers
32 views

What are some elementary books which discuss projective lines on surfaces with examples?

I have the books: W. H. Blythe, On models of cubic surfaces (1905) and A. Henderson, The twenty-seven lines upon the cubic surface, and a couple more modern algebraic geometry books including I. R. ...
9
votes
2answers
119 views

How to select the right books?

As the saying goes, "Give a man a fish, feed him for a day. Teach a man how to fish, feed him for life." I've always had a problem with selecting appropriate books. It could be a problem that I'm a ...
9
votes
1answer
138 views

Source of Hardy-Littlewood's 2nd Conjecture

In what paper do Hardy and Littlewood first mention, specifically, their 2nd conjecture? It is not mentioned specifically in Partitio Numerorum III. This conjecture is usually expressed as ...
3
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0answers
52 views

A name for the automorphisms induced by the normalizer by conjugation?

Let $N$ be a subgroup of a group $G$, $H := \operatorname{N}\left( N \right)$ the normalizer of $N$. There is a natural morphism from $H$ to $\operatorname{Aut}\left( N \right)$ given by $h \mapsto ...
6
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2answers
42 views

Gallian: is it true that the well-ordering principle can't be proven from properties of arithmetic?

I just started reading Gallian's Abstract algebra and on page 3 it says "An important property of the integers...is the so-called Well Ordering Principle. Since this property cannot be proved from the ...
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0answers
72 views

Understanding infinity [on hold]

I want to understand in a greater depth the concept of infinity. Can someone give me any reference/ text from where I can study and understand about the concept of infinity in mathematics? I would be ...
4
votes
1answer
40 views

Jones Polynomial from Statistical Mechanics

I've been told that, given a knot projection, there is a way of associating a statistical system in such a way that the partition function of the system corresponds to the Jones polynomial of the ...
5
votes
0answers
78 views

A More Advanced Version Of Aluffi

Paulo Aluffi's Book, Algebra, Chapter 0 aims to teach basic algebra from a categorical viewpoint. The first chapters of the book, however, introduce groups and rings using very basic categorical ...
0
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0answers
30 views

Integration by parts in Sobolev space

I'm looking for a reference of the following fact (if it is true...): if $u\in W^{1,1}(\Omega)$ and $v \in W^{1,\infty}(\Omega)$ ($\Omega$ a open subset of $\mathbb{R}^n$ ($n \ge 1$) with a regular ...
0
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0answers
46 views

Statistical research question [on hold]

I'm preparing for an exam and I came across this question in a book. An experiment is done to examine ways to detect phlebitis during the intravenous administration of a particular drug. Phlebitis ...
4
votes
1answer
59 views

Is there a “unifying framework” for harmonic analysis?

Recently, I was exposed to a basic harmonic analysis course. Although the course is almost over, I still can't put my finger on what harmonic analysis is about. I have a vague idea that it is ...
4
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1answer
51 views

If a nilpotent group $A$ act on a group $G$ then $G$ is solvable.

Theorem: If a nilpotent group $A$ act on $G$ by automorphism and $C_G(A)=e$ then $G$ is solvable. I hope that the statement of theorem is true. It should belong to Hartley, but when I googled it I ...
3
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0answers
42 views

Reference request for studying on Fiber bundles

I am looking for some material (e.g. references, books, notes) to get started with Fiber bundles and vector bundles. Can someone help me? Thanks.
0
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0answers
21 views

Reference about $p$-homogeneous functions

I'm looking for a book about $p$-homogeneous functions. I am particularly interested in the associated (nonlinear) eigenvalue problems. However, a reference containing most of the known properties of ...
2
votes
1answer
51 views

Ways of proving that $A=0$

I was solving a problem where you had to prove that some number $=0$. My strategy was to show that $Ak=A$ for some $k$ not equal to 1, hence $A(k-1)=0$ from which it follows that $A=0$. Abstracting ...
4
votes
3answers
56 views

Reference for $(\infty,1)$-Categories

I am looking for an organized source from which I can learn about $(\infty,1)$-categories. I am unable to learn the concept from the $n$lab alone. Here it is said that Lurie called ...
0
votes
0answers
49 views

Book/lecture notes on algebraic curves

Although there surely is plenty of references on MSE about algebraic curves, my need are very specific and so I will open this topic anyway. I follow this year a course on (hyper)elliptic curves ...
2
votes
1answer
18 views

A more general Bessel Function

I am reading a paper where the author considers the more general Bessel equation $$x^2y'' + c_1xy' + (c_2x^{\alpha} + c_3)y =0.$$ The solutions are given, referencing some archaic text that my ...
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votes
1answer
31 views

Good, free source for counting (combinations, permutations) and/or probability?

I'm a freshman CS major and find both of these topics really interesting, but I also find them difficult (I've been told this isn't much of a surprise!). I was hoping some of you could direct me ...
3
votes
1answer
126 views

When does the Putnam release solutions to this year's exam? Has anyone released their own solutions?

I was just wondering when the Putnam committee releases the solutions to this year's exam or if anyone has posted their own solutions.
3
votes
1answer
31 views

Prerequisites for Hartshorne: Euclid and beyond?

as the title suggests, I am looking for the prerequisites to Hartshorne's Euclid and beyond. I just found this book and I think it's wonderful, but the downside is that I only know math up to single ...
0
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0answers
34 views

Nullifying columns of a matrix by nullifying rows

Let $A$ be a real rectangular matrix. Each column of $A$ is a nonzero vector. Now each row of $A$ is nullified with probability $p$, all independently of each other. What is the probability that ...
3
votes
1answer
56 views

Examples of applications of category theory to chemistry

What is some simple application of category theory to chemistry, namely, something that is much easier to do in chemistry with category theory than without. It does not need to be bleeding edge, or to ...
3
votes
1answer
71 views

Castelnuovo-Mumford regularity of Cohen-Macaulay modules

Let $S=K[X_1,\ldots,X_n]$ and $M$ be a Cohen-Macaulay $S$-module. This equality holds $$ \operatorname{reg}(M)=\dim(M)+\max\{i\in\mathbb{Z}\colon P_{M}(i)\neq H(M,i)\}. $$ It's been proved in ...
1
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0answers
45 views

Are there any articles (or otherwise) that discuss the idea that the set-theoretic universe should be as “free” as possible?

Question. Are there any articles (or otherwise) that discuss (and perhaps attempt to formalize) the idea that the set-theoretic universe should be as "free" as possible? Discussion. ...
1
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1answer
78 views

Is this a good abstract algebra text?

I will start university next year and I want to prepare for abstract algebra. I was recommended a book called "basic abstract algebra, by Jain, Nagpaul et al", but I don't know how good this is for a ...
2
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1answer
62 views

Homotopy Type Theory prerequisites.

I've done some undergraduate level study of algebraic topology (most Hatcher's book) and the smallest amount of type theory in a foundations of mathematics course. Homotopy type theory sounds amazing ...
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7answers
123 views

Good Pre-Calculus book?

I was reading this article and the author mentioned I should come here and get some advice. I'm 17, currently taking Pre-Calc in high schooling doing really good, but I feel like I'm not getting the ...
2
votes
0answers
14 views

Motivation behind automorphism bases?

Given a model $\mathcal{M}$ with a domain $M$ and $B \subseteq M$, $B$ is an automorphism base for $\mathcal{M}$ iff $\forall f \in Aut(\mathcal{M}). (\forall b \in B. f(b)=b) \implies f = ...