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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19 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. ...
5
votes
2answers
84 views

How to select the right books? [on hold]

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 ...
6
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0answers
40 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.
3
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0answers
42 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
votes
2answers
39 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 ...
1
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0answers
70 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 ...
3
votes
1answer
33 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
72 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
22 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
53 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
votes
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
20 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
55 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
45 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 ...
-1
votes
1answer
30 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
124 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
30 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
53 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
68 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
44 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
votes
1answer
51 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 ...
5
votes
7answers
120 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 = ...
3
votes
2answers
110 views

Is “mixed math” a useful way to learn math?

I was reading a book about how mathematics was taught in Cambridge in the 19th century, and it struck me how much physics was included in the syllabus, and it wasn't optional but everyone had to learn ...
1
vote
2answers
73 views

References for Riemann Hypotheis giving the best bound for Prime Number Theorem

Which books cover the proof that Riemann Hypothesis is equivalent to the best error bound for the Prime Number Theorem? My understanding is that Riemann Hypothesis is equivalent to the best bound of ...
2
votes
1answer
88 views

Learning math by asking question here. [closed]

How do you learn math in general? I saw today that I learned much better by asking three questions here than by trying to find the answers alone. Also, the teachers often don't understand my questions ...
0
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0answers
18 views

Orbit closure is uncountable, unless there is a periodic element.

Let $a = (a_i)_{i \in \mathbb N}$ be a sequnece over some finite alphabet $\Sigma$. We may define on the space $X = \Sigma^{\mathbb N}$ a shift operation by $(Sx)_i = x_{i+1}$. Let $A$ be the orbit ...
0
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0answers
10 views

Verification and presentation of anisotropic sobolev space results

Hi I am interested anisotropic Sobolev spaces. Can someone with knowledge of this topic check if the following is correct in presentation. I am finding it hard to find a good book which deals with the ...
27
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7answers
4k views

Genius mathematicians who never published anything

Amongst philosophers, Socrates is an example of a genius with a great influence on human history who never wrote anything. Almost all facts which are known about his revolutionary ideas are written by ...
5
votes
1answer
82 views
+50

Good source on current 'views and thoughts' on mathematics

Recently I've become interested in the history of the way people think about mathematics. What I mean by this is for example how Godels proof basically put an end to the whole school of thought ...
8
votes
1answer
116 views

“Novel” proofs of “old” calculus theorems

Every once in a while some mathematicians publish (mostly on the Montly) a new proof of an old (nowadays considered "basic") result in analysis (calculus). This article is an example. I would like to ...
1
vote
1answer
78 views

Moving frame in a semi-Riemannian manifold

Can someone point me some reference for the moving frame theory in semi-Riemannian manifolds, using differential forms? In special, I'm looking for a version of Cartan's structural equations. I've ...
1
vote
1answer
38 views

A book with heuristics or general techniques used in real analysis?

I have been looking for a book with some good heuristics for real analysis and point set topology. Any ideas?
2
votes
0answers
45 views

Weight of topology related to sizes of open sets?

I'm wondering if there is a notion relating the weight of a topological space (=minimal base cardinality) to the sizes of its open sets. In particular I'm looking for properties of spaces, whose ...
1
vote
2answers
41 views

About the Erdős-Borwein Constant

The Erdős-Borwein Constant can be found in http://mathworld.wolfram.com/Erdos-BorweinConstant.html My question is : Is there is a document or website containing the value of $E$ with a bigger number ...
1
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0answers
29 views

Reference for Analytic Number Theory

Are there any good video lectures available on Analytic Number Theory? I have a decent background of complex analysis but I have just started Analytic Number Theory.
3
votes
2answers
55 views

Galois theory reference request

I ran into the following description of Galois theory in Gelfand and Manin's Methods of Homological Algebra. But this looks like nothing like the Galois theory I know that deals with subgroups and ...
3
votes
4answers
186 views

Formula for $1! \times 2! \times \cdots \times n!$?

Are there any useful forms for the expression $1!\cdot 2!\cdot 3!\cdot ...\cdot n!$? I'm trying to solve a problem that involves this expression and thought it might help to find a more "workable" ...
0
votes
1answer
23 views

About a Morrey's type inequality

Let $\Omega \subset R^n$ an open bounded domain and consider $B_r(x_0) \subset \Omega$ an open ball. Let $u \in W^{1,p}(\Omega)$ ($p \geq 2$). Let $s > n$ and suppose that $\int_{B_r(x_0)} |\nabla ...
0
votes
0answers
13 views

Fundamental group and Fuchsian group

We know that the fundamental group of a compact surface of genus larger or equal to 2 is a Fuchsian group, i.e. a discrete subgroup of the automorphism group of the hyperbolic plane PSL(2,R). And any ...
1
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0answers
46 views

An elementary Algebraic Geometry text, similar to Kempf's Algebraic Varieties

Is anyone familiar with an elementary Algebraic Geometry book, which takes a similar approach to that of Kempf's Algebraic Varieties, but is more user friendly ?
0
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0answers
22 views

Treatments of probability that gives the subject justice

I was watching a Joe Blitzstein lecture the other day on conditional expectation (https://www.youtube.com/watch?v=gjBvCiRt8QA). Mr Blitzstein noted a remarkable way of thinking about expectations, ...
0
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0answers
16 views

Criterion for $\mathcal{O}_{Y,X}\cong\mathcal{O}_{Y',X'}$ for $Y,Y'$ closed, irreducible subvarieties.

Suppose you're working over an algebraically closed field $F$, and let $X$ and $X'$ be quasi-affine varieties, with $Y\subseteq X$ and $Y\subseteq X'$ closed, irreducible subvarieties. I read the ...
4
votes
1answer
140 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 ...