This tag is for questions where the poster seeks references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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7 views

What is spectrum for Laplacian in $\mathbb{R}^n$?

I know very well that Laplacian in bounded domain has a discrete spectrum. How about Laplacian in $\mathbb{R}^n$?(not in some fancy-shaped unbounded domain, but the whole domain) Where can I find ...
0
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1answer
23 views

What the best math books/articles by topic and level? [on hold]

This question is modeled on Classical texts that should not be missing from any shelf but I changed the wording as I was not interested in the 1 decade requirement. I always enjoyed good ...
3
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2answers
47 views

Frattini subgroup of a finite group

I have been looking for information about Frattini subgroup of a finite group. Almost all the books dealing with this topic discuss this subgroup for p-groups. I am actually willing to discuss the ...
3
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3answers
53 views

Prerequisite for Petersen's Riemannian Geometry

A professor recently told me that if I can cover the chapters on curvature in Petersen's Riemannian geometry book (linked here) within the next few months then I can work on something with him. ...
3
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0answers
28 views

Suggestion about Algebraic Topology talk

following the content of the title I am writing here to ask some suggestions concerning a talk I will be presenting at my university in a week or two. The main topic I chose is the fundamental ...
0
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0answers
9 views

Unitary Farey Sequence Matrices

Take the Farey sequence $\mathcal{F}_n$ with values $a_m\in \mathcal{F}_n$ and put them into a vector $$ \vec v_k=\frac1{\sqrt{|\mathcal{F}_n|}}\biggr(\exp(2\pi i k a_m)\biggr)_m $$ The dimension of ...
2
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1answer
33 views

Ring structure on $Ext$ and $Tor$

Wikipedia says that in certain situations, $Ext^\ast_A(R,R)$ becomes a ring, such as when $A$ is an augmented $R$-algebra, but the outline is too sketchy for me to understand. I can't find this in ...
1
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0answers
16 views

Question about definition of some classes of bimodules.

Suppose that we have a ring $R$ and a $R$-$R$ bimodule $M$ such that: For every $r\in R$ and $m\in M$ there exists $r'\in R$ such that $mr=r'm.$ I want to know if there is a name for this kind of ...
1
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0answers
56 views

Errors of Euler interpretation? [on hold]

To complement the recent post on Euler's errors, I would pose the following question: what common errors of Euler interpetation appear in the literature? What errors are attributed to Euler's work in ...
2
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0answers
40 views

categorification and linear algebra

Vect is the category with objects as vectors and arrows as linear transformations between them. Then these arrows have quite a bit of structure. We can take the transpose, trace, determinant, ...
22
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4answers
2k views

Euler's errors?

What mathematical errors is Leonhard Euler known to have made? PS: As I wrote in a comment below: "However, I would not consider proof to be an error merely because it's not a proof by present-day ...
2
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0answers
33 views

The automorphism group of the real line with standard topology

How much is known about the automorphism group of the real line with the standard topology? Can it be described by a set of generators? I've been told that $\mathbb R$ has many weird and unexpected ...
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0answers
16 views

Distributive lattices (interpretation of distributivity)

Simple counter example Ok, there is a very simple counter-example ^^ : This lattice isn't distributive, because $M=x\wedge(a\vee b)=x>0=(x\wedge a)\vee(x\wedge b)=m$, but for all $n<N$ the ...
2
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2answers
72 views

Logic and number theory books

I've recently decided to start preparing for uni, so I figured I need to learn logic and some number theory. I picked up Burton's Elementary Number Theory and wasn't quite comfortable with it, seemed ...
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2answers
19 views

Joint Game Theory?

I am confused. A Game is, generally, defined by: $\mathcal{G}=(\mathcal{P}, \mathcal{A}, \mathcal{U})$ where $\mathcal{P}$ is the set of players, $\mathcal{A}$ is the set of actions $\mathcal{U}$ is ...
2
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0answers
32 views

Good topologies on $\mathcal{P}(X)$

Let $X$ be a topological space, and let $\mathcal{P}(X)$ (resp. $\mathcal{P}_0(X)$) be the set of all subsets of $X$ (resp. the set of all non empty subsets of $X$). Finally, let ...
1
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1answer
48 views

Examples for intensional set theories.

The normal set theory of todays mathematics (ZFC) is extensional, i.e. it has the axiom of extensionality $$\forall A \, \forall B \, ( \forall X \, (X \in A \iff X \in B) \Rightarrow A = B)$$ Are ...
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1answer
87 views

First usage of the symbol ∈

Concerning a book [1] I am reading the symbol $\in$ was first used by Giuseppe Peano and is the first letter $\epsilon$ (epsilon) of the word ἐστί (means "is"). Does anyone know in which work of Peano ...
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0answers
7 views

Polytopes generated as the convex hull of the orbit of a finite reflection group acting on a given vector

Consider a finite reflection group acting on $\mathbb{R}^N$. Pick a vector $x \in \mathbb{R}^N$ and look at the convex hull of its orbit. This is a polytope. There are some interesting particular ...
1
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1answer
38 views

Request for online reference to Hamilton's “The Ricci Flow on Surfaces”

Does anyone know of an online source for Richard Hamilton's paper "The Ricci Flow on Surfaces?" I've searched Google for it and it doesn't seem to give any results.
1
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1answer
27 views

What are the roots of unity quadratic integers?

The article of Roots of unity in wikipedia implies that the following roots of unity are quadratic numbers: $$ \{\pm 1\}, \{\pm 1,\pm i\}, \{\pm 1,\pm \zeta,\pm \zeta^2\}. $$ where $\zeta=\exp(2\pi ...
2
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1answer
37 views

Got stuck with this $L^2(-1, 1)$ optimization problem. Any ideas where it comes from?

Statement Let $u(x) \in L^2(-1, 1)$. Solve the following optimization problem: $$ \begin{cases} J(u) = 4 \int_{-1}^{1} \sqrt{|x| (1 - |x|)} u(x) dx + \left(\int_{-1}^1 \sin(3\pi x) u(x) dx\right)^2 ...
0
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1answer
20 views

Sylvester domains

I'm an undergrad mathematics student and I'd like to request some books about Sylvester domains. Specifically I'd like to understand the fact that not all modules are Sylvester domains. I just proved ...
1
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1answer
36 views

Primitive elements for $K=\Bbb{Q}(\sqrt{2},\sqrt{3})$

The key lemma for proving the primitive Element Theorem (for finite extension of a field $F$ with characteristic $0$) in Artin's Algebra (2nd edition) is the following: Suppose $char F=0$ and ...
2
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0answers
39 views

A few identities on differential forms

I just started studying differentiable manifolds, and I've encountered a few allegedly simple questions that aren't really simple to me. If possible, I'd be very happy to see full proofs (without ...
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0answers
9 views

what does well posdeness results tells us concerning non linear evolution equations?

Consider a nonlinear Shr\"odinger equation, $$iu_{t}+\bigtriangleup u + f(u)= 0, u(0)= u_{0}$$ where $u(t, x)$ is complex valued function of $(t,x) \in \mathbb R \times \mathbb R^{n}$, $i=\sqrt{-1}, ...
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0answers
7 views

deterministic limit of gaussian distribution

Let $a$ be a random variable over some set $A$, and let $\mathcal A \subseteq A$ be an event. Let $\mathcal E \subset \mathbb R^n$ be another event, and let $x_1, \dots, x_n$ be several Gaussian ...
6
votes
1answer
91 views

Which textbook of differential geometry will introduce conformal transformation?

Which textbook of differerntial geometry will have these formulas about conformal transformation? $$\tilde g_{ij} = e^{2\varphi}g_{ij}$$ $$\tilde \Gamma^k{}_{ij} = \Gamma^k{}_{ij}+ ...
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0answers
20 views

Basic questions about descriptive complexity

I'm trying to learn descriptive complexity, and I'm having trouble on a basic level wrapping my head around what it means for a logical formula to define a computational language. I've tried and ...
5
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9answers
372 views

Good Textbooks for Real Analysis and Topology.

I'm currently in my 3rd year of my undergrad in Mathematics and moving onto my 4th year next year. I took a course in Real Analysis I, but the professor was very confusing and we didn't use a textbook ...
7
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1answer
88 views

How to learn inequalities and become good at proving them?

I am taking a real analysis course next year and I want to start slowly preparing for that class now, so I hope you can help me. The class is quite challenging and the fail rate is relatively high. ...
1
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1answer
46 views

Nonorientable surfaces: genus or demigenus?

The genus $g$ of a closed, orientable surface is the maximum number of disjoint simple closed curves that can be drawn on the surface without disconnecting it. In terms of the Euler characteristic, ...
1
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1answer
29 views

Video lectures and reference book Multivariable calculus

I am in a particular situation that I am doing Master's in a Computer Science related degree, and I would like to take the course on Convex Optimisation which is taught by the Machine Learning ...
0
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0answers
11 views

Book recommendation for introductory algebraic combinatorics?

Preferably: It should have plenty of motivation (as I am self-learning). It should not be skimpy on proofs (as I am self-learning), but perhaps I can make do since I can ask questions elsewhere. It ...
2
votes
1answer
59 views

Easy to read books on Graph Theory

I was asked to read about Graph Theory. First got the book "Graph Theory with Applications" by Bondy and Murty. As a Computer Science student its becoming difficult to read and understand. Then I ...
1
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0answers
35 views

Generalizations of results on the sum of divisors function over $\mathbb{Q}$ to number fields

Consider the sum of divisor function $$ \sigma_0(n) = \sum_{d\mid n} 1. $$ This is known to satisfy $\sum_{n\leq x} \sigma_0(n) = (x\log x)+2\gamma x+\mathcal{O}(\sqrt{x})$. If, instead, we shift the ...
2
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1answer
50 views

What sort of algebra is this?

Let us say that I have a set of symbols, $S$. The symbols can be operated on by a set of $n$-ary operators, $O$. Importantly, some of these operators are in the set of symbols, i.e. $S \cap O \neq ...
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0answers
37 views

Enlightening books giving a guided tour of mathematics, in a style that Gian-Carlo Rota would not mind?

I am currently reading Gian-Carlo Rota's Indiscrete Thoughts. What more can I say apart from "the man can write"? (In other words, you should really read it if you are interested in mathematics.) I ...
2
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5answers
144 views

Book recommendation for Linear algebra.

I am looking for suggestions, it has to be a self study book and should be able to relate to applications to real world problems. If it is more computer science oriented , that would be great.
4
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7answers
483 views

Interesting calculus problem advice [on hold]

Can someone suggest a really hard calculus problem that can be solved with the knowledge of a high school student ? I would really like to work my brains on something interesting . Thanks a lot !
0
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0answers
26 views

Introductory material on discrepancy theory

I'm interested in learning about discrepancy theory. By this I mean material such as http://math.mit.edu/classes/18.095/lect6/notes.pdf . However, I've been unable to get much from "Chazelle, ...
1
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0answers
31 views

Nagata Smirnov Metrization Theorem

I am looking for a proof for Nagata-Smirnov Metrization Theorem, but I couldn't find one that is readable. I found the paper by Nagata written in 1954 but it is unreadable and uses old notation. ...
2
votes
5answers
128 views

Reference Book on Special Functions

Now I'm studying the topic that uses the special functions frequently, so I find myself in need for some good reference book on the properties and equalities of the special functions. The optimal one ...
1
vote
1answer
22 views

How to solve this problem? Distributed Game theory?

I have this problem: We dispose of some resources, say $\{f_1, f_2, \dotsc, f_m\}$; We have some agents or players, say $\{\mathrm{p}_1, \mathrm{p}_2, \dotsc, \mathrm{p}_n\}$; Every player has some ...
3
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0answers
53 views

Saddle point method: a rigorous proof?

I am trying to prove in a fully rigorous way the Saddle Point method for holomorphic functions of 1 complex variable. In books I find only complicated general statements or non-rigorous proofs. Hence ...
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0answers
49 views
+50

Book suggestions on projective geometry

I want to be acquainted with projective geometry, so I'm asking for a reference. I need some words to explain my specific background and motivation. There are many things I learnt related to ...
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2answers
130 views
+50

A conjecture relating Multiple Zeta Values and the Polya Enumeration Theorem

Let me state my motivation. I believe that the Polya Enumeration Theorem and Multiple Zeta Values (the classic being the Basel problem and the values of the Riemann zeta function at the even ...
0
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1answer
33 views

Recommend resources on dynamical systems and singularities

I'm looking for resources on bifurcation theory and systems of non-linear differential equations, but am very particular about the way it is taught/explained. I would like the approach to be based on ...
10
votes
6answers
841 views

Mathematics needed in the study of Quantum Physics

As a 12th grade student , I'm currently acquainted with single variable calculus, algebra, and geometry, obviously on a high school level. I tried taking a Quantum Physics course on coursera.com, but ...