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
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1answer
20 views

Survey on large deviation bounds of queuing delay in CSMA scheduling

I am trying to do some literature survey on the theoretical guarantees in uplink scheduling algorithms. I found there exist a series of papers from UIUC and UC Berkeley by L.Jiang, J. Walrand, R. ...
0
votes
0answers
6 views

General theory of Galerkin approximations for evolution equations

I'm studying parabolic evolution equations from Lawrence Evans's book and I encounter the Galerkin method for finding weak solutions. I wonder if there is a general theory (for abstract equations on ...
1
vote
2answers
31 views

Reference book for Brownian Motion

I want to know about books for reading Brownian motion. I am aware of measure theoretic probability theory.
4
votes
1answer
69 views

Casson handles neighborhoods are representable by $D^2$-bundles over $S^2$.

On 250 page of Scorpan's book Wild world of 4-manifolds. there is a construction of an exotic $\mathbb{R}^4$. It starts from taking manifold $M = \mathbb{C}P^2 \# 9 \overline{\mathbb{C}P}^2$ and ...
3
votes
0answers
20 views

Intuition for homotopy (co)limits in triangulated categories

The following definition is taken from Daniel Murfet's Triangulated Categories Part I notes. Let $\mathcal T$ be a triangulated category with countable coproducts. Suppose we are given a ...
1
vote
0answers
21 views

Analysis for Lie groups

So my goal would be to learn some Lie algebras. I was told that I should study firstly Lie groups, I will have better picture and more motivation in mind. For now, I don't want to study it in depth. ...
5
votes
1answer
139 views

The locker puzzle - predetermined strategy

The question is related to the famous locker puzzle: The director of a prison offers 100 prisoners on death row, which are numbered from 1 to 100, a last chance. In a room there is a cupboard with ...
8
votes
5answers
114 views

$32$ Goldbach Variations - Papers presenting a single gem in number theory or combinatorics from different point of view

A short time ago I found the nice paper Thirty-two Goldbach Variations written by J.M. Borwein and D.M. Bradley. It presents $32$ different proofs of the Euler sum identity \begin{align*} ...
17
votes
10answers
2k views

Entering math through the side door [duplicate]

I am not really good at math, I'd say I'm a lot worse than good when it comes to math but I am a programmer so I have to learn to get over that fact. A lot of times if I want to implement some code I ...
1
vote
0answers
24 views

Pre-College Algebra Book

I am looking for a high school/ pre-college level Algebra book that is self contained for self-study. Nothing special, I don't want a book about number theory, but a book in preparation of high school ...
1
vote
1answer
28 views

A compact, connected, abelian Lie group is a torus?

How to prove that a compact, connected, abelian Lie group is a torus? It seems very intuitive. Any reference?
0
votes
0answers
35 views

Soviet Optimization books

I am aware of an answer on Soviet math books here: Soviet Russian Mathematical Books and the book by Boris Polyak on non linear optimization. I am also aware of a few books by Kantorovich which I do ...
0
votes
0answers
13 views

“One-sided” Morita equivalence and Hochschild homology

Suppose $A$ and $B$ are $k$-algebras. Then we have the Hochschild homologies $HH(A) = HH(A,A)$ and $HH(B) = HH(B,B)$. Now suppose that $P$ is an $A$-$B$ bimodule and $Q$ is a $B$-$A$ bimodule so ...
2
votes
1answer
22 views

Dual Cone Construction $\{z \; | \;z \perp v \text{ for some } v \in \Lambda \}$

In a linear algebra computation, in order to estimate the second eigenvalue we consider a collection of vectors. Let $\Lambda$ be a cone in $\mathbb{R}^d$ then $$ \Lambda' = \Big\{z \;\Big| \;z ...
0
votes
0answers
20 views

Representing an order relation with a real-valued function

Let $\succeq$ be a relation on a set $X$. The function $u: X\to \mathbb{R}$ represents the relation $\succeq$ if $x\succeq y \iff u(x)\geq u(y)$. I am looking for a good reference on questions such ...
1
vote
1answer
23 views

What is the name of the transform which finds the number of ways to make partitions of the given sizes?

I'm looking for the name of a transform which takes a sequence giving the number of 'prime' elements of a given size to the number of ways to make a number out of a sum of 'prime' elements, up to ...
2
votes
0answers
110 views

Kock Frobenius algebras and 2D TQFTs

My mathematical career consists of selfstudy of the first 7 chapters of Lee topological manifolds. I want to read the book Kock Frobienius algebras and 2d TQFTs. Can you suggest which books and what ...
6
votes
3answers
78 views

Arbitrarily large values for $|Li(x) - \pi(x)|$

I was wondering whether there are arbitrarily large values for the $|Li(x) - \pi(x)|$. I do know that $Li(x) - \pi(x)$ changes sign infinitely often, but this does not imply that the difference stays ...
0
votes
0answers
13 views

Reference Request for Cartier Modules, Dieudonne Modules

The question is pretty self-explanatory from the title. I'd be very grateful if someone could recommend a readable, fairly comprehensive introduction to these topics. Many thanks
3
votes
0answers
27 views

Reading references about the process of proving a theorem, or doing mathematics in general

Doing mathematics is a very unique process, that puzzles non-mathematicians. All PhD students or professional mathematicians regularly hear things like "What? There are still theorems to prove? In ...
10
votes
1answer
123 views

Is anyone talking about “ball bundles” of metric spaces?

In differential geometry: Each smooth manifold $M$ is equipped with a tangent bundle $TM,$ which is a manifold equipped with a projection back to $M$ Given a smooth map $f : M \rightarrow N$ between ...
1
vote
0answers
20 views

Finding locally and globally closing loops in a graph with toroidal topology

I have a two dimensional square lattice (with periodic boundary) with loops on it, i.e., collections of connected links which form closed loops. The lattice has the topology of a 2-torus and therefore ...
1
vote
2answers
54 views

Looking for a Great book on Proving, on Mathematical Logic in general

I'm looking for a good/great book on Mathematics. More specifically one that focuses on how I should go about to prove various things, e.g. given equations what are the methods I can use in order to ...
2
votes
1answer
20 views

Reference request on Fourier Analysis

I would like to ask for some books on Fourier analysis treating it in more abstract way (possibly more on orthogonal systems, not just focusing on the trigonometric fourier series), not the ...
1
vote
0answers
27 views

Imbedding a smooth manifold in Euclidean space - elementary proof for non-compact manifolds

The statement that there is an imbedding $$M \to \mathbb{R}^K$$ for some finite $K$ has a rather elementary proof provided that $M$ is compact. I have failed to find a proof of the same statement for ...
0
votes
2answers
26 views

Reference Request: Soft handed text on duality theory?

Can anyone recommend a text on duality theory which includes basic formulation of the primal and dual formulation and some introduction to minimax problems? Preferably having some computation in ...
2
votes
0answers
37 views

Detail regarding tangent spaces and dual varieties from Harris's Algebraic Geometry: A First Course

In Harris's Algebraic Geometry: A First Course, Example 16.20, the author shows that the dual of the dual variety $X^{*}$ is the original variety $X$. I think in chapter 15, Harris mentions that he'll ...
1
vote
0answers
59 views

Please guide me books and online materials for this course

I have recently taken Course on Numerical Analysis. It is correspondence course. So i to do self study. I will be glad if someone mentions online videos and elementary books which contains following ...
1
vote
1answer
66 views

Version of Stone Weierstrass for functions not vanishing at infinity

I am trying to see what is known about uniform density of function spaces in $C(\mathbb{R}^n)$ or $C_b(\mathbb{R}^n)$ (bounded continuous functions on $\mathbb{R}^n$). By uniform density, I mean ...
1
vote
0answers
38 views

Graph Isomorphism Algorithm of Vertex Transistive Graphs and other.

What are the best known Graph-Isomorphism algorithms for below graph classes- 1.vertex-transitive, 2. edge-transitive, 3.arc-transitive (or symmetric) 4.distance-transitive. Provide ...
1
vote
1answer
27 views

Is there a way to estimate moments of strong solution to SDE

Suppose the SDE $$\mathsf dX_t =b(t,X_t)\mathsf dt + \sigma(t,X_t)\mathsf dW_t,\; X_0 = x$$ where $t\in[0,T]$ has a strong solution. I know in general we can't find an explicit formula for the ...
0
votes
1answer
30 views

About Noether's theorem - question about how can I do such that I can study this theorem

My teacher asked me to try to write the main important steps which I have to learn such that I can understand the Noether's theorem. Some few steps are: Lagrangian Formalism Hamiltonian Formalism ...
1
vote
0answers
33 views

Looking for a reference that explains connections and curvature by double tangent space

I'm looking for a book or a set of lecture notes on differential manifolds that explain connections (Levi-Cevita connection, prinicipal connections) and curvature on an abstract manifold from the ...
5
votes
1answer
103 views

A beautiful book on arithmetic doesn't treat you like a little baby

The state of arithmetic today is disgusting. The textbooks on it are absolutely repelling, the authors treat it like a subject that will be of concern to only babies. They don't show any love, they ...
0
votes
0answers
48 views

Who are the mathematicians in US who are working on expander graphs right now?

I am familiar with only the "big" names doing this research like Gharan, Nikhil Srivastava, Dan Spielman, Jean Bourgain, Luca Trevisan, Elina Fuchs, Peter Sarnak , Amin Saberi and Terence Tao. I would ...
2
votes
1answer
51 views

Gradient descent method with random perturbation

Suppose there is a function $f:\mathbb R^n \to \mathbb R$. One way to find a stationary value is to solve the ODE $\dot x = - \nabla f(x)$, and look at $\lim_{t\to\infty} x(t)$. However I want to ...
1
vote
2answers
37 views

Notation Clarification: $M\odot N$ for von Neumann algebras $M$ and $N$

Given a Banach space $E$, $y\in E$, $\phi\in E^{*}$, I am led to the understanding that $y\odot \phi$ denotes the operator in $B(E)$ defined by $$x\mapsto \phi(x)y,\text{ for all } x\in E$$ Now I ...
5
votes
1answer
116 views

$\sin x$ as a sum involving fractional parts

Does there exist a formula giving a sense to the formal equation $$ \sin x=-\pi\sum_{n=1}^{+\infty}\frac{\mu(n)}{n}\left\{\frac{nx}{2\pi}\right\}, $$ where $\mu$ is the Möbius function, $\{\cdot\}$ ...
3
votes
1answer
35 views

Metrics on integers

I am looking for a list of distances that are defined on the set of the positive integers. I am mostly interested in metrics that make the set complete, but I also consider other metrics. Any ...
0
votes
1answer
24 views

Linear/Integer programming reference request

There are a few other similar questions out there, but I think mine is not a duplicate because I am looking for a different kind of references than most people. I am primarily a discrete ...
0
votes
1answer
42 views

Curvatures in differential geometry-interpretation

The are various notions of curvatures in differential geometry: soft such as full curvature tensor for a given connection (which is tensor of type $(1,3)$), Ricci curvature tensor (type $(0,2)$ ...
0
votes
0answers
101 views

Are Lang's books reliable?

Serge Lang wrote a lot of textbooks on mathematics. However, Goro Shimura criticized him for writing so many books containing a lot of mathematical errors(he did not mention the name of the author, ...
1
vote
2answers
40 views

Finite sums of integers and similar problems: book request

I recently learned about Faulhaber's formula, which says that for each integer $p \geq 1,$ we can simplify the finite sum $\sum_{k \in \mathbb{N}}[k<n]k^p$ so that it becomes an (integer-valued) ...
4
votes
2answers
90 views

Gluing diagrams: is it possible to glue a surface with itself in the same point? how is the diagram drawn?

I am learning the basic concepts of Topology, and playing now with the gluing diagrams (describing the fundamental domain of a topological space), this is an excerpt of a basic description I took from ...
2
votes
1answer
35 views

What is the Haar measures on $SL(2, R$ And $SL(2,R) / SL(2, Z)$?

How does one parametrize those spaces in order to do integration over them? What's a good reference for doing integral a with Haar measures over matrix groups?
3
votes
0answers
55 views

Quick question: Determinant bundle is Cartier?

$X$ is an algebraic surface (i.e. compact complex, which embeds in a projective space). $V$ is a vector bundle of rank 2 over $X$. Why is $\det{V}=\mathcal{O}_X(D)$ for some divisor $D$? Is there a ...
2
votes
1answer
38 views

Is there a summary of all rules for each type of logic?

I am learning about rules in logic and type systems and am having to piece together fragments of them from different articles and books, which makes it difficult to see the subtle differences in each ...
3
votes
0answers
21 views

What was Gauss' 2nd Factorization Method?

Reading Jean-Luc Chabert's A History of Algorithms, I learned that Gauss, prompted by the poor state-of-the-art, designed two distinct methods for fast integer factorization. Chabert's book discusses ...
2
votes
0answers
23 views

Analytic version of Hilbert's XIX problem

The famous Hilbert's nineteenth problem, initially stated in the $C^\omega$ category, was reduced by Bernstein and Petrowsky to the analogous statement in the $C^\infty$ category (and, after ...
2
votes
1answer
77 views

Intuitive functional analysis book

I want to know a functional analysis book like Terence tao's real analysis and measure theory book, full of intuition. I am aware of linear algebra, real analysis, measure theory, Probability theory.