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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14 views

Reductions of structure groups and sections of coset bundles

I'm looking for a reference for the following proposition: Let $G$ be a Lie group and $H$ a (closed) Lie subgroup of $G$. Let $E \to B$ be a principal $G$-bundle. Then reductions of the ...
3
votes
1answer
56 views

High School Geometry Text?

This year I will be teaching 8 hard-working home-educated teens a Geometry course. Back in 1994-1999 I worked full time as a High School educator, taking a turn teaching everything from Pre Algebra ...
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2answers
52 views

Reference request for Heine-Borel theorem

I would like to know a nice reference for the Heine-Borel theorem. In a text, I have the compactness argument for the following two sets. The reference should be able to cover these two cases. ...
2
votes
2answers
184 views

Problem-solving

I just finished my second year as a mathematics student at university. At university, we learn about advanced mathematics and problems. However, I'm also interested in some problems that doesn't ...
1
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0answers
19 views

Generalized Hyperbolic and Circular Functions

I have recently posted a couple of questions in regards to Generalized Hyperbolic and Circular Functions and I was hoping to find a couple more papers available on the particular subject. The papers ...
2
votes
1answer
20 views

Textbook recommendation for Complexity?

I'm interested to learn more about complexity and would like a textbook recommendation. In my undergraduate degree I've done a couple of modules on relevant topics in computational complexity. I do ...
1
vote
1answer
32 views

Where can I find “On the significance of the principle of excluded middle in mathematics, especially in function theory”?

I'm looking for L.E.J. Brouwer's article "On the significance of the principle of excluded middle in mathematics, especially in function theory". I've searched my university catalogues and every open ...
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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 ...
0
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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 ...
5
votes
1answer
141 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 ...
1
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0answers
84 views

First examples in triangulations

I am starting to study about triangulations in my algebraic topology course. We have seen the triangulation of the sphere, the closed disc and so on. Intuitively it's ok, however I couldn't find any ...
0
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0answers
19 views

Orbit closures of symmetric bilinear form

Let $A$ and $B$ be two real symmetric matrices in $M_n(\mathbb{R})$. I would like to learn about necessary and sufficient conditions for knowing when $B \in \overline{GL_n(\mathbb{R})\cdot A}$; where: ...
2
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0answers
32 views

$\Delta$-Complexes Are Hausdorff

I am using the definition of a $\Delta$-complex as given in Hatcher's book here on pg 103. Now on pg. 104, just before the section on Simplicial Homology, Hatcher remarks that if $X$ has a ...
1
vote
1answer
24 views

Lower semicontinuous integer valued function

I remember reading in some book a characterization of lower semicontinuous functions that are integer valued (for example, rank of a matrix), along the lines that it can either not jump abruptly or ...
0
votes
1answer
159 views

Book for differential equations

I generally use Rudin's book to prepare for my analysis lectures, however, we started doing Lagrange multipliers and differential equations (e.g. Picard-Lindelöf Theorem) which unfortunately isn't ...
2
votes
1answer
58 views

Good book about differential forms

I'm a looking for a good book to self-study differential forms. Particularly, I'm looking for a book that is as similar as possible to Bert Mendelson's "Introduction to topology" (i.e. a book that ...
16
votes
4answers
2k views

Status of The Triangle Book

I am interested in finding out about the current status of the planned book: The Triangle Book by John H. Conway and Steve Sigur. I understand that Steve Sigur died some time back. I got no reply from ...
1
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3answers
37 views

Is convergence in probability sometimes equivalent to almost sure convergence?

I was reading on sufficient and necessary conditions for the strong law of large numbers on this encyclopedia of math page, and I came across the following curious passage: The existence of such ...
0
votes
0answers
13 views

Sufficient conditions for integration by parts in higher dimensions

If $\Omega\subset {\mathbb R}^n$ is a bounded open set with $C^1$ boundary and $\nu$ denotes the outward unit normal to $\partial \Omega$, then the following formula holds for every pair of $C^1$ ...
4
votes
1answer
3k views

Probability of finding at least k consecutive heads in N coin tosses?

There are quite a few topics on this question already but I couldn't find a well-explained solution. Please point me towards some relevant literature or theory to analyze this problem. $K$ ...
2
votes
1answer
23 views

Omission in Jacobson's BAI regarding extension of isometries.

Suppose $V$ is a finite dimensional vector space over a field of characteristic $\neq 2$ equipped with a nondegenerate quadratic form $Q$. Witt's cancellation theorem says that if $U_1,U_2$ are ...
7
votes
2answers
159 views

Mathematics in French

I am pretty good at Français. But I learned mathematics in English. Trying to translate mathematical statements from English to French can often be accompanied with many errors because the way ...
0
votes
1answer
18 views

Permutation of a finite number of measurable functions is measurable?

Let there be a finite number of measurable functions $\{f_i\}_{i=1}^n$ with common domains of definition. Is it then true that a permutation of these functions $\{h_i\}_{i=1}^n$ also measurable? By ...
0
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0answers
23 views

Reference for Ramsey Numbers

Just wondering about diagonal Ramsey numbers $R(n)$. Can anyone provide reference on either of the following? Have there been any notable attempts to make sense of $R(n)$ by using non-combinatorial ...
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5answers
2k views

Beginner's text for Algebraic Number Theory

What's good book for learning Algebraic Number Theory with minimum prerequisites? Assume that the reader has done an basic abstract algebra course.
2
votes
0answers
50 views

$V$-bundles and vector bundles

I am looking for more information on $V$-bundles. They are hard to search for as either vector bundles come up or something like GL($V$)-bundles come up. I am looking for some nice expository ...
3
votes
0answers
60 views

Reference Request: Group Theory via the Group Action Perspective

I am looking for a higher undergraduate or graduate level textbook that introduces group actions after groups just as many textbooks introduce modules after rings. I think the semigroup/semigroup ...
1
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0answers
47 views

What families of transcendental equations do we have solved?

I'm particularly interested in transcendental equations but searching in internet gives me only results about the classical linear-exponential equation (which is solved with Lambert's W) and its ...
37
votes
3answers
1k views

Small primes attract large primes

$$ \begin{align} 1100 & = 2\times2\times5\times5\times11 \\ 1101 & =3\times 367 \\ 1102 & =2\times19\times29 \\ 1103 & =1103 \\ 1104 & = 2\times2\times2\times2\times ...
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votes
3answers
51 views

Function on $\mathbb Z^2$ whose value equals the average of values at adjacent points $\Rightarrow$ function is constant

This is a reference request. I am not asking for a proof. If I remember correctly, there is a theorem that states that if a bounded [criterion added after editing] function $f:\mathbb Z^2\to\mathbb ...
5
votes
0answers
31 views

Are the ring of integers of the constructible numbers a Euclidean domain?

I suspect that since Euclid uses the Euclidean Algorithm to perform division on constructible numbers in Elements, the ring of integers of the constructible numbers are a Euclidean Domain, but I have ...
3
votes
1answer
38 views

What is the Wedderburn decomposition of $\mathbb{R}[D_{2n}]$?

I have been looking everywhere and can't seem to find a general formula for the Wedderburn decomposition of the real group ring of the dihedral group ring of order $2n$, $\mathbb{R}[D_{2n}]$. Does ...
-1
votes
2answers
26 views

Differential Equations applications in Computer Science

I'm writing a project on differential equations and their applications on several scientific fields (such as electrical circuits, polulation dynamics, oscillations etc) but i'm mainly interested in DE ...
2
votes
1answer
73 views

Request derivative and integral problems bank [closed]

I need derivative and integral problems in many numbers (I prefer >100 questions, multiple sources are okay). Scope: Start from high school material then raise to pre-college. Derivative, ...
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 ...
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 ...
3
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0answers
42 views

Generating Sets for Subgroups of $(\Bbb Z^n,+)$.

The question Finite Generated Abelian Torsion Free Group is a Free Abelian Group led me to conjecture and prove an interesting thing about generating sets for $\Bbb Z^n$ and certain subgroups. If ...
13
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2answers
2k views

Category Theory vs. Universal Algebra - Any References?

After seeing the answer to the question Category theory, a branch of abstract algebra, I would like to ask Are there literature discussing the difference/indifference/comparison between category ...
3
votes
2answers
159 views

Modules that have finitely many submodules

Drawing the lattice of submodules of a given module helps me to gain some intuition about the structure of module. Sometimes, however, it is not possible to draw in neat manner; For example vector ...
5
votes
3answers
404 views

From a deterministic discrete process to a Markov chain: conditions?

When will a probabilistic process obtained by an "abstraction" from a deterministic discrete process satisfy the Markov property? Example #1) Suppose we have some recurrence, e.g., $a_t=a^2_{t-1}$, ...
2
votes
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. ...
2
votes
1answer
143 views

Is there any new improvement in the proof or disproof of the twin prime conjucture?

I think this is not the first question about twin primes here, but my own is the latest one! I am a postgraduate student in Mathematics interested in the field of number theory. While searching on ...
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 ...
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
226 views

Cryptography textbook

Might come as a rather strange request but does anyone know a textbook on cryptography that is small and short, say around 300 pages max. I am tired of having a sore shoulder from carrying 5 heavy ...
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.
1
vote
1answer
52 views

Special Properties of Real Matrices With Real Distinct Eigenvalues

Are there any special properties of real matrices (not necessarily symmetric) with "real" distinct eigenvalues, other than the well-known properties like being diagonalizable, which has nothing to do ...
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. ...
8
votes
5answers
115 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*} ...