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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2answers
179 views

Why Study Homological Algebra?

I'm very interested in learning Homological Algebra. But I'm not sure about the prerequisites for learning this. My current knowledge in algebra consists of Abstract Algebra (Group,Rings,Fields), ...
2
votes
0answers
45 views

Constructing $\text{Hilb}_P(X/S)$ as a locally closed subscheme of $\text{Hilb}_P(\mathbb{P}^n/S)$?

For a projective scheme $X/S$, how do I construct $\text{Hilb}_P(X/S)$ as a locally closed subscheme of $\text{Hilb}_P(\mathbb{P}^n/S)$? ($P$ is Hilbert polynomial.) Can I get a reference to this ...
4
votes
1answer
72 views

2011 USAMO Problem 3, Hexagons.

In hexagon $ABCDEF$, which is nonconvex but not self-intersecting, no pair of opposite sides are parallel. The internal angles satisfy $\angle A = 3\angle D$, $\angle C = 3 \angle F$, and $\angle E ...
0
votes
1answer
23 views

Fourier Series Relation Time - Frequency

I want to study and understand the relation between time and frequency with the help of Fourier Series. Can you indicate me some papers, or some example?
0
votes
0answers
11 views

Metropolis Markov Chain and Mixing Time

I have a statistical mechanical system, which I would like to sample with the Gibbs distribution using a Metropolis-Markov chain. I think the following are standard questions, but I am not sure what ...
1
vote
1answer
21 views

Lusin property (N) for functions of several variables

I just read in a paper by Martio and Zeimer$^1$ that smooth functions ($C^1$) of several real variables have the have the Lusin property (N). I have two questions. First, could someone give me a ...
0
votes
0answers
37 views

Does any one have a link to Jorm Steuding's Probablistic Number Theory? [closed]

I was reading it through the browser and the link on CiteSeer died. :( I will download it this time. Thanks. Regards, -EM
0
votes
0answers
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 ...
2
votes
1answer
33 views

Orbit closures of real symmetric bilinear form

Let $\alpha$ and $\beta$ be two real symmetric bilinear forms in $\operatorname{sym}(\mathbb{R}^n)$, with signatures $(p_{\alpha},n_{\alpha},z_{\alpha})$ and $(p_{\beta},n_{\beta},z_{\beta})$. I ...
0
votes
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. ...
0
votes
1answer
101 views

Is there a term called 'GRAIL'?

I've been a talk with a PhD student about some graph issue and told me about GRAIL graph and have drawn it for me as you see in the picture, however, I try to generalize so-called "Grail graph" to ...
1
vote
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 ...
0
votes
1answer
61 views
+50

Soft Question: Weblinks to pages with explanation on quadratics.

I recently placed a question based on quadratics and received a few valuable answers. One of them was a comment in an answer with a link in it which I found useful. But unfortunately the webpage (of ...
3
votes
0answers
63 views
+50

Mathematical structures textbook recommendation

I am busy doing an undergraduate course called "Fundamentals of Mathematics". It is not well-defined as there is no syllabus nor recommended textbook (there are lectures and notes), but the course ...
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 ...
0
votes
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
votes
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 ...
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 ...
2
votes
1answer
55 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 ...
0
votes
0answers
12 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 $C^1$ ...
2
votes
1answer
20 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 ...
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 ...
7
votes
2answers
155 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
votes
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 ...
2
votes
0answers
49 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
58 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
vote
0answers
45 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 ...
1
vote
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 ...
5
votes
0answers
30 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 ...
-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 ...
0
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 ...
3
votes
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 ...
2
votes
0answers
46 views

How does commutative and/or differential algebra think about total derivatives?

If we apply the "operator" $\frac{d}{dx}$ to the polynomial $xy$, we get the expression $y+x\frac{dy}{dx}.$ (Source: high school.) Thinking of $xy$ as an element of the polynomial ring ...
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. ...
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
138 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
113 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
19 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 ...