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.
1
vote
0answers
13 views
Ask book to deeply understand partially ordered sets
I learn little about ordering and poset before, but I think it's not enough and want to learn more about ordering and Poset. Can anyone please recommend some best books to learn about this topic. I ...
1
vote
1answer
17 views
Split multiplicative reduction question
Let $E/\mathbb{Q}$ be an elliptic curve and $E_{d}$ be the quadratic twist of $E$ by a squarefree integer $d$. Let $\ell$ be a prime of multiplicative reduction for $E$. If $(d, \ell) = 1$, then ...
6
votes
4answers
72 views
Modify the rules of Gomoku (Five-in-a-row) or Connect Four type games to enforce the fairness among players
One colleague and me were discussing this problem during lunch today, and I did a little bit digging for several hours after returning to my office.
Fact: For an $(m,n,k)$-game, there does not exist ...
6
votes
0answers
55 views
Mathematics of Torrenting
It is more or less common knowledge that a bittorrent network has the potential to be much faster than direct downloads, but I have never seen any real math describing why, or any theoretical bounds ...
2
votes
1answer
45 views
Tails of family of integrable functions
It is well known that tail of an integrable function on $\mathbb{R}^d$ is small, i.e., Given $\epsilon>0$, there is $R>0$ such that $$\int_{\{|x|>R\}}|f(x)|dx<\epsilon.$$
I was wondering ...
2
votes
1answer
52 views
Topics to Study and Books to Read?
I'm an undergraduate studying materials science and engineering with a concentration in polymer science. I would like to go to graduate school and focus on theory and computation of synthetic polymer ...
2
votes
4answers
52 views
Differential Equations Reference Request
Currently I'm taking the Differential Equations course at college, however the problem is the book used. I'll try to make my point clear, but sorry if this question is silly or anything like that: the ...
2
votes
0answers
25 views
Looking for online matlab-based differential equations course/text.
I am looking for an online ODE course that would be matlab/project-oriented. A full online text/course in the spirit of this linear algebra text is preferred.
I know about the following
CODEE and ...
2
votes
1answer
35 views
inequality applied to Matrix possible?
My question is this : when is it possible to apply (if at all) a polinomial inequality like this little inequality conjecture ,for example, to a $n\times n$ Matrix $A$ (change the variable $x$ with ...
1
vote
1answer
41 views
How to find instances when $d(a,b) = p^2$ for $p$ a prime.
Suppose I have a dimension formula (for a Lie algebra representation) given by
$\mathrm{dim}_{a,b} = {(a+1)(b+1)(a+b+2) \over 2}$. I now would like to find pairs $(a,b)$ where $\dim_{a,b} = p^2$ for ...
1
vote
1answer
41 views
Is there a text book containing a self-contained and complete proof of the Jordan Curve theorem?
I seem to remember (in my undergraduate years) encountering a book on complex analysis which contained a proof of the Jordan Curve Theorem, building up from first principles - so self-contained and ...
12
votes
1answer
103 views
Why is the dimension of $SL(2,\mathbb{H})$ equal to $15$?
Let me ask a very basic question which is inspired by reading M. Atiyah's "Geometry and physics of knots". Could you explain me (or give a reference to) the definition of the special linear group ...
3
votes
1answer
73 views
Grothendieck topology on pre/sheaves
Given a Grothendieck topology $T$, say subcanonical, on a category $C$, we are able to talk about sheaves in $(C, T)$. Since pre/sheaves can be viewed as generalized objects of $C$ (via Yoneda ...
0
votes
0answers
34 views
Do you have a good source for the determinant of the multilinear operator?
I want to calculate the determinant of the multilinear operator. Do you have a good source for my questions that could help me? Thanks.
1
vote
2answers
56 views
Proving Bijections in $\mathbb{R}^n$
I have a question that may seem trivial or silly, however I'll try to make my point clear. I'm a student of Mathematical Physics and unfortunately my college doesn't offer a set theory course, so that ...
4
votes
3answers
44 views
Introductory/Intuitive Functional Analysis Book
Can you recommend a gentle introduction to the abstract thinking and motivation of functional analysis? I'm looking for a book that holds you by the hand and shows the details of exercises, etc.
...
3
votes
1answer
28 views
Introductory text on voting theory
Some years ago I read about a famous theorem by K. Arrow on rank-order voting systems. My interest in voting theory topic has been spurred by the use of MeekSTV in our moderator elections.
As such, ...
2
votes
1answer
42 views
What subjects should I study to learn about eigenfunctions? What good textbooks would you recommend for learning the subject?
I googled eigenfunction and look it up in wikipedia, but still I do not know where I should start to learn the subject. I have two questions, and allow me to repeat the title of this question.
What ...
1
vote
2answers
35 views
Improvment of $W^{1,p}$ regularity of a elliptic equation solution.
I'm looking for some reference for results like
$$ \mbox{div}(A(x) \nabla u) = 0, \ \ u \in H^1=W^{1,2} \Rightarrow u \in W^{1,p}, p>2 $$
where $A(x)$ is elliptic, this is, $Id\lambda \le A(x) \le ...
0
votes
0answers
20 views
Cachazo-Douglas-Seiberg-Witten conjecture.
In order to know what is Chacazo-Douglas-Seiberg-Witten conjecture I'd like to try to read the article of Kumar "On the CDSW conjecture for simple Lie algebras". What books give me a strong basis for ...
3
votes
1answer
36 views
A short exact sequence of groups and their classifying spaces
Suppose that we have a short exact sequence of topological groups:
$$1 \to H \to G \to K \to 1.$$
I have found some papers mentioning that the above sequence induces a fibration:
$$BH \to BG \to BK.$$
...
3
votes
2answers
112 views
Sums of powers being powers of the sum
I'm looking for literature on solving problems of the form
$$
n_1^\alpha+\cdots+n_k^\alpha=(n_1+\cdots+n_k)^\beta
$$
for positive integers $n_1,\ldots,n_k$ and fixed parameters $k$ and ...
1
vote
0answers
33 views
Helly's selection theorem
Can someone guide me to a reference (preferably open access online) stating and proving Helly's selection theorem for sequences monotone uniformly bounded functions on $[0,1]$. Something that can ...
1
vote
1answer
33 views
What kind of functions can be moment-generating functions for a random variable?
Given an infinitely differentiable function $ g: \mathbb{R} \rightarrow \mathbb{R}$, can we always find a distribution function $f_X$ of some random variable $X$ so that
$g(t) = \int_{-\infty}^\infty ...
2
votes
2answers
72 views
Study of Set theory: Book recommendations?
Can you suggest a good book for set theory?
I have just started reading about Group theory and want to learn set theory on my own.
Thanks in advance
1
vote
0answers
20 views
Simplification of Kampé de Fériet function
I was dealing with a convolution type integral
$$
\int^z_0 t^m {}_0F_1(;1;-t) \: {}_2F_3\Big( 1,1;2,m,m+1 ; -a t\Big) \:\mathrm{d}t
$$
By applying one of the identities in Exton's book, the solution ...
6
votes
2answers
59 views
Good book on topological group theory?
I'm looking for a good introduction to the theory of locally compact groups and their representations. It may assume the reader to be familiar with basic group theory, topology and measure theory.
1
vote
0answers
18 views
Chern Character Isomorphism for non-CW complexes
Atiyah and Hirzebruch showed in their paper "Vector bundles and homogeneous spaces" that $\mathrm{K}^\ast(X) \otimes \mathbb{Q} \cong \mathrm{H}^\ast(X; \mathbb{Q})$, where $\mathrm{H}^\ast$ denotes ...
-4
votes
0answers
40 views
Find ebook A.V. Pogorelov, “Foundations of geometry”. [closed]
Can you help me find ebook : A.V. Pogorelov, "Foundations of geometry" , Noordhoff (1966).
Or book write about axoxiom systems Pogorelov in Euclidean geometry.
3
votes
0answers
59 views
looking for reference or nice proof of trig lemma
Math people:
I am looking for a reference or a nice proof of the following fact. I have proven it myself, but my proof is messy: let $\theta \in (0,1]$ and $\alpha \in (0, \frac{1}{2}\theta^2]$. ...
1
vote
1answer
27 views
Good introductory book for self-studying quasigroups?
I'm looking for an undergraduate or beginning graduate level text from which to self-learn quasigroup theory. An emphasis on using quasigroups to understand the structure of groups would be ...
0
votes
1answer
31 views
Post-Uni Calculus/Probabilities Book Suggestion
I have a Computer Science Background, recently graduated and I would like to refresh/improve my knowledge about probabilities and statistics (also calculus). The priority is probabilities and ...
1
vote
2answers
239 views
A less known definition of the definite integral of a continuous function
The definite integral of a continuous function can be defined using the bounded monotone sequence property: see Osgood's Functions of Real Variables, p.110.
(link to full book) (screenshots: page ...
1
vote
0answers
18 views
Lebesgue covering dimension of a manifold
I have found many sources saying that the Lebesgue covering dimension of a (topological or smooth) manifold is the same as the dimension of the manifold. Does anyone know where I can find the proof?
1
vote
1answer
52 views
Groups of transformations
I tried to find literature and articles about groups of transformations, but mostly what I found is either about groups or about transformations.
Can you suggest me literature where groups of ...
3
votes
1answer
41 views
Reference request for ordered groups
I've been reading Pete Clark's notes on commutative algebra, and I especially liked section 17 on valuation rings, and ordered groups in particular.
I'm looking for more introductory material ...
1
vote
0answers
22 views
Bernstein type inequalities. Is there a standard list?
Suppose I have a sequence of iid random variables $X_i\geq 0$ with mean $\mu$ and $\mathbb E \left(e^{tX_i}\right) = G(t)$. Set $$S_n = \sum_{i=1} X_n.$$
For the purpose of this question the ...
4
votes
0answers
55 views
Differentiable manifolds, Serge Lang
I have started reading "Introduction to differentiable manifolds" by Serge Lang. In this book, Lang takes a different approach, by immediately introducing manifolds on arbitrary Banach spaces. His ...
0
votes
1answer
98 views
Which topics of real-analysis should be studied if you have already done calculus
Which parts of real-analysis are worth studying if you have already taken several calculus courses? I know that real-analysis is more 'rigurous', but still I wonder whether it is worth to again go ...
1
vote
0answers
32 views
About the Generalized singular value decomposition (GSVD).
I have studied about Singular value decomposition (SVD) and had solved few numerical examples to understand SVD. Now I am studying Generalized singular value decomposition (GSVD). I followed this ...
1
vote
0answers
40 views
Extending a rational entry matrix to an orthogonal matrix.
Suppose $M \leq N$ are positive integers and let $r_1,\ldots,r_M$ represent the rows of an $M\times N$ matrix $A$ in which: (i) the rows of $A$ are orthogonal and having the same norm, (ii) the ...
4
votes
1answer
41 views
Book on quadric surfaces with linear algebra
Most information that I can find about quadric surfaces is written from a calculus perspective - without using any matrices or vectors. However, I would like to have a reference that tells me the ...
1
vote
1answer
39 views
Exponential decay of Heat equation solution
I'm refereeing a paper and the authors go to great lengths to prove the following fact.
Let $W(t,x)$ be the solution to the linear heat equation on the half-line: $\partial_t W = D \partial_{xx} W $, ...
6
votes
1answer
123 views
Is “cofunctor” an accepted term for contravariant functors?
People are used to the prefix co- flipping arrows in a concept1, and I have seen people using cofunctor to mean a functor that flips arrows, i.e. that takes $A \to B$ to $FB \to FA$. I know this ...
3
votes
1answer
64 views
Optimal probability measure
Let $A$ be a finite set and let $\Bbb P$ be a probability measure on $A^{\Bbb N_0}$. Further, let $x_i:A^{\Bbb N_0}\to A$ be projection maps, so that $(x_i)_{i=0}^\infty$ can be treated as a ...
3
votes
0answers
34 views
Reference for the following topics in Linear Algebra
I'm getting prepared for a competitive exam (entirely based on problem solving skill) for which I need to study the following topics in Linear Algebra:
Canonical forms,
Diagonal forms,
Triangular ...
2
votes
3answers
122 views
On integral of a function over a simplex
Help w/the following general calculation and references would be appreciated.
Let $ABC$ be a triangle in the plane.
Then for any linear function of two variables $u$.
$$
\int_{\triangle}|\nabla ...
2
votes
4answers
92 views
Book Suggestions for an Introduction to Measure Theory [duplicate]
Couldn't find this question asked anywhere on the site, so here it is! Do you guys have any recommendations for someone being introduced to measure theory and lebesgue integrals?
A mentor has ...
3
votes
1answer
39 views
Dual of holomorphic functions (with the $L^1$ topology)
Let $\Omega$ be a connected domain of the complex plane, and let $E$ be the vector space of integrable holomorphic functions on $\Omega$. Then it can be checked that $E$ is a closed subspace of ...
3
votes
1answer
55 views
looking for reference for integral inequality
Math people:
I would like a reference for the following fact (?), which I proved myself (I am 99% sure the proof is valid) but which has probably been done before. My proof was a little messy. If ...
