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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3
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4answers
87 views

Is there a shorter path to these results?

I'm a student of Physics, however I usually study mathematics on texts aimed at mathematicians to gain a deeper understanding. Currently I'm studying differential geometry on Spivak's book and one of ...
10
votes
3answers
145 views

Computing $\int_0^\pi \sin(x) \; dx$ using the definition.

A colleague of mine and I, in the course of teaching integral calculus for the umpteenth time, were wondering if we could expand the class of examples that our students are exposed to when computing ...
1
vote
0answers
22 views

Automorphism group of a bipartite regular graph

Showing an automorphism group of complete bipartite graph $K_{n,m}$ is easy. I'm wondering if there is an classification of automorphism groups of bipartite regular graphs. Did anyone heard something ...
2
votes
0answers
26 views

History of Morse theory.

How can I get good references which give many information about history of Morse theory? Now I am interested in how and who found that Hessian have a lot of data. Thank you for your helping!!
4
votes
2answers
64 views

Works on Calculus by Newton and Leibniz (primary sources)

I'm trying to find PDFs or hard copies of the following works from the dawn of calculus. Does anyone know where I could find English translations of them? Newton - De analysi per aequationes numero ...
1
vote
0answers
26 views

Reference needed for the following sobolev inequalties

I'm reading a paper and the authors applied the following sobolev type estimates $$ ||(Dv)^{2}||_{H^{3k-2}(\Omega)}\leq C||v||_{H^{3k-1+\alpha}(\Omega)}^{2} $$ for $\alpha>\frac{1}{4}$, where $v$ ...
0
votes
0answers
19 views

How we compute expectation of a singular random variable?

In probability (or measure) courses, we often see the Cantor distribution that is singular with respect to the Lebesgue measure. Its CDF is increasing but whenever its differentiable, the ...
1
vote
0answers
23 views

Smoothness of solutions to Fredholm integral equation

Let $K(x,y)=k(|x-y|)$ where $k$ is continuous on $(0,1]$, and assume function $f\in L^2[0,1]$ satisfies $f(x)=\int_0^1 f(y)K(x,y)dy$. Is $f$ necessarily $C^\infty $ ? under what condition on kernel ...
0
votes
1answer
48 views

Book for advanced homological algebra

I already read the books: 1.- An introduction to homological algebra - Rotman (the two versions of it) 2.- An introduction to homological algebra - Weibel 3.- A course on homological algebra - ...
0
votes
0answers
39 views

coalgebra/algebra of the identity endfunctor

Let $\mathbb{C}$ be a small/locally small category and let $T:\mathbb{C} \to \mathbb{C}$ be an endofunctor. One can then have $T$-algebras and $T$-coalgebras in the usual way: for $X,Y \in ...
2
votes
3answers
77 views

From groups to groupoids.

Let $\mathcal{G}$ be a groupoid and $p$ an object in $\mathcal{G}.$ It is well known that the set ${\rm Mor}_{\mathcal{G}}(p,p)$ is a group. I would like to know if there is a way to recognize a ...
0
votes
0answers
14 views

Classification of second order PDE

I am trying to understand the classification of second order PDE's from this article. In page 45, line 1 can somebody please explain to me how $\partial^2U \over {\partial x_i\partial x_j} $ was ...
2
votes
1answer
65 views

Book to prepare for university math?

Can you suggest some books to prepare for university math?
1
vote
0answers
35 views

Books explaining differentiation under the integral sign

I've heard that this is a great tool to have in you math toolkit, but I cannot comprehend this method just from the wiki entry and 2 page pdf files. I'm looking for a book which has problems ...
0
votes
1answer
28 views

Reference about the Conley index thoery

I'm reading "Isolated invariant sets and the Morse index" by Charles Conley.But I'm lost in some of the concise description or definition.Could you recommend me some references or textbooks for the ...
0
votes
0answers
14 views

Reference for elliptic regularity for $-\triangle \phi + u \cdot \nabla\phi=f$ under minimal assumptions

I have a distributional solution to $-\triangle \phi + u \cdot \nabla \phi= f$ in $U \subseteq \mathbb{R}^n$ and $\phi=0$ on $\partial U$. I have that $U$ is open, bounded, connected, ...
1
vote
4answers
94 views

Nice book on geometry to gift an undergraduate in mathematics

I would like some suggestions on a nice book on geometry to gift an undergraduate. I'm not searching for something that is common: I need something new and exciting. Suggestions?
5
votes
0answers
105 views

What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
0
votes
0answers
14 views

algorithm for traversing a fractal in a “maximally ordered” way

consider a multidimensional fractal that can be "traversed" in an arbitrary order. is there an algorithm for traversing a fractal in a "maximally ordered" way? in other words the algorithm has ...
3
votes
3answers
120 views

$1992$ IMO Functional Equation problem

The problem states: Let $\Bbb R$ denote the set of all real numbers. Find all functions $f : \Bbb R \rightarrow \Bbb R$ such that $$f(x^{2}+f(y))=y+(f(x))^{2} \space \space \space \forall x, y \in ...
0
votes
1answer
11 views

about lower semicontinuous functional

Let $X$ a topological space.My book define : A functional $\varphi: X \rightarrow R$ is lower-semicontinuous (l.s.c) if $\varphi^{-1}(a, + \infty)$ is open in $X$ for any $a \in R.$ (1) And the book ...
3
votes
1answer
57 views

Book/Books leading up to the the axiom of choice?

I am familiar with the axioms of ZF set theory and some basic uses of them to completely formally construct more complex objects such as natural numbers etc. However I have pretty much no background ...
8
votes
0answers
60 views

Statistics Primer for the Unwary Mathematician

I have a new position in a biology department (after being housed in a maths department) working on cognitive and population modeling. People in my lab are asking for help with applying statistical ...
4
votes
2answers
163 views

Interaction of completeness and second incompleteness theorems

So I was reading the Wikipedia article on Godel's completeness theorem, the section on its relation to completeness. It says that completeness gives the existence of a model of arithmetic $\mathcal M ...
1
vote
1answer
53 views

Recreational Mathematics title search

I once read part of a book on recreational mathematics that told a variety of stories. A central part of each story was a piece of non-trivial, and very interesting mathematics: the sofa moving ...
1
vote
0answers
16 views

Non-Intersecting up-right lattice paths and standard Young Tableaux

Consider the Lattice $\mathbb{Z}^2$ and an initial set of points with coordinates $(0,u_1)$, $(0,u_2)$, $\cdots$ $(0,u_n)$, final set of points $(m,v_1),(m,v_2),\cdots,(m,v_n)$, where $v_i,u_i$ are ...
5
votes
0answers
37 views

A theorem of Kan regarding fibrant replacement

Recall that there is an adjunction $$\mathrm{Sd} \dashv \mathrm{Ex} : \mathbf{sSet} \to \mathbf{sSet}$$ where $\mathrm{Sd} (\Delta^n)$ is the first barycentric subdivision of $\Delta^n$. There is a ...
0
votes
1answer
27 views

Analyticity of Logarithmic Integrals

Assume $f\in L^2[0,1]$ and let $g(x)=\int_0^1f(y)\ln|x-y|dy$. Is it true that $g\in C^\infty(0,1)$? Is it true that $g$ is analytic in $(0,1)$? Can you refer me to a right reference to look up such ...
1
vote
1answer
20 views

Lebesgue-Radon-Nikodym Theorem without Hilbert spaces

In my analysis class we are seeing the so called Lebesgue-Radon-Nikodym Theorem. But we prove it the "old fashioned way" without using Hilbert space theory. More precisely, we prove the minimality ...
1
vote
0answers
43 views

Books in Russian

I'm studying Russian language and I would like to know if this can add me something mathematically speaking. For example, I know French and this give me the possibility to read a lot of undergraduate ...
2
votes
1answer
54 views

Need help locating a paper

One of the references of the paper Paulo Régis C. Ruffino, A Criticism on "A Mathematician's Apology" by G. H. Hardy (arXiv:1112.4499 [math.HO]) is: Vershik, A. M. – A Dangerous Joke, The ...
0
votes
2answers
28 views

Alternative reference for number of restricted partitions

I am looking for the number of partitions of some number $n$ into $k$ parts. Following the Wikipedia article on partitions, I ended up with Andrew's book [1]. Judging by Google's preview Chapter 3 ...
1
vote
1answer
14 views

looking for Theorem 3.22 of Cardinal functions in topology

read an article which uses Theorem 3.22 of "Cardinal functions in topology, ten years later". I searched this book on internet but is not there. I searched it in my university library but isn't there ...
5
votes
1answer
30 views

Proof of the Barrow's Inequality?

Barrow's inequality states that if $P$ is any point inside triangle $ABC$, and $PU$, $PW$, and $PV$ are the angle bisectors, then the following inequality holds, $PA+PB+PC\geq 2(PU+PV+PW)$. I know ...
7
votes
2answers
94 views

Techniques for showing an ideal in $k[x_1,\ldots,x_n]$ is prime

An affine variety $X$ over a field $k$ is irreducible if and only if its defining ideal $I(X)$ is prime (in this post we use the convention that varieties are not necessarily irreducible). Hence, it ...
3
votes
1answer
61 views

What are some examples of “homogeneous” linear orders, other than $\mathbb{R}$ and $\mathbb{Q}$?

Let $L$ denote a linear order that is unbounded. Then it may or may not satisfy: Globally homogeneous. For all $x,y \in L \cup \{-\infty,\infty\}$, if $x < y$ then the interval $(x,y)$ is ...
0
votes
0answers
22 views

Fourier-Stieltjes Transform of the Cantor measure

I am looking for an elementary derivation of the formula for the Fourier-Stieltjes Transform of Cantor measure on the Cantor middle-third set as an infinite product of cosines (with all the details ...
1
vote
1answer
57 views

Reference-request for $Monomial\ Ideals$

I newly started to study the book Monomial Ideals by Jürgen Herzog, Takayuki Hibi, but it is difficult in some cases for a beginner like me. Is any other reference which have similar topics (part I) ...
0
votes
0answers
29 views

Graph algebra papers

The following graph multiplication appears to be quite natural: Let $g_1=(V_1,E_1)$ and $g_2=(V_2,E_2)$ be two graphs ($V_i$ are sets of vertexes and $E_i$, sets of edges). Intuitively, the product I ...
5
votes
1answer
38 views

Reference for a Cantor set in the plane formed from series of roots of unity

This is a long shot, but I'm looking for a particular article that I once read, and I'm trying to find it again. It deals with a certain Cantor set in the plane. The set could be written as something ...
1
vote
1answer
38 views

Hermitian matrix the only diagonizable

During the last lecture one of my professors claimed that the hermitian matrix is the ONLY complex matrix which was diagonizable. This seems strange to mee (not to say a very very strong claim to ...
0
votes
0answers
24 views

General solution of the recurrence equation with real shifts

How to find a general solution of the following functional (recurrence) equation: $$f(x) = c_1 f(x - a_1) + \dots + c_n f(x - a_n), \tag{1}$$ where $c_i, a_i$, $i = 1, ... n$ are arbitrary real ...
1
vote
0answers
63 views

Joseph Kitchen's Calculus (reference)

I'm asking about one textbook: Kitchen's Calculus. I tried to get a copy in different libraries but nothing. I tried buying it and I cannot find it wherever I've been. I've heard that is an ...
4
votes
1answer
99 views

iterated dual vector spaces

Let $K$ be a field and $\mathcal U$ a universe such that $K\in\mathcal U$. (Here, "universe" means "uncountable Grothendieck universe".) Let $\mathcal C$ be the category of $K$-vector spaces belonging ...
1
vote
0answers
51 views

Necessity of writing Math in a patent?

I don't know if its appropriate question here...but I anyway want to try... I have an algorithm in which I have a finite data in which each element is assumed as an element of a metric space with a ...
2
votes
1answer
55 views

Srinivasa Ramanujan conjectures

I searched internet for the whole list of conjectures by Srinivasa Ramanujan , but its not fruitful . I came to know that recently a book of Ramanujan was out and contains many conjectures related to ...
0
votes
0answers
14 views

generalizing taylor expansions to incorporate arbitrary constraints

Taylor expansions give us a concrete method for approximating functions up to any desired accuracy. But what if I want the resulting function to be constrained somehow? For example, Let $f$ be a ...
1
vote
1answer
31 views

Name for grammars with rules $A \to uA$

Recall that a right-linear grammar is a grammar that consists of rules of the form $A\to uB$, where $A$ and $B$ are non-terminals and $u$ is a (possibly empty) word of terminals. Similarly for ...
2
votes
0answers
44 views

References on the Evaluation of Series

What are the best introductory resources for learning how to evaluate tricky series? I don't have any specific series in mind, I am looking for general methods to solve a variety of series. The ...
3
votes
2answers
123 views

Smooth spectral decomposition of a matrix

Let $A : x \mapsto A(x)$ be a $C^\infty$ map from the half-plane $\left\{ (x_1,x_2,\cdots,x_n) \in \mathbb{R}^n,\ x_n>0\right\}$ to the space of symmetric matrices with real coefficients. Suppose ...