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.

learn more… | top users | synonyms (3)

0
votes
0answers
31 views

Lagrangian and Hamiltonian Mechanics

I am interested in how Lagrangian and Hamiltonian mechanics and then symplectic geometry was developed starting from Newtonian mechanics. We can start by assuming that Newtonian mechanics tells us ...
3
votes
1answer
32 views

Existence of a probability space

Let us assume that we are given a family of Markov chains $(X^\alpha_t)_{t\geq0}$ in continuous time. Kolmogorov's result ensures that for each $\alpha \in I$ there exists a probability space ...
1
vote
1answer
49 views

Resource for coordinate geometry

I am looking for a good resource (preferably in the form of textbooks) for coordinate geometry. Rather than a comprehensive coverage of topics, I am looking more for depth in a particular topic. It is ...
0
votes
0answers
27 views

Looking for an English translation of Descartes's mathematical works

Good day to everyone! I am looking for an English translation of Descartes' mathematical works (particularly in elementary number theory). Would someone be kind enough as to point me to an ...
0
votes
1answer
55 views

$\limsup$ and $\liminf $ of $\sum_{k=1}^n \frac{X_k}{\sigma \sqrt{n}} $

Suppose $(\Omega, \mathfrak{F}, p)$ is a probability space; $X_n$ are i.i.d. random variables defined on $\Omega$, with $E(X_i)=0$ and $Var(X_i)= \sigma$ for all $i$. Then $$ \limsup_n \sum_{k=1}^n ...
2
votes
3answers
80 views

geometry developments during the Islamic Golden Age (7-13 century)

Can anybody refer me to publications on geometry during the Islamic Golden Age? My interest is especially on Arab geometry an non-Euclidean geometry. But searching for sources was a saddening ...
1
vote
0answers
34 views

Coequalizers in categories of relations and partial functions

Let $\mathbf{Rel}$ be the category whose morphisms are triples $(X, R, Y)$ where $X$ and $Y$ are sets and $R$ is a relation between $X$ and $Y$ and let $\mathbf{PFun}$ be the subcategory of ...
11
votes
1answer
114 views

Rings in which binomial theorem holds for at least one integer $n>2$

Let $R$ be a ring ; if $(a+b)^2=a^2+2ab+b^2 , \forall a,b \in R$ , then we know that $R$ is commutative ; also if $R$ is commutative then we know that $(a+b)^n=\sum _{r=0}^n {n \choose r} a^{n-r}b^r , ...
0
votes
0answers
12 views

Unable to find paper: R.G. Laha: “On some properties of the Bessel function distributions”

Can anybody provide me this paper? R. G. Laha, "On some properties of the Bessel function distributions," Bull. Calcutta Math. Soc., 46 (1954), 59-71. Thanks in advance.
2
votes
1answer
69 views

Three people want to personally meet each other as fast as possible: optimization problem.

Problem: Three people want to be all gathered at the same place, and they want it to happen as soon as possible. Where should they head to? P.S. Assume they all travel with the same speed. Think of ...
2
votes
1answer
32 views

Help finding a good book on Finsler geometry

I want to learn more about Finsler geometry. I have just studying the book "An Introduction to Riemann-Finsler Geometry" by Bao, Chern and Shen, but i would like to study Finsler Geometry approach to ...
0
votes
0answers
17 views

Reference request for valuations in algebraic number theory

I am going through the book "Primes of the form $x^2$ + n$y^2$" and I understand the background material about algebraic number fields and class numbers(from Ireland and Rosen). However, I do not have ...
0
votes
1answer
31 views

About a classic “primitive”

A long time ago I heard somethings about the following primitive $\int e^{x^2} \ dx$ : 1 ) It doens't exist 2) It cannot be expressed by means of "elementary functions" Someone could point me a ...
1
vote
1answer
30 views

Is the biconjugate of a continuous functions also continuous?

Let $f:\mathbb{R}^n\to\mathbb{R}$ be given and assume that $|f(x)|\leq C|x|^2$. Is it true that the bi-(convex/Fenchel)-conjugate $f^{**}$ is also continuous. It was claimed in a book without a ...
4
votes
1answer
39 views

$L$-Zariski closure of subgroup $SL_n(F)$ as subset of $M_n(F)$ also a subgroup of $SL_n(F)$

Let $F$ be a field, and $SL_n(F)$ be the group of $n \times n$ matrices with determinant $1$. Let $\Gamma \subset SL_n(F)$ be a subgroup. We can consider $\Gamma$ to be a subset of $M_n(F) \cong ...
0
votes
1answer
27 views

Examples of of non-commutative rings with no multiplicative identity ( finite and infinite ) other than matrix rings

Can anyone please give some examples or give a reference where I can find examples of non-commutative rings with no multiplicative identity other than matrix rings ? Also examples of finite ...
-1
votes
0answers
21 views

Finite Groups of Isometries of Euclidean spaces

Six years before, I had a collection of articles on finite groups of rotations of sphere, from Monthly, Gazette, Intelligencer. But I lost these articles. Since I am teaching this topic, I would like ...
1
vote
2answers
52 views

Graph Theory book with lots of Named Graphs/ Graph Families

I'm doing a research about an operation on graphs and I am now in the point where I want to apply it to some named graphs or to some of the graph families like paths, cycles, wheels, etc. I am ...
0
votes
0answers
23 views

About teaching an advanced principle mainly with pictures.

There is a concept I have seen on Pinterest called Infographics. The use of colourful pictures and graphics and diagrams that can show in a pictorial way some explanation of advanced math principles. ...
0
votes
1answer
57 views

Curiosity : An inequality involving logarithms

Does exists $\alpha \in R $ and a positive constant C such that $\displaystyle{% \left[\,x\ln\left(\, x\,\right) - x\,\right] -\left[\, y\ln\left(\, y\,\right) - y\,\right]\ \leq\ C\,\left\vert\, ...
2
votes
1answer
77 views

prerequisites for serre's FAC?

Is the knowledge of undergraduate's basic algebra and general topology enough to reading FAC? Do I need learn some algebraic topology and homological algebra, commutative algebra, or several complex ...
1
vote
1answer
62 views

Relationship between the cocountable and standard topologies on $\mathbb{R}$

Where can I find a proof of the fact that the cocountable topology on $\mathbb{R}$ is coarser than, finer than, or not comparable with the standard topology on $\mathbb{R}$? For a seemingly standard ...
2
votes
2answers
113 views

Nice book on integrals [duplicate]

On this site I usually see very amazing techniques to solve integrals; contour integrals, differentiating under the integral sign, transforming the integral into a series and son on and so forth. ...
2
votes
2answers
36 views

Clifford Algebras for Projective and Conformal Geometry

According to Clifford Algebra: A Visual Introduction, A Clifford Algebra over $\mathbb{R}^3$ may describe the rigid motions in space (namely, conjugation acts as a reflection by a plane). A ...
0
votes
1answer
40 views

Good recommendations for solving PDE's by integral transforms

I look for good books on solving partial diffrential equations (PDE's) using integral transforms specially Fourier and laplace transforms. Do you have any recommendations for such books? I don't ...
1
vote
1answer
51 views

Can $\pi(x)-\operatorname{Li}(x)=O(\sqrt x\log(x))$ be proven without using $\psi(x)$?

Assuming the truth of the Riemann hypothesis, $\pi(x)-\operatorname{Li}(x)=O(\sqrt x\log(x))$. Apparently the proof that $\psi(x)$ approaches $1$ for sufficiently large $x$ proves the error term. ...
2
votes
1answer
39 views

Reference for secondary cohomology operations

I am learning some homotopy theory and am currently reading Mosher and Tangora. I love the content of this book, it's very terse and comes straight to the point. At the same time I find it very ...
2
votes
0answers
38 views

Name for classes of algebras closed under products and quotients

A class of algebras closed under products, quotetiens and subalgebras is a variety. Is there a name for a class of algebras closed under products and quotients? Could you refer me to any theorems ...
2
votes
1answer
28 views

Introductory text for Group Rings

Is there any other text books on Group rings except The algebraic structures of Group Rings by D.Passman. This book is really good but it will help if I know about other books on the topic too. ...
0
votes
1answer
9 views

reference request on besov spaces and bounded variation functions.

Would someone have any good references which address besov spaces, and functions of bounded variations. I don't know anything about theses spaces so I am looking for something that would introduce me ...
0
votes
0answers
22 views

Given a function $f(x)$ is there any terms describing the value of $\frac{|f(x_1)-f(x_2)|}{||x_1-x_2||}$

Given a function $f(x)$, is there any jargon for the value of $\frac{|f(x_1)-f(x_2)|}{||x_1-x_2||}$? Can I call it the sensitivity of $f$ on $x$?
1
vote
0answers
18 views

Comparing two fundamental domains for $\Gamma(2)$

(0). My question concerns the relation between two different fundamental domains for the group $$ \Gamma(2)= \left\{ \begin{bmatrix} a & b \\ c & d \end{bmatrix}\in SL_2(\mathbb Z) \; ...
1
vote
2answers
68 views

Does this function have closed form?

Define $$f(p,n)=\sum_1^n s_i$$ where $s_i$ is defined as the maximal integer value such that $i= p^{s_i}r_i$ for integer $r_i$. For example, we'd have $$f(2,15)=\sum_1^{15} s_i=1+2+1+3+1+2+1=11.$$ ...
4
votes
1answer
68 views

Help needed to understand statements about torus

I am having trouble understanding two statements: Let $A$ be an algebraic curve in $\mathbb{P}^2$ over $\mathbb{C}.$ Consider its normalization $$\pi: \hat{A} \to A.$$ If genus $g(\hat{A})=1,$ ...
0
votes
0answers
26 views

“outer product” of modules

What is the "outer product" of modules? Can someone link me a definition and maybe an example? In my book the outer product is noted with $\bigwedge ^tF$, $F$ a $A$-Module, $A$ principle ideal domain. ...
0
votes
0answers
40 views

Convolution of a pdf $f$ with a Gaussian $g$: distance between $g\ast f$ and $g$?

I have been looking for references on the following matter: let $f$ be the pdf of any real-value random variable ($f$ is not necessarily continuous wrt Lebesgue measure), and $g=g_{\mu,\sigma}$ be a ...
0
votes
0answers
7 views

What would be references for oscilatorry integrals in the context of Pseudo-Differential Operators?

Is there any good reference dealing with oscillatory integrals? More precisely, I'm looking for something in the context of pseudo-differential operators. I need to learn about those integrals to ...
4
votes
4answers
123 views

Asking for Various proofs of uncountability of $[0,1]$

How many different proofs are there of the uncountability of the set $[0,1]$ ? I know of the nested interval proof and the Baire Category theorem proof ; please suggest other proofs . Thanks in ...
3
votes
1answer
74 views

General Distributive Law and Axiom of Choice

Where can I find the proof of the fact that general distributive law of union over intersection and intersection over union is equivalent to Axiom of Choice? The mathematical formulation of the ...
1
vote
1answer
94 views

Reference request - Outline of Edward Nelson's Inconsistency Proof

Edward Nelson retracted his inconsistency proof before it was published. Unfortunately, the outline given by Nelson has been removed. Is there a copy of it on the web? I am interested in how the ...
1
vote
1answer
24 views

Condition for existence of a unique solution for a desired variable in a system of linear equations

Consider a system of linear equations of the form $$\mathbf{A}\mathbf{x}=\mathbf{b}, \mathbf{A} \in \mathbb{R}^{L\times K}, \mathbf{x} \in \mathbb{R}^{L}, \mathbf{b} \in \mathbb{R}^{K} $$ with $L$ ...
2
votes
0answers
38 views

intersection property holdds for every Veronese embedding?

The Veronese Embedding Doesn't the nice intersection property listed near the end here hold for every Veronese embedding? If so/not, where I could find a proof/counterexample? Thanks.
2
votes
0answers
28 views

Good and thorough online and/or free Matroid Theory references?

I'm studying a course on Matroid theory. Sadly, I can't really afford buying the textbook, so I only use the lecture notes, which aren't enough for me. Are there any good and thorough online and ...
0
votes
0answers
55 views

Picard group of affine scheme of a UFD

In which book/notes can I find proofs of the following facts? 1) Pic(Spec$A)$ is $0$ where $A$ is a UFD. 'Pic' is the Picard group. 2) The invertible sheaves on projective space P$^n(k)$ for $k$ a ...
2
votes
2answers
63 views

Rationalizing the denominator in general

How do you rationalize the denominator of something like $$\frac{1}{\sqrt[n]{a_1}+\sqrt[n]{a_2}+...+\sqrt[n]{a_n}}$$? I'm thinking roots of unity.
0
votes
1answer
49 views

(Near) complete euclidean geometry theorems and postulates list

I‘ve been looking for a euclidean geometry book filled with as many theorems and axioms as possible, even better if it‘s as condensed as possible (say, proofs given separately in another book, or not ...
0
votes
0answers
22 views

English translation of Lagrange's reflexions sur la resolution…?

I'm looking for an English translation of Lagrange's paper "Reflexions sur la resolution algebrique...". I could swear I downloaded .pdf of it once, but I probably deleted it since then. In other ...
2
votes
0answers
46 views

Which books of Euler are accessible to high school students?

I am currently a first year undergraduate but I still feel as if I cannot read many undergraduate level books. At the moment I am interested in reading some classics. I have already read Euler's ...
0
votes
0answers
35 views

Reference about elliptic integral and Jacobi Inversion Problem

I read the section about Abel's theorem and the Jacobi Inversion Problem on the book of Forster, "Lectures on Riemann Surfaces". I would like if there were some books which treats more in detail this ...
2
votes
1answer
23 views

Nonattacking configurations of bishops on squares of the same color

It is known that the number of possible configurations of $i$ bishops on squares of the same color of an $n\times n$ chessboard for even $n$ is given by: $$\sum_{j=0}^{n-i-1}\frac{(-1)^j{n-i-1\choose ...