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.

learn more… | top users | synonyms (3)

5
votes
0answers
102 views

Is there a book only about epsilon delta proofs?

I want to know if there is such book, with beautiful epsilon delta proofs of all kind.
1
vote
0answers
17 views

Embed one Coxeter System into another

What is a good reference that explains all the braid relations and diagrams for Coxeter systems concisely? In particular, how do I embed $H_3$ inside $D_6$, or $H_4$ inside $E_8$? Any hints?
0
votes
0answers
6 views

Literature on interpolation in Hardy spaces

I'm an undergraduate mathematics student and I'm searching for notes and books on Hardy spaces $H^p$, in particular interpolation theory including topics like Carleson measures, Carleson's $H^\infty$ ...
0
votes
1answer
24 views

Book suggestion for practicing tough Ordinary DE problems

I am preparing myself for a post undergraduate (masters) entrance exam in mathematics. Can someone suggest a really good practice material with challenging questions of all types for ordinary ...
2
votes
1answer
93 views

Reference request: Some theorems in an article of Grothendieck.

In "Standard conjectures on algebraic cycles" Grothendieck says: "The first is an existence assertion for algebraic cycles (considerably weaker than the Tate conjectures), and is inspired by and ...
2
votes
1answer
47 views

Where can I find a set of probability problems?

Is there a database of solved probability problems available? I am currently studying probability (and statistics) and, while I think I have a decent grasp of permutations, combinations, conditional ...
1
vote
2answers
52 views

Book on periodic Schrödinger operators

I am looking for good books about the spectral theory of periodic (1-dimensional) Schrödinger operators on a compact interval. A good reference I found was Reed/Simon Analysis of Operators (and a ...
0
votes
1answer
49 views

Is there a 10-digit emirp?

Does a 10-digit emirp exist? Unfortunately, the lists of emirps I could find on the Web are quite small and my programming skills aren't good enough to write a program to check all the primes up to ...
6
votes
1answer
67 views

Where can I download the approx 1500 Appel-Haken reducible configurations in the Four-Color-Theorem proof?

Where can I download computer representations of the approximately 1500 Appel-Haken reducible configurations in the Four-Color-Theorem proof? The Wikipedia article ...
1
vote
1answer
45 views

Pre- calculus and calculus practice questions

I'll be taking pre-calculus this fall, and I am wondering if anyone on here can recommend a good problem solving workbook with lots of questions for practice.Also,any ideas for calculus I and calculus ...
4
votes
0answers
42 views

The Kähler form and the anticanonical line bundle

Let $M$ be a Kähler manifold. We say that $M$ is Fano if the anticanonical line bundle $K_M^*$ of $M$ is ample (or positive). On the other hand, I sometimes see the following definition (or ...
2
votes
1answer
13 views

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$, how to call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$?

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$ How do people call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$? Sum of positive components of $X$? The positive semi definite part of $X$? ...
7
votes
1answer
241 views

Dynkin diagram automorphisms and weights

Let $\sigma$ be a nontrivial Dynkin diagram automorphism of a finite-dimensional complex simple Lie algebra $\frak g$ (of type A, D or E) and let $\frak h$ be a Cartan subalgebra of $\frak g$. Let $I$ ...
1
vote
1answer
21 views

Supplement for reading Group cohomology from Serre Local Fields

I am doing a reading course on Group cohomology... I am supposed to start reading Group cohomology part in Serre's Local fields Book ...
1
vote
1answer
41 views

Approximate Equivalent To Michael Spivak's text, “Calculus” but for Linear Algebra?

Does anyone know of an approximate equivalent To Michael Spivak's text, "Calculus" but for Linear Algebra? I love the way this book is written! It is simultaneously rigorous and thorough without ...
11
votes
3answers
1k views

Exercises on Galois Theory

I need a source for exercises on classical Galois Theory, or to be more specific, Galois extensions of finite fields and the rationals as well as applications (solvability by radicals, for example). ...
1
vote
0answers
16 views

Reference request: About some important result in a book of Lefschetz.

Is there a (modern)book in which the most important results of L'analysis situs et la géométrie algébrique, Lefschetz" are exposed?
11
votes
2answers
345 views

Linear independence of the numbers $\{1,\pi,{\pi}^2\}$

Does someone know a proof that $\{1,\pi,{\pi}^2\}$ is linearly independent over $\mathbb{Q}$ ? The proof should not use that $\pi$ is transcendental. $\{1,e,e^2,e^3\}$ is linearly independent over ...
0
votes
1answer
15 views

Definitions of hemicontinuity

can anyone see the equivalence or relation between the following two definitions of hemicontinuity that I encountered: Assume that $K$ is a closed, convex subset of Banach space $X$. Let $X^{*}$ be ...
0
votes
2answers
274 views

Multivariable Product Rule, Integration by Parts, Derivative, etc.

I am searching for a book on multi-variable calculus that explains multi-variable product, multi-variable integration by parts, etc. As an example, here's a simple problem that I would like to be ...
2
votes
0answers
20 views

harmonic functions: comparison of gradients

Consider $\Omega$ a open, bounded, convex domain in $R^n.$ I am trying to justify this: Let $u, v$ non negative harmonic functions in $\Omega$ (in the Sobolev sense). Suppose that $ u = v =0$ in ...
1
vote
0answers
35 views

Extending a measurable map $f: G \to \mathbb{R}/\mathbb{Z}$ to a continuous group homomorphism

Let $G$ be a compact abelian metrizable group (where the group operation is written as $+$) and $\mu$ is the Haar measure on $G$. Suppose we have a measurable function $f: G \rightarrow ...
1
vote
1answer
32 views

Quantum Cohomology of Affine Toric Varieties

I would like to know whether quantum cohomology rings of affine toric varieties have been calculated, if this is possible. Does anyone have a relevant paper they could refer me to? I have seen it ...
0
votes
1answer
64 views

Formulas for Schrödinger unitary groups of operators

Let $\Omega$ an open set of $\mathbb{R}^n$. Consider the Hilbert space $X=L^{2}\left(\Omega\right)$ and the Schrödinger operator $A=i\Delta$ defined on the domain $D(A)=H^2(\Omega)$. Is there any ...
2
votes
1answer
52 views

Characterization of solvable groups in terms of subgroups of certain orders?

In this question, the OP mentions the following result: a finite group $G$ is solvable if and only if $$\text{for all $n$ dividing $|G|$ such that $\gcd(\frac{|G|}{n},n)=1$, $G$ has a subroup order ...
1
vote
0answers
49 views

Grothendieck-Serre duality for complete smooth varieties

Let me fix a complete (but not necessarily projective) smooth variety $X$ over an algebraically closed field $k$ of characteristic $0$. Denote $d=\operatorname{dim}X$, and $\omega=\Omega^d_X$. I'd ...
1
vote
1answer
63 views

where can I get math book reviews?

The only two freely available choices are maa.org and zbmath.org ,where can get other mathematical book reviews? any one?
0
votes
1answer
69 views

defining the group law on elliptic curves in general

Let $k$ be an arbitrary field and $C \subset \mathbb{P}^2(k)$ an elliptic curve. In order to define the group law on $C$ we need to establish some geometric facts first, e.g. Any line intersects $C$ ...
0
votes
0answers
33 views

On achieving the maximal correlation

I am reading the famous paper of Renyi, entitled "On measures of dependence" (see here1). He redefined the maximal correlation in a very general form for both discrete and continuous random ...
0
votes
0answers
32 views

Prerequisites for Hilbert Cohn-Vossen's Geometry and the Imagination?

I've not read this book(not really),but I would like to know how much is assumed by the reader. can I recommend this to the layperson? Also ,any more recent similar books? I already know of Courant ...
1
vote
1answer
164 views

Gilbert Strang's books on calculus and linear algebra?Are they for math majors?

I would to know what are the best resources to use to teach and learn elementary subjects (calculus,linear algebra),I remember when learning calculus, I used Spivak's book which had wonderful ...
2
votes
1answer
128 views

Math enthusiast wants to learn math

I'm an english major with a vivid interest in mathematics,I've read and enjoyed What Is Mathematics? by Courant and Robbins (does this count as some background?),and I've decided to begin a serious ...
2
votes
1answer
75 views

Looking for an identity connecting polylogarithm and polygamma functions of arguments $\frac14$ and $\frac34$

I have a recollection of seeing an identity connecting polylogarithm and polygamma functions of arguments $\frac14$ and $\frac34$. But I don't remember details, and searching my books and the Internet ...
1
vote
0answers
30 views

Lecture notes on holomorphic Yang-Mills theory

Some time ago I've found these lecture notes on the gauge theory. In particular, in these lecture notes the author introduces and studies the Yang-Mills equations in the case of real bundles and ...
7
votes
1answer
128 views

Reference request: a differential equation arising in geometry

$$ \frac{d\beta}{d\alpha} = \frac {\sin\beta}{\sin\alpha} $$ In what contexts (if any) is this equation known to occur?
6
votes
2answers
63 views

Does the data of Galois group, ramified places, and inertia groups, determine a Galois number field?

Suppose I tell you that $K/\mathbb{Q}$ is a finite Galois extension, and I specify the Galois group $G$, and suppose further that I give you a finite list $S$ of places of $\mathbb{Q}$ and for each ...
1
vote
1answer
33 views

Generalizing primality to other operations

(By "number" below I always mean an element of $\mathbb{Z}^+\setminus $$\left\{1\right \}$.) We all know that a number $p$ is prime iff it cannot be represented as $ab$ for any two numbers $a$ and ...
0
votes
1answer
14 views

Multi-dimensional Feynman Kac Theorem

I am trying to understand how to prove the multi-dimensional version of the Feynman-Kac formula. The single-dimensional version is proved on this page: en.wikipedia.org/wiki/Feynman–Kac_formula ...
1
vote
2answers
102 views

Property of set of prime numbers

let $\{p_1,p_2,p_2,\cdots ,p_r\}$ be the set of $r$($\ge2$) pair wise distinct prime numbers i.e.., $(i\ne j \implies p_i \ne p_j)$ for all $1\le i,j\le r$ ${Statement}$ : For any such ...
4
votes
0answers
79 views

Any abstract algebra book with programming (homework) assignment?

All: I had studied abstract algebra long time ago. Now, I would like to review some material, particularly about Galois theory (and its application). Can anyone recommend an abstract algebra book ...
3
votes
2answers
60 views

Canonical isomorphism between Cauchy sequence completion and inverse limit

I'm studying chapter 10 of Atiyah Macdonald. The book introduces two ways to construct the completion of an abelian topological group: Equivalence classes of Cauchy sequences and inverse limit. I can ...
0
votes
1answer
25 views

References on “Measure and Integration: History and Development”

I would like to get references for Measure and Integration", since I want to study the subject from historical perspective. The references could be books, articles or the online resources.
0
votes
0answers
18 views

Where can I read about the techniques for computing areas and volumes before calculus?

I've read the following here: The key insight, however, that earned them this credit, was the fundamental theorem of calculus relating differentiation and integration: this rendered obsolete most ...
1
vote
2answers
50 views

Looking for a proof that the diameter of the smallest bounding circle is less than or equal to $\frac{2}{\sqrt{3}}$ times the diameter of the set

This came up while I was attempting to solve an old journal problem. It's not the easiest result to search for so I figured I would ask. Let $E$ be a subset of $\mathbb{R}^2$, then the diameter of ...
10
votes
2answers
242 views

What meaning did Riemann assign to $dx$?

Detlef Laugwitz wrote a monumental biography of Riemann. The book was translated into English by Shenitzer. Laugwitz discusses Riemann's fundamental essay Uber die Hypothesen, welche der Geometrie ...
1
vote
1answer
44 views

Gromov hyperbolic metric spaces are quasi-convex

I'm aware about the fact stated above, but I'm not able to find some references or proofs besides Gromov's Hyperbolic Groups - Essays in Group Theory. I'll state things precisely. I will consider a ...
3
votes
0answers
133 views

Any comments on Lax's “Calculus with Applications, 2e”

There's a new calculus book titled Calculus with Applications by Peter Lax (2nd edition of an old one). I really liked his linear algebra and functional analysis books, and I was wondering if this ...
1
vote
0answers
52 views

Any complex analysis book with programming assignment and exercises?

All: I had studied complex analysis long time ago. Now, I would like to review some material, particularly about Analytic function, Riemann zeta and Analytic function. I have been a software ...
0
votes
1answer
66 views

Reference-Request: Symmetric Product Schemes

Is there a good reference for the theory of symmetric product schemes? (I only need a few basic things, the construction, etc.) Googling it turned up a lot of papers which use it as if it's common ...
0
votes
1answer
11 views

Quadratic Variation of Diffusion Process and Geometric Brownian Motion

I'm looking to find out the stochastic differential equation satisfied by the quadratic variation of Geometric Brownian Motion, Diffusion Process. For example, for a diffusion process that ...