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)

15
votes
3answers
3k views

Best way to learn Algebraic Geometry?

I've been reading the book Commutative Algebra with a view towards Algebraic Geometry. I was wondering is the best way to learn algebraic geometry through commutative algebra? As the book I'm ...
4
votes
1answer
196 views

Is there an overview of several logical systems?

I've heard about many kinds of logic like combinatory logic, relevance logic, higher order logic, paraconsistent logic... but I don't know anything about those logical system except higher order ...
6
votes
2answers
408 views

Banach-Saks property and reflexivity

On the German Wikipedia page on the Banach-Saks property, they claim that every Banach space with the Banach-Saks property is reflexive but that the converse is not true. There should be a proof due ...
5
votes
1answer
658 views

Where can I find the paper by Guy Robin?

\begin{equation} \sigma(n) < e^\gamma n \log \log n \end{equation} In 1984 Guy Robin proved that the inequality is true for all n ≥ 5,041 if and only if the Riemann hypothesis is true (Robin ...
4
votes
0answers
427 views

Interchanging the order of limits

Would you advise me on the references of Pringsheim Convergence about interchanging the order of limits? Where can I find the most general statement?
1
vote
1answer
218 views

Steady distribution for the reflected random walk

Let us consider the state space being $0,1,\dots,M$ for some $M\in \mathbb N$ and put there $N$ walkers: $$ X = (X_1,\dots,X_N). $$ Each of the walkers move independently, they can be in the same ...
1
vote
0answers
358 views

Second order central difference of the Nth order

I'm trying to find some tabulated data in some big-and-smart-book with regards to second order central difference of a function of just one variable: f''(x). I did find formula for 7th order [1], but ...
1
vote
2answers
427 views

Discussion on twin prime conjecture

I understand where I am wrong in my previous post. Also, I am very thankful to all members, who answered and showed my errors in post. Now, I would like to know the proof for the following. "The ...
7
votes
2answers
200 views

Reference for densities and pseudoforms and non-tensorial representations of $\operatorname{GL}(n)$ and associated vector bundles

I'm looking for a reference that will set me straight on a few things. It started out with densities. In John Lee's book, "Introduction to Smooth Manifolds", densities on vector spaces are functions ...
5
votes
1answer
410 views

Lawvere category of categories for foundations

Does anybody know where I can find this article "Lawvere, F. W., 1966, “The Category of Categories as a Foundation for Mathematics”? I've looked long for the web without any luck, I'll be grateful ...
2
votes
1answer
913 views

Similar Triangle Theorem in the Incommensurable Case

The following is a geometry theorem whose proof is examinable in the Irish 'High School' Exam. Let $\Delta ABC$ be a triangle. If a line $L$ is parallel to $BC$ and cuts $[AB]$ in the ratio $s:t$, ...
3
votes
0answers
151 views

How to prove that this series $f(z)=1+\sum_{k=1}^{\infty}2^{-k z}$ converges using the theory of continued fractions?

Consider the following series \begin{equation} f(z)=1+\sum_{k=1}^{\infty}\frac{1}{2^{k z}} =1+ \sum_{n=1}^{\infty}\left( \prod_{k=1}^{n}\frac{1}{2^{z}} \right) \end{equation} Using Euler's continued ...
4
votes
1answer
744 views

Finding a generating function for the Laguerre polynomials

I've started learning some quantum physics and one often encounters special functions (like Legendre polynomials, Laguerre polynomials, Bessel functions, ...). Many calculations with these functions ...
4
votes
1answer
103 views

Sequences convergent to 'cycles'

Consider sequences $(x_n)_{n=1}^\infty\subset\mathbb R$. Is there a name for the following property? There exists $L\in\mathbb N$ such that: ...
5
votes
2answers
215 views

Rigorous Development of Relational Algebra

Can anyone suggest a text that provides a rigorous and modern development of the relational algebra? A chapter out of a rigorous survey text on algebra, for example, would probably be sufficient. In ...
2
votes
0answers
146 views

Linearly independent rows in a square matrix

Suppose $m,n \in \mathbf{N}, m\le n$. Let $A$ be a matrix with $\mathbf{Q}$ linearly independent $b_{1},...,b_{m}$ in $\mathbf{Z}^{n}$. a) Show that there are $v_{1},...,v_{m} \in \mathbf{N}$ so ...
2
votes
2answers
193 views

Question about Fixed Point Theorem Hypotheses

Consider the following (less general than possible) statement of Schauder's fixed point theorem: Suppose that $X$ is a Banach space, that $B_1$ is the unit ball of $X$ and that $f: X \to X$ is a ...
24
votes
2answers
3k views

Books to study for Math GRE, self-study, have some time.

I just graduated from a regional university in the US with a minor in mathematics. There is a masters program overseas, for economics, that I want to attend but they require applicants to take the ...
1
vote
0answers
75 views

Looking for specific resource on the classification of complex irreducible representations of metacyclic groups

My apologies in advance if this question is in any way out of place. I'm currently need of a classification of complex irreducible representations of metacyclic groups. My current reference ...
1
vote
2answers
196 views

Something like : “recursive” harmonic numbers? Where can I read more?

In my other thread I discussed a matrix-decomposition; for one matrix (U) I found now a description of its entries, which may best be denoted as "recursive harmonic numbers". However, googling with ...
7
votes
3answers
4k views

Shortest proof for 'hairy ball' theorem

I want to make a project at differential geometry about the Hairy Ball theorem and its applications. I was thinking of including a proof of the theorem in the project. Using the Poincare-Hopf Theorem ...
4
votes
1answer
324 views

Preparation for a modular forms course

I'm trying to get a sense of what type of math to brush up on in order to take a course based on the book A First Course in Modular Forms by F. Diamond and J. Shurman. The text claims to be accessible ...
17
votes
4answers
2k views

probability textbooks

Has anyone compiled a moderately comprehensive list on the web or elsewhere of textbooks on probability For students who have not been introduced to the subject before That introduce both discrete ...
1
vote
1answer
74 views

Looking for references on results on powers of primes dividing $y^n-1$

For a prime $p$ and positive integer $n$, let $E(n,p)$ be the greatest $k$ such that $p^k \mid n$, and $E(n,p) = 0$ if $p \nmid n$. Let $E(n) = E(n, 2)$. A number of years back, I proved the ...
3
votes
0answers
413 views

$L^p$ spaces with negative $p$

First of all: I have seen the question $L^p$ with negative $p$ and this is not intended to be a duplicate of it. (Despite the similar title.) Let $p$ be a negative real number and $X$ a measure ...
2
votes
2answers
478 views

Differential Equations reference for Putnam preparation

I have two problem collections I am currently working through, the "Berkeley Problems in Mathematics" book, and the first of the three volumes of Putnam problems compiled by the MAA. These both ...
6
votes
1answer
265 views

Laguerre polynomials and inclusion-exclusion

Does anyone know a reference for the solution of the generalized derangement problem via Laguerre polynomials? The Wikipedia article here says that this is an application of inclusion-exclusion, but ...
2
votes
2answers
256 views

Tamagawa numbers and Genus class numbers

I was reading the paper of Prof.Franz Lemmermeyer titled "Pell-conics" which is here, in that the author writes in page 9 that one can define Tamagawa numbers as $$ c_p = \begin{cases} 2 & \text{ ...
32
votes
4answers
6k views

Learning Roadmap for Algebraic Topology

I am now considering about studying algebraic topology. There are a lot of books about it, and I want to choose the most comprehensive book among them. I have a solid background in Abstract Algebra, ...
12
votes
1answer
378 views

Understanding sub-atomic particles, for mathematicians

I have a masters degree in pure mathematics and I'm working towards my dream of a PhD, but I know very very little about sub-atomic particles. I would like to find some good popular science books or ...
8
votes
5answers
3k views

A good book for metric spaces?

I'm looking for a book to study metric spaces. Two years ago, I used a book written by Burkill. While using multiple topological concepts, I studied Munkres (chapters 2, 3, 4, 5, 6 & 9). I do not ...
1
vote
2answers
698 views

Recommendation of Book about Linear Programming and Linear Algebra?

I'm going to take this course next semester Description Formulation, solution and applications of integer programs. Branch and bound, cutting plane, and column generation algorithms. Combinatorial ...
3
votes
0answers
160 views

How do I look up applications of this type of convergence?

I was in a class and the professor said he knew of no applications (in a proof or elsewhere) of these two generalizations of Fatou's lemma and Lebesgue's dominated convergence theorem that I write ...
2
votes
3answers
2k views

What is a good Algebra reference text?

I'm looking for a reference text with classic results in algebra, like Fundamental theorem of finitely generated abelian groups Every field has a unique smallest prime field, which is either ...
3
votes
0answers
120 views

In a triangulated category with coproducts any idempotent splits

In a triangulated category with coproducts any idempotent splits. Is there a proof of this fact different from that in Neeman, Prop. 1.6.8? In particular I'm looking for one which doesn't use the ...
8
votes
1answer
752 views

Old French papers which haven't been translated into English

So I've been studying French for a few years now and I've decided that translating an old French math paper into English would be a good exercise to further improve my French competency. I would also ...
2
votes
2answers
3k views

Best books on A Second Course in Linear Algebra [duplicate]

Possible Duplicate: Prerequisites/Books for Linear Algebra I've studied from David Poole's Linear Algebra: A Modern Introduction However, it's not very complete. I want to study subjects as ...
33
votes
10answers
7k views

“Immediate” Applications of Differential Geometry

My professor asked us to find and make a list of things/facts from real life which have a differential geometry interpretation or justification. One example is this older question of mine. Another ...
1
vote
2answers
106 views

Standardized Notation for Well-Known Categories

It seems that every author has rather personal and unique conventions for designating "well-known" categories. This raises the question: Is there a reference available, on-line or otherwise, that ...
5
votes
1answer
479 views

Eigenvalues for matrices over general rings

I am aware of the theory of eigenvalues for matrices over fields. I was wondering to what extent this theory extends? Do we have a corresponding theory for matrices over integral domains, or at least ...
6
votes
1answer
171 views

Mathematical Research Formatting [duplicate]

Possible Duplicate: What are or where can I find style guidelines for writing math? In mathematical research papers, in what tense is it most appropriate to write? From my understanding, ...
2
votes
1answer
179 views

Reference about product of elliptic curves

I am wondering if there is some accessible reference to learn about product of elliptic curves and their 'properties'. For dimension 1, there is plenty to find. I think the dimension 2 case is done as ...
2
votes
2answers
139 views

Distributive sublattices of geometric modular lattices

I found a copy of Lattice Theory (by Birkhoff) in a dusty corner of our library. I just picked it up for fun and seems really interesting. I was mainly interested in geometric modular lattices. My ...
7
votes
3answers
265 views

Encyclopedic dictionary of Mathematics

I'm looking for a complete dictionary about Mathematics, after searching a lot I found only this one ...
2
votes
0answers
230 views

What is the origin of the (nearly obsolete) term “binary decimal”?

What is the origin of the (nearly obsolete) term "binary decimal"? At least two important publications in the 1930s used this oxymoron to mean what is now ...
6
votes
1answer
1k views

Definition of “interior derivative” and “exterior derivative”?

In Willie Wong's reply to one question, he used some concepts: "interior derivative" of a differential form and "exterior derivative" of a scalar function on $\mathbb{R}^3$. For "exterior ...
7
votes
2answers
532 views

Chaos and ergodicity in hamiltonian systems

EDIT : I formerly claimed something incorrect in my question. The Liouville measure needs NOT be ergodic on hypersurfaces of constant energy. Also, I found out that NO hamiltonian system can be ...
1
vote
2answers
114 views

High order methods for solving ODEs

I would like to know about really high order methods for solving ODEs. Say of order 30 and higher. What are they? Any surveys/reviews?
9
votes
1answer
2k views

Learning Homology and Cohomology

I want to learn homology and cohomology. I heard that Massey's Algebraic Topology book is a good one for this. Also some people suggest Bredon's Topology and Geometry. Our professor insists on Lee's ...
1
vote
0answers
222 views

Quadratic fields and solving Diophantine equations

I would like to learn to solve Diophantine equations and I think my next step would be quadratic fields or number fields. What are kind of methods there are to use those on solving equations? And what ...