0
votes
0answers
45 views

The set of (property) elements of a locally compact group is closed

For which properties $(P)$ is the following statement known to be true? In any locally compact group $G$, the elements of $G$ that satisfy $(P)$ form a closed subset of $G$. In other words, the ...
11
votes
2answers
414 views

References for particular topics related to Langlands

I have never really concentrated on Langlands, which explains my poor level of understanding of it. But I have read quite a few introductory papers related to Langlands, and to the circle of ideas ...
19
votes
0answers
640 views

The most important facts, modern surveys, and readable introductions to p-adic cohomology theories (crystalline cohomology and the mysterious functor)

I would like to organize a seminar on crystalline cohomology; I dream of understanding the Beilinson's recent paper on the mysterious functor ...
6
votes
4answers
1k views

Interactions of number theoretic conjectures and other fields of mathematics

There are many interesting open conjectures in number theory. My question is not about partial results or possible ways to prove them. It is about their interactions with the other fields of ...
22
votes
4answers
965 views

Multiplying by irrational numbers in combinatorial problems

This is getting no attention on stackexchange. Everybody knows that the number of derangements of a set of size $n$ is the nearest integer to $n!/e$. It had escaped my attention until last week, ...
18
votes
5answers
634 views

Online high quality colloquium talks

In my department we're thinking about showing online lectures one day per week at lunch, as sort of a virtual colloquium appropriate to mathematics undergraduates as well as faculty. To start with ...
12
votes
1answer
338 views

Applications of non-separable Hilbert spaces

In applications, Hilbert spaces of interest are often assumed to be separable. In addition to being extremely convenient mathematically, this assumption can often be justified on computational or ...
4
votes
2answers
1k views

List of Charlatans in Mathematics [closed]

Recently, while looking for articles and documents to learn about the Riemann Hyopthesis, I came across a strange funny document of a chinese "mathematician" called Jiang Chun-Xuang who claimed to ...
5
votes
0answers
772 views

“Must read ”papers on analytic number theory

Question: What would be some must-read papers for an aspiring analytic number theorist? In other words, what are the papers that any analytic number theorist would have read? (Background: ...
19
votes
10answers
2k views

Learning through guided discovery

I have been working through Kenneth P. Bogart's "Combinatorics Through Guided Discovery". You can download it from this page: http://www.math.dartmouth.edu/news-resources/electronic/kpbogart/ I've ...
11
votes
7answers
2k views

What are some Applications of Teichmüller Theory?

I'm trying to collect some specific examples of applications of Teichmüller Theory. Here are some things I have collected thus far: No-wandering-domain Theorem (Sullivan) Theorems of Thurston ...
5
votes
2answers
1k views

Consequences of Legendre's conjecture

I am looking for a list/reference which explores the consequences of Legendre's conjecture, which states that one can always find a prime number between $n^2$ and $(n+1)^2$.
4
votes
3answers
576 views

Quotations about the power of simple ideas [closed]

I'm looking for quotations about how very simple mathematical ideas can be very powerful. I know of a few, but they're not quite what I'm looking for insofar as they contain criticism of other ...
6
votes
4answers
1k views

Discrete Mathematics textbooks for undergraduates

For the first time, I will be teaching a course on Discrete Mathematics for electrical and computer undergraduates students. I intend to focus on practical applications. I would be grateful if ...
18
votes
19answers
3k views

History Question: AUTObiography of Mathematicians

According to Wikipedia, an autobiography is an account of the life of a person, written by that person sometimes with a collaborator. An autobiography offers the author the ability to recreate ...
28
votes
11answers
5k views

“Must read” papers in numerical analysis

In 1993, Prof. L.N. Trefethen published a NA-net posting with a list of thirteen paper he used for teaching the seminar Classic Papers in Numerical Analysis. In Trefethen's words, ... this course ...
7
votes
10answers
3k views

Music: mathematical point of view (revised) [closed]

Mathematical analysis of music started when Pythagoras made his observations about consonant intervals and ratios of string lengths. ADDED: In the paper Mathematical Music Theory -- Status Quo 2000, ...
3
votes
11answers
541 views

A list of symmetric statistics

I would like to have a list of pairs (or tuples) of combinatorial statistics that are (known or conjectured) to have symmetric distribution. Ideally, something like this has already been compiled, ...
37
votes
30answers
4k views

Fundamental problems whose solution seems completely out of reach [closed]

In many areas of mathematics there are fundamental problems that are embarrasingly natural or simple to state, but whose solution seem so out of reach that they are barely mentioned in the literature ...
3
votes
2answers
1k views

Papers whose title defines a new terminology [duplicate]

To explain a new signal processing technique based on Fourier Transform, Bogert et al went on to define a new vocabulary. The new terminology was published in a paper with the title: The Quefrency ...
6
votes
1answer
644 views

On the concept of point in category theory

In principle, many different abstractions of the set-theoretic notion of point / element are available in the framework of categories, but they are not equally effective and, what is more interesting ...
5
votes
5answers
1k views

Application of polynomials with non-negative coefficients

Question 1: Are there any deeper applications (in any field of mathematics) of polynomials (with possibly more than one variable) over the real numbers whose coefficients are non-negative? So far I ...
0
votes
1answer
386 views

Weak algebraic structures

The following question can be thought as a sequel of this one. Here I'm looking for a big list of example of weak algebraic structures: here weak means that the structure (i.e. operations) need not ...
38
votes
24answers
6k views

The concept of Duality

I have been thinking for sometime about asking this question, but because I did not want to have two "big-list" questions open at the same time, I did not ask this one. Now its time has come. ...
8
votes
9answers
2k views

Mathematical Advice for Interested Highschool Students

This may not be a research level math question, but I believe it is still relevant to Math Overflow. What general resources exist for students in highschool who are very interested in ...
8
votes
5answers
672 views

Asymptotic Methods in Combinatorics

What are good texts to acquaint oneself with standard asymptotic techniques, particularly as they relate to probabilistic combinatorics?
28
votes
17answers
6k views

Computer Science for Mathematicians

This is a big-list community question, so I'm sorry in advance if it is deemed too soft but I haven't seen anything similar yet. I've seen computer scienctists post questions looking to learn things ...
6
votes
2answers
866 views

Applications of periodic continued fractions

Some answers from Applications of finite continued fractions in fact are Applications of periodic continued fractions. I think that it should be separate question. What can you add to the following ...
19
votes
14answers
4k views

Applications of finite continued fractions

I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For for Applications of periodic continued fractions I have made a special topic.) 1) (Trivial) ...
25
votes
6answers
836 views

Link Repository of International Dissertations

This question (cry for help?) grew out of Colin Tan's question: does anyone have a copy of schmid’s effective work on hilbert 17th? which was a request for a copy of an Habilitationsschrift. We've ...
1
vote
1answer
558 views

What are the topological properties of the metric space retained (inherited) for its completion

Let $(X,d)$ be a metric space and $(\bar{X},\bar{d})$ its completion. There is a list of topological properties Wikipedia - Topological property Does anybody know list which of them are retained ...
6
votes
3answers
3k views

Are there extensive tables of Fourier transforms available online?

I hope this is suitable for MO... I was wondering if someone can suggest a website (or some online document) containing an $extensive$ table of Fourier transforms? When I try obvious Google searches, ...
7
votes
2answers
2k views

Linear/Non-linear sigma model

This is slightly an open-ended invitation to discuss references and reasons for excitement about the linear and non-linear sigma model. I gauge from some other interactions that it has considerable ...
10
votes
5answers
2k views

References for complex analytic geometry?

I'm looking for references on the "algebraic geometry" side of complex analytis, i.e. on complex spaces, morphisms of those spaces, coherent sheaves, flat morphisms, direct image sheaves etc. A ...
23
votes
1answer
789 views

Good user manuals for technical topics?

This question is motivated by this (highly recommended) comment by Emerton on Terry Tao "Learn and relearn your field" post. In particular, the following paragraphs: In particular, the first ...
5
votes
2answers
2k views

Constant curvature manifolds

In two different books I found these two related statements. The book by Jost defines a ``locally symmetric space" as one for which the curvature tensor is constant and which is geodesically ...
26
votes
5answers
5k views

Doing geometry using Feynman Path Integral?

I have often heard in the folk-lore that Feynman Path Integral can be used to compute geometric invariants of a space. Coming from a background of studying Quantum Field Theory from the books like ...
2
votes
4answers
2k views

Any reference on multilinear algebra [closed]

Do you know any good reference on multilinear algebra?
14
votes
2answers
718 views

Collecting various theories on toy examples: Projective space

I am looking for text books/notes/papers/documents playing with toy examples: projective space, in particular, $P^{1}$. Because I think this is really a cute example. Although algebraic geometry on ...
9
votes
12answers
3k views

probability in number theory

Hi, I am hearing that there are some great applications of probability theory (or more general measure theory) to number theory. Could anyone recommend some good book(s) on that (or other types of ...
11
votes
17answers
22k views

Suggestions for a good Measure Theory book

I have taken analysis and have looked at different measures, but I am currently looking at realizing a certain problem in a different light and feel that I need a better background in various measures ...
79
votes
41answers
23k views

Ways to prove the fundamental theorem of algebra

This seems to be a favorite question everywhere, including Princeton quals. How many ways are there? Please give a new way in each answer, and if possible give reference. I start by giving two: ...
18
votes
8answers
3k views

What are some good resources for mathematical translation?

I am currently in the process of translating a lecture on the étale topology by John Hubbard from French into English (and from transparencies into Beamer). For the most part, the translation is ...
167
votes
61answers
86k views

Proofs without words

Can you give examples of proofs without words? In particular, can you give examples of proofs without words for non-trivial results? (One could ask if this is of interest to mathematicians, and I ...
38
votes
13answers
9k views

A reading list for topological quantum field theory?

Can you suggest a reading list, or at least a few papers that you think would be useful, for a beginner in topological quantum field theory? I know what the curvature of a connection is, know basic ...