# Tagged Questions

**18**

votes

**0**answers

595 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

**4**answers

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 ...

**23**

votes

**4**answers

931 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

**5**answers

610 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

**1**answer

324 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

**2**answers

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 ...

**3**

votes

**0**answers

714 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

**10**answers

1k 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

**7**answers

1k 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 ...

**4**

votes

**3**answers

819 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

**3**answers

566 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

**4**answers

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 ...

**16**

votes

**19**answers

2k 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

**11**answers

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

**10**answers

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

**11**answers

518 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, ...

**34**

votes

**30**answers

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

**2**answers

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

**1**answer

625 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

**5**answers

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

**1**answer

384 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 ...

**34**

votes

**23**answers

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.
...

**7**

votes

**9**answers

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

**5**answers

648 views

### Asymptotic Methods in Combinatorics

What are good texts to acquaint oneself with standard asymptotic techniques, particularly as they relate to probabilistic combinatorics?

**26**

votes

**17**answers

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

**2**answers

838 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 ...

**18**

votes

**14**answers

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) ...

**15**

votes

**5**answers

685 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

**1**answer

534 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

**3**answers

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

**2**answers

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 ...

**8**

votes

**5**answers

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

**1**answer

779 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

**2**answers

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 ...

**25**

votes

**5**answers

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

**4**answers

2k views

### Any reference on multilinear algebra [closed]

Do you know any good reference on multilinear algebra?

**14**

votes

**2**answers

702 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

**12**answers

2k 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 ...

**9**

votes

**17**answers

20k 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 ...

**74**

votes

**41**answers

21k 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

**8**answers

2k 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 ...

**36**

votes

**13**answers

8k 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 ...