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13
votes
7answers
3k views

Nice applications of the spectral theorem?

Most books and courses on linear algebra or functional analysis present at least one version of the spectral theorem (either in finite or infinite dimension) and emphasize its importance to many ...
0
votes
1answer
271 views

Helpful services based on mathoverflow API [closed]

My area of research is math information retrieval. In particular, I come up with several basic ideas how to make use of a promising discussion platform offered by mathoverflow.net (MO). That's why I'd ...
2
votes
2answers
1k views

Rotationally-Invariant 2D Discrete Transforms

Hello all, I'm interested in 2D discrete transforms (such as discrete wavelet transforms, Curvelets, Ridgelets, Beamlets etc.) that operate on a discrete unit disk and: Are invariant to rotations ...
6
votes
4answers
1k views

Robust black box function minimization with extremely expensive cost function

There is an enormous amount of information about the common applied math problem of minimizing a function.. software packages, hundreds of books, research, etc. But I still have not found a good ...
7
votes
4answers
2k views

Applications of Math: Theory vs. Practice

I have a problem: I learned about a lot of the applications of mathematics from academics. Neither they nor I have had much contact with the "real world" to go and see for ourselves how mathematics ...
2
votes
2answers
250 views

Given a function f(t): t -> R^n, can 2D, or nD DFTs be used on f(t) to perform frequency analysis?

Frequency analysis is often performed on wave forms (1D DFT), and images (2D DFT), where the function in question often takes the form: $f(t): \Re \mapsto \Re$ $f(x,y): \Re^2 \mapsto \Re$ $f(x_1, ...
26
votes
18answers
6k views

Interesting applications (in pure mathematics) of first-year calculus

What interesting applications are there for theorems or other results studied in first-year calculus courses? A good example for such an application would be using a calculus theorem to prove a ...
3
votes
3answers
1k views

Why are divisible abelian groups important?

I just quote wikipedia: "Divisible groups are important in understanding the structure of abelian groups, especially because they are the injective abelian groups." I am asking for detail ...
11
votes
0answers
1k views

How connected are you? [closed]

I apologize if this question seems frivolous, but the motivation for it is quite serious. When I encounter the endless topic of the 'relevance' of mathematics, I am rather fond of referring to a ...
15
votes
2answers
811 views

Applications of topological and diferentiable stacks

What are some examples of theorems about topology or differential geometry that have been proven using topological/differentiable stacks, or, some examples of proofs made easier by them? I'm well ...
18
votes
11answers
3k views

Algebraic geometry used “externally” (in problems without obvious algebraic structure).

This is a request for a list of examples of problems (or other mathematical situations) that are not initially of algebro-geometric nature, but can be solved or understood by using algebraic geometry. ...
14
votes
11answers
3k views

Does the Axiom of Choice (or any other “optional” set theory axiom) have real-world consequences? [closed]

Or another way to put it: Could the axiom of choice, or any other set-theoretic axiom/formulation which we normally think of as undecidable, be somehow empirically testable? If you have a particular ...
15
votes
8answers
2k views

Where have you used computer programming in your career as an (applied/pure) mathematician?

For background: I'm working on a book to help mathematicians learn how to program. However, I need to see some examples from people in the field that have done different kinds of things than I have. ...
5
votes
2answers
2k views

Can I relate the L1 norm of a function to its Fourier expansion?

I would like to express the integral of the absolute value of a real-valued function $f$ (over a finite interval) in terms of the Fourier coefficients of $f$. Failing that, I would like to know of any ...
21
votes
17answers
6k views

Applications of Brouwer's fixed point theorem

I'm presenting Brouwer's fixed point theorem to an audience that knows some point-set topology. Does anyone have any zippy / enlightening / cool applications or consequences of it? So far, I have: ...
4
votes
1answer
173 views

Rectifying texture from image

I have a camera matrix $P$ which defines a projective transformation $\mathbb{P}^3 \rightarrow \mathbb{P}^2$. In the former space there is a plane $[ x|\pi^Tx=0 ]$. The image of the plane under $P$ ...
8
votes
1answer
2k views

Defining “average rank” when not every ranking covers the whole set

Here's a mathematical modeling problem I came across while working on a hobby project. I have a website that presents each visitor with a list of movie titles. The user has to rank them from most to ...
15
votes
10answers
3k views

Applications of infinite Ramsey's Theorem (on N)?

Finite Ramsey's theorem is a very important combinatorial tool that is often used in mathematics. The infinite version of Ramsey's theorem (Ramsey's theorem for colorings of tuples of natural numbers) ...
13
votes
2answers
595 views

Archaeogenetics

This question is meant to be applied to recover historic information from genetic data. The following model, is (probably) the simplest possible which takes recombinations into account. First, let ...
39
votes
28answers
18k views

Applications of the Chinese remainder theorem

As the title suggests I am interested in CRT applications. Wikipedia article on CRT lists some of the well known applications (e.g. used in the RSA algorithm, used to construct an elegant Gödel ...
3
votes
2answers
447 views

Applications of propositional dynamic logic

Propositional dynamic logic (PDL) is an example of a (multi)modal logic with a structure on the set of modalities. In particular, the set of its modalities is indexed by "programs" and one can use ...
110
votes
29answers
33k views

Real-world applications of mathematics, by arxiv subject area?

What are the most important applications outside of mathematics of each of the major fields of mathematics? For concreteness, let's divide up mathematics according to arxiv mathematics categories, ...
6
votes
6answers
2k views

Applications and Natural Occurrences of Prime Numbers

I'm fascinated by prime numbers, and over the years, I've found multiple applications and natural occurrences for them. But can anyone suggest some alternatives that aren't in my list? Applications ...