Questions tagged [applications]

Applications of mathematics to any field inside or outside mathematics

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4 votes
0 answers
409 views

Applications of moduli of curves theory

Are there some applications of moduli of curves theory? I was wondering if moduli of curves theory is used (or could be used) for doing research in applied mathematics. I am doing my PhD in algebraic ...
5 votes
1 answer
562 views

Distances on generalizations of the symmetric group

I'm a computer vision student, and I'm looking for some symmetric group literature guidance. I'm going to provide some context, and finally ask two questions. The Cayley distance and other distances ...
emchristiansen's user avatar
0 votes
1 answer
1k views

Frequency calculation using fourier transform [closed]

How to calculate the frequency of an audio file using Fourier Transform
Gaushick's user avatar
30 votes
4 answers
4k views

Elementary applications of Krein-Milman

This is a cross-post from MSE: Elementary applications of Krein-Milman. I'm starting to suspect that the question just doesn't really have a great answer, it's worth a try. Recall that the Krein-...
2 votes
2 answers
1k views

Application of Catalan number [closed]

Hi guys just a quick questions What are the real life application of catalan numbers? Thanks a lot!
user23731's user avatar
6 votes
2 answers
1k views

Non-trivial consequences of Löb's theorem

Informally, Löb's theorem (Wikipedia, PlanetMath) shows that: a mathematical system cannot assert its own soundness without becoming inconsistent [Yudkowsky] In symbols: if $PA\vdash$ $Bew$(#P) $\...
Sniper Clown's user avatar
9 votes
2 answers
5k views

Applications of algebraic geometry/commutative algebra to biology/pharmacology

Are there applications of algebraic geometry/commutative algebra to biology/pharmacology? It might be that some Gröbner basis technique is used somewhere? I know there are some applications to ...
10 votes
3 answers
2k views

Applications of knot theory to biology/pharmacology

What are the applications of knot theory to biology/pharmacology? I guess there should be some, since proteins are quite long and some of their properties are probably related to whether they are ...
1 vote
3 answers
528 views

"Graphical models" and "gene finding and diagnosis of diseases" ?

Quote Wikipedia: Applications of graphical models include ... gene finding and diagnosis of diseases... Unfortunately there is no comment what are these applications... Can one comment on this ? ...
25 votes
7 answers
8k views

Applications of group theory to mathematical biology (pharmacology)

Are there applications of group theory — broadly, say, representation theory, Lie algebras, $q$-groups, etc — to mathematical biology? In particular, I am interested in applications to pharmacology — ...
10 votes
1 answer
1k views

Any applications integrable systems (pde,ode, q-,...) to math. biology (pharmakinetics, pharmadynamics)?

Question Are there any relations/applications of integrable system theory (take it as broadly as one can: ODE, PDE, quantum, box-ball,...) to mathematical biology (in particular pharmacokinetics, ...
1 vote
2 answers
2k views

Stochastic process with Bessel function autocorrelation. (Rayleigh (Jakes) fading for radiowave propagation)

Have the following stochastic process $f(t)$ been studied in mathematics ? It is stationary, Gaussian, $f(t)-$complex independent Gaussians $N(0,1)$. The autocorrelation is given by the zero-order ...
Alexander Chervov's user avatar
25 votes
5 answers
2k views

Sperner Lemma Applications

I was always fascinated with this result. Sperner's lemma is a combinatorial result which can prove some pretty strong facts, as Brouwer fixed point theorem. I know at least another application of ...
14 votes
1 answer
610 views

Application for Morse-Smale systems

All my life I do topological classification of Morse-Smale systems (flows and cascades). Today, fundamental science is not in fashion, to receive grants require an application. Can you please tell ...
Olga's user avatar
  • 179
29 votes
20 answers
7k views

Mathematics and cancer research

What are applications of mathematics in cancer research? Unfortunately, I heard quite little about applications of mathematics, but I heard something about applications of physics, and let me put this ...
0 votes
0 answers
266 views

L1-regularized Least Squares on a matrix with Toeplitz Blocks (not block-Toeplitz)

I am trying to speed up a sparse signal recovery algorithms. My sensing matrix is a set of Toeplitz Blocks, M = [T1,T2,T3,...,Tk] The objective is min ||Mx - b||_2^2 + ||x||1 What I'm actually ...
DoubleJay's user avatar
  • 2,353
4 votes
1 answer
388 views

Applications of Chevalley groups theory for dummies

As an algebraist i frequently receive questions from my friends-mathematicians and non-mathematicians about applications of my topic "in real life". I study algebraic groups in the stream of ...
11 votes
4 answers
2k views

Applications of Hilbert's metric

Among the fascinating constructions in mathematics is the Hilbert metric on a bounded convex subset of ${\mathbb R}^n$. Where, within mathematics, is it used ? I know at least a proof of the Perron--...
9 votes
1 answer
747 views

Any nice examples of small cancellation theory appearing in applied mathematics?

Are there any nice discussions of applications of small cancellation theory, or other cases of the word problem, in applied mathematics or algorithms for seemingly non-group theoretic problems? I ...
Jeff Burdges's user avatar
2 votes
2 answers
348 views

Diffusion processes in probabilistic modelling

I'm working on a PhD project that involves parameter estimation for diffusion processes. I'm based in a machine learning research group, and the emphasis here is strongly on "practical" research. I'...
18 votes
3 answers
2k views

Applications of and motivation for von Neumann's mean ergodic theorem

I stated von Neumann's mean ergodic theorem (VNMET) in a talk recently and someone in the audience asked what it was good for. The only application I knew of VNMET was to prove Birkhoff's ergodic ...
Quinn Culver's user avatar
3 votes
0 answers
428 views

Concrete questions that turn into math problems [closed]

I'm writing an article about the way we teach math, trying to find out why so many people are discouraged from learning, and have no interest for math and logic. At some point, I want to show that ...
salezica's user avatar
  • 131
41 votes
12 answers
7k views

Recent Applications of Mathematics

What are the recent and new applications of Mathematics in other Sciences ? Let me try to be more precise about the question: By "recent" I mean the last 15 years. By "new" I want to exclude the ...
13 votes
6 answers
7k views

Applications of commutative algebra

Hi. I'm preparing a thesis in commutative algebra, and when I say this to my friends they always ask me what are the applications to "real-world", and I don't know what to answer. This let me think ...
142 votes
24 answers
18k views

Occurrences of (co)homology in other disciplines and/or nature

I am curious if the setup for (co)homology theory appears outside the realm of pure mathematics. The idea of a family of groups linked by a series of arrows such that the composition of consecutive ...
77 votes
11 answers
13k views

Applications of mathematics

All of us have probably been exposed to questions such as: "What are the applications of group theory...". This is not the subject of this MO question. Here is a little newspaper article that I found ...
20 votes
8 answers
11k 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 ...
Mark's user avatar
  • 4,804
0 votes
1 answer
354 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 ...
Nikita Zhiltsov's user avatar
4 votes
2 answers
3k views

Rotationally-Invariant 2D Discrete Transforms

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 only Output a ...
33 votes
21 answers
11k views

Applications of finite continued fractions

I know some applications of finite continued fractions. Probably you know more. Can you add anything? (For Applications of periodic continued fractions I have made a special topic.) 1) (Trivial) ...
10 votes
5 answers
2k 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 ...
MathMonkey's user avatar
9 votes
4 answers
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
1 answer
395 views

Given a function $f(t): \mathbb{R}\to\mathbb{R}^n$, can 2D, or $n$D discrete Fourier transforms be used on $f(t)$ to perform frequency analysis?

$\DeclareMathOperator{\R}{\mathbb{R}}$Frequency analysis is often performed on wave forms (1D DFT = discrete Fourier transform), and images (2D DFT), where the function in question often takes the ...
Brian Vandenberg's user avatar
35 votes
19 answers
9k 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 ...
9 votes
3 answers
3k 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
0 answers
2k 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 ...
22 votes
3 answers
1k 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 ...
David Carchedi's user avatar
20 votes
11 answers
4k 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. ...
6 votes
14 answers
5k views

Applications of compactness [closed]

Similar to this question: Applications of connectedness I want to collect applications of compactness. E.g.: compact + discrete => finite, which can be used to prove the finiteness of the ...
28 votes
11 answers
7k 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 ...
DoubleJay's user avatar
  • 2,353
36 votes
8 answers
16k views

Practical applications of algebraic number theory?

I'm interested in learning about any applications, the more worldly the better*. Pointing to a nice reference on the number field sieve, for example, would be fine. However, let me mention one ...
35 votes
14 answers
4k 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. ...
6 votes
2 answers
4k 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 ...
Gregory Putzel's user avatar
106 votes
15 answers
35k views

Most striking applications of category theory?

What are the most striking applications of category theory? I'm trying to motivate deeper study of category theory and I have only come across the following significant examples: Joyal's ...
31 votes
17 answers
14k 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
1 answer
207 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 $P$ ...
Ben's user avatar
  • 567
8 votes
1 answer
4k 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 ...
RexE's user avatar
  • 195
44 votes
15 answers
28k views

What are the applications of hypergraphs?

Hypergraphs are like simple graphs, except that instead of having edges that only connect 2 vertices, their edges are sets of any number of vertices. This happens to mean that all graphs are just a ...
21 votes
10 answers
5k 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) ...
alexod's user avatar
  • 757
13 votes
2 answers
632 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 ...
Anton Petrunin's user avatar