The applications tag has no wiki summary.

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### 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 ...

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**6**answers

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### 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 ...

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### 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 ...

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### 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 ...

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### 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**

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**1**answer

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### 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 ...

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**2**answers

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### 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 ...

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**4**answers

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### 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 ...

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### 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**

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**2**answers

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### 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, ...

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### 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 ...

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**3**answers

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### 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 ...

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**0**answers

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### 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

**2**answers

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### 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 ...

**19**

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**11**answers

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### 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. ...

**16**

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### 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 ...

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### 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.
...

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**2**answers

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### 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 ...

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### 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

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### 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 $P$ ...

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votes

**1**answer

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### 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 ...

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### 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

**2**answers

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### 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 ...

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**28**answers

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### 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 ...

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**2**answers

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### 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 ...

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### 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, ...

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### 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 ...