Questions tagged [applications]
Applications of mathematics to any field inside or outside mathematics
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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, e.g....
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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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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 ...
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Deep learning / Deep neural nets for mathematician
I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets".
Most of the papers/books that are often quoted in papers/...
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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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What practical applications does set theory have?
I am a non-mathematician. I'm reading up on set theory. It's fascinating, but I wonder if it's found any 'real-world' applications yet. For instance, in high school when we were learning the ...
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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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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 ...
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How does the work of a pure mathematician impact society? [closed]
First, I will explain my situation.
In my University most of the careers are doing videos to explain what we do and try to attract more people to our careers.
I am in a really bad position, because ...
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Applications of Lawvere's fixed point theorem
Lawvere's fixed point theorem states that in a cartesian closed category, if there is a morphism $A \to X^A$ which is point-surjective (meaning that $\hom(1,A) \to \hom(1,X^A)$ is surjective), then ...
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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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Is algebraic geometry constructive?
Notes: 1) I know next to nothing about algebraic geometry, although I am greatly interested in the field. 2) I realize that "constructive" might be a technical term, here I am using it only in an ...
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Interesting and surprising applications of the Ising Model
One of the most famous models in physics is the Ising model, invented by Wilhelm Lenz as a PhD problem to his student Ernst Ising. The one-dimensional version of it was solved in Ising's thesis in ...
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Listing applications of the SVD
The SVD (singular value decomposition) is taught in many linear algebra courses. It's taken for granted that it's important. I have helped teach a linear algebra course before, and I feel like I need ...
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What "real life" problems can be solved using billiards?
Recently I gave an interview to local media where I explained some basic open problems in billiard dynamics.
After a 45 min interview the reported asked me what "real life" problems can be ...
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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
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Examples of mathematics motivated by technological considerations
I would like examples of technological advances that were made possible only by the creation of new mathematics. I'm talking about technology that was desired in some period of history but for which ...
35
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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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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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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) ...
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How is differential geometry used in immediate industrial applications and what are some sources to learn about it?
Intuitively it might be clear that differential geometry is a very applicable subject in engineering and industry. I'd like to know how some industries/companies use differential geometry. I'd guess ...
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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:
...
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Applications of mathematics in clinical setting
What are some examples of successful mathematical attempts in clinical setting, specifically at the patient-disease-drug level?
To clarify, by patient-disease-drug level, I mean the mathematical work ...
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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-...
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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 ...
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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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Algebra and cancer research
Let me start by acknowledging the existence of this thread: Mathematics and cancer research
It is well-known that mathematical modeling and computational biology are effective tools in cancer research....
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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 — ...
25
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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 ...
25
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Caramello's theory: applications
In this text, the author says (well, he says it in French, but I am too lazy to fix all the accents, so here is a Google translation):
In any case, contemporary mathematics provides an example of ...
user140765
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Research in applied algebraic geometry that essentially needs a background of modern algebraic geometry at Hartshorne's level
By applied algebraic geometry, I don't mean applications of algebraic geometry to pure mathematics or super-pure theoretical physics. Not number theory, representation theory, algebraic topology,...
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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 ...
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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) ...
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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 ...
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What are some nice uses of ultraproducts/ultrapowers?
Motivated by a recent post (Non-definability of graph 3-colorability in first-order logic), I was wondering: what are some nice arguments based on ultraproducts? I don't mind definability results, but ...
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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. ...
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Examples of research on how people perceive mathematical objects
What examples are there on research related to human perception and mathematical objects?
For example, the shape of a beer glass influences drinking habits,
since people are bad at integrating.
...
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Signal processing reference for pure mathematician
Before giving a more detailed question below, the basic one is: can anyone recommend a good signal-processing reference which would be maximally readable by a pure mathematician (who nevertheless ...
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Applications of complex exponential
In calculus we learn about many applications of real exponentials like $e^x$ for bacteria growth, radioactive decay, compound interest, etc. These are very simple and direct applications. My question ...
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Applications of linear programming duality in combinatorics
So, I know that one can apply the strong LP duality theorem to specific instances of maximum flow problems to recover some nontrivial theorems in combinatorics, such as Hall's theorem, Koenig's ...
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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 ...
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Applications of visual calculus
Mamikon's visual calculus (see Mamikon, Tom Apostol, Wikipedia) is a very beautiful and surprisingly efficient tool.
The basis is
Mamikon's theorem. The area of a tangent sweep is equal to the area ...
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Mathematicians learning from applications to other fields
Once upon a time a speaker at the weekly Applied Mathematics Colloquium at MIT (one of two weekly colloquia in the math department (but the other one is not called "pure")) said researchers ...
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Tools from other disciplines useful to mathematics research?
Obviously, mathematics provides essential tools for physicists, biologists, economists, engineers and many others to use in their research. Equally obviously, physics, biology, economy and engineering ...
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Robotics, Cryptography, and Genetics applications of Grothendieck's work? [closed]
I was reading about the passing of Alexander Grothendieck, and something caught my interest:
Mr. Grothendieck was able to answer concrete questions about these relationships by finding universal ...
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Longest increasing subsequence as measure of randomness
Although I am by no means an applied mathematician, I like to occasionally explain applications of the math I teach to real world problems. Right now I am teaching some students about longest ...
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Applications of space filling curves
I am seeking articles where a space filling curve has been used as a theoretical application, such as in the study of general orthogonal polynomials.
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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 ...
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Which journals publish applied mathematics with mostly pure mathematics content?
In the spirit of Which journals publish expository work? please advise:
What consistently high quality journals (1) today publish results that would otherwise go to a pure mathematics journal were ...
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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 ...