Questions tagged [applications]

The [application] tag is meant for questions about applications of mathematical concepts and theorems to a more practical use (e.g. real world usage, less-abstract mathematics, etc.)

Filter by
Sorted by
Tagged with
16
votes
7answers
22k views

Real life applications of general vector spaces

Students familiar with Euclidean space find the introduction of general vectors spaces pretty boring and abstract particularly when describing vector spaces such as set of polynomials or set of ...
16
votes
6answers
8k views

What sorts of problems can fractals solve?

After doing a bit of research on fractals, I was wondering what sort of real-life applications do fractal have and in what way would they be used to help solve a problem. I already know people use ...
16
votes
3answers
2k views

Applications of the Hahn-Banach Theorems

Question: What are some interesting or useful applications of the Hahn-Banach theorem(s)? Motivation: Most of the time, I dislike most of Analysis. During a final examination, a question sparked my ...
15
votes
7answers
2k views

Applications of ultrafilters

I'm looking for some interesting applications of ultrafilters and also everything of interest involving ultrafilters. Do you know some applications or interesting things involving ultrafilters? I'm ...
15
votes
7answers
28k views

Applications of the Mean Value Theorem

What are some interesting applications of the Mean Value Theorem for derivatives (both the 'extended' or 'non-extended' versions as seen here are of interest)? So far I've seen some trivial ...
15
votes
4answers
2k views

Applications of Gröbner bases

I would like to present an application of Gröbner bases. The audience is a class of first year graduate students who are taking first year algebra. Does anyone have suggestions on a specific ...
15
votes
2answers
552 views

Why are noetherian and artinian modules important?

As a TA I was recently asked to give the students an introduction to two (quite related) concepts that are new to me, noetherian and artinian modules. I intend to prove the characterisation theorem (i....
14
votes
5answers
2k views

What are some applications of Chebotarev Density Theorem?

Let $L/K$ be a Galois extension of number fields and let $\mathcal{C}$ be a conjugacy class in $Gal(L/K)$. Let $\mathbb{P}(K)$ be the set of all prime ideals in $K$ and let $\left(\frac{L/K}{\mathfrak{...
14
votes
10answers
396 views

Examples of limits in nature with $\lim_{x \to c}f(x) \neq f(c)$

Next week I will start teaching Calculus for the first time. I am preparing my notes, and, as pure mathematician, I cannot come up with a good real world example of the following. Are there good ...
14
votes
2answers
3k views

Elementary proof of the Prime Number Theorem - Need?

Although I am very much new to "Analytic Number Theory", there are some non mathematical questions which puzzle me. First of all, why was G.H.Hardy so keen to have an elementary proof of the Prime ...
14
votes
4answers
7k views

Real-world uses of Algebraic Structures

I am a Computer science student, and in discrete mathematics, I am learning about algebraic structures. In that I am having concepts like Group,semi-Groups etc... Previously I studied Graphs. I ...
14
votes
3answers
224 views

Applications of functions of the form $f(x)^{g(x)}$

Early on in my calculus education, I learned how to take the derivative of $x^x$ by re-writing it in the form $e^{x\ln x}$. More generally, this technique is helpful in finding the derivative of ...
14
votes
6answers
982 views

In what fields would you like to see applications of mathematics? [closed]

There are very few disciplines which mathematics has not penetrated. As a pupil finds such gem in the calculus problem of theory of rumors, he wonders if such field has application in vaudevillian ...
13
votes
4answers
974 views

Mathematics applied to biology

Can anyone suggest reference material on mathematics applied to biology, in particular the study of the behavior of say simple unicellular organisms or cells? Ideally the level of complexity should be ...
12
votes
2answers
2k views

Using math for interior decorating with lamps

When I was in college, I owned three lamps and had a dark apartment. I kept trying to position them in different areas of the room, but it was still dark. Then I decided to model the problem with math:...
12
votes
2answers
2k views

Abstract algebra book with real life applications

Is there an abstract algebra book that emphasizes the applications to "real world" problems? Update: By real world, I mean mostly related to physics or other sciences. But references to coding theory ...
12
votes
1answer
916 views

Torsion in two dimensions?

This question is about the notion of a connection with torsion in differential geometry, i.e., a connection that is not Levi-Civita. (It's not about the torsion of a curve in three dimensions.) ...
11
votes
4answers
2k views

Is there any abstract theory of electrical networks?

Designing electrical networks is among the highly mathematical engineering disciplines, which uses a vast scope of techniques from Fourier analysis and complex function theory, to logic, combinatorics ...
11
votes
2answers
829 views

Applications of topology to logic?

At Ieke Moerdijk's homepage, one can read that his research interests include "applications of topology to mathematical logic". I know very few such applications (essentially I only know topological ...
11
votes
2answers
414 views

Physical meaning of linear ODE $xy''+2y' + \lambda^2 x y = 0$

As reported by Wikipedia - Sinc function, $y(x)=\lambda \operatorname{sinc}(\lambda x)$ is a solution of the linear ordinary differential equation $$x \frac{d^2 y}{d x^2} + 2 \frac{d y}{d x} + \lambda^...
11
votes
3answers
5k views

What are applications of rings & groups?

I am following a course in basic algebra, and we have covered rings & groups in class, but I am having trouble visualising them. Are there applications of group &/or ring theory that can be ...
11
votes
3answers
3k views

What is the purpose of K-Theory?

I have recognized that there is a theory called K-Theory in mathematics is used also for applications in mathematical physics. There is existing algebraic K-Theory and topological K-Theory. Are ...
11
votes
1answer
4k views

Why does GPS require a minimum of 24 satellites?

From Wikipedia, The GPS design originally called for 24 SVs, eight each in three approximately circular orbits, but this was modified to six orbital planes with four satellites each. [...] The ...
11
votes
3answers
318 views

How do you estimate the flow rate of one fluid into another like the Deep Horizon Oil leak?

How have experts estimated the amount of oil that was shooting out of that pipe in the Gulf? I bet there's some neat math or physics involved here, and some interesting assumptions considering how ...
10
votes
8answers
5k views

Applications of Probability Theory in pure mathematics

My (maybe wrong) impression is that while probability is widely used in science (for example, in statistical mechanics), it is rarely seen in pure mathematics. Which leads me to the question - Are ...
10
votes
3answers
1k views

Is there any result that has applications that can't be proved in constructive mathematics?

Constructive mathematics is distinguished from its traditional counterpart, classical mathematics, by the strict interpretation of the phrase “there exists” as “ we can construct”. Is there any ...
10
votes
5answers
3k views

What is Cramer's rule used for?

Cramer's rule appears in introductory linear algebra courses without comments on its utility. It is a flaw in our system of pedagogy that one learns answers to questions of this kind in courses only ...
10
votes
2answers
763 views

Does variance do any good to gambling game makers?

People always like to evaluate the variance, but is there any way for variance to be interesting to the gambling game makers? In another word, what is a pratical gambling game that involving some ...
10
votes
3answers
8k views

Practical applications of chaos theory in engineering or physics

Can anyone give me some examples of practical applications of chaos theory in engineering or physics? Do you know any good books about chaos theory or its applications?
10
votes
4answers
219 views

“Class” of functions whose inverse, where defined, is the same “class”

Please excuse the amateurish use of the term "class", I don't know what the exact term is for what I'm looking for. Anyway, details. I'm asking specifically about real-valued functions on the real ...
10
votes
2answers
2k views

Applications of Geometry to Computer Science

How is differential geometry (or any type of theoretical math) being used in computer science? Any research I have done on this topic leads me to some sort of applied math concept. I know that there ...
10
votes
1answer
284 views

What precisely is the Friendship Paradox (and is Wikipedia wrong?)

Friendship paradox is the somewhat well-known statement that "statistically speaking, your friends have more friends than you do". To my mind, which is surely ignorant of any complexities of social ...
10
votes
3answers
2k views

Applications of Banach Algebras and Operator Algebras

I am trying to learn operator algebra theory (I am tempted to start with Douglas' "Banach Algebra Techniques in Operator Theory"). One aspect that I am curious about is whether there are significant ...
10
votes
1answer
332 views

Mathematics and cinema

I wander if anyone of you have some knowledge about relations between abstract algebra and cinema. I'm not searching for movies about mathematics or algebra; I'm searching for some kind of application ...
9
votes
7answers
7k views

What is the best base to use?

When I typed this question in google I found this link: http://octomatics.org/ Just from the graphic point of view: this system seems to be easier (when he explains that you can overlap the line). He ...
9
votes
3answers
2k views

Useless math that become useful

I'm writing an article on Lychrel numbers and some people pointed out that this is completely useless. My idea is to amend my article with some theories that seemed useless when they are created but ...
9
votes
4answers
9k views

Does the concept of infinity have any practical applications?

I know what you're thinking: "of course it has, for example, it can be used to tell you how many times you can go around a circle". But that isn't really true, now is it? You'd be dead or the world ...
9
votes
3answers
2k views

Error-correcting codes used in real life

I am very interested in coding theory and I wonder if there is a particular kind of codes used in practice. For example I read that Reed-Solomon codes are often used for encoding data on a compact ...
9
votes
4answers
447 views

An unexpected application of non-trivial combinatorics

PROBLEM STATEMENT Given two finite sets $A$ and $B$, each containing $s \in \mathbb N$ elements, how many pairs of functions $f \colon A \rightarrow B$ and $g \colon B \rightarrow A$ are there, ...
9
votes
2answers
3k views

Applications of category theory and topoi/topos theory in reality

I am an amateur mathematician with an interest in the subjects named in the title. I have recently come to understand that my B.A. in math gives me absolutely no qualification at all in the Swedish ...
9
votes
2answers
532 views

Open problems in Mathematical Tomography?

Since I feel that Tomography can be applied to a wide range of sciences, I was wondering what the current open problems in Tomographic Reconstruction are. Furthermore, I am curious as to how these ...
9
votes
3answers
162 views

Applications of “finite mathematics” to physics

Disclaimer: I know that what follows is a biased view on applications, one of the points of the question is to eliminate some of that bias. When I think of applications of maths outside of itself, I ...
9
votes
1answer
527 views

Application of Combinatorics/Graph Theory to Organic Chemistry?

Recently, I have been self-teaching graph theory and having an organic chemistry course at school. When I was learning isomer enumeration I found great resemblance between organic molecules and ...
9
votes
2answers
348 views

What is the simplest mathematical concept that does not map to a physical phenomenon?

One of my colleagues argues that everything in math proves something in the physical world. For instance, he claims that the existence of math to describe fractals proves the infinite divisibility of ...
9
votes
1answer
366 views

Your Favourite Application of the Birkhoff Ergodic Theorem

Here we have a big list of great applications of the Baire category theorem. I recently read the Birkhoff ergodic theorem and I think perhaps this theorem is on par with Baire's theorem in terms of ...
9
votes
1answer
176 views

How can one tell if a PDE describes wave behaviour?

I have been looking at a lot of different non-linear PDEs which describe waves lately and have come to the realisation that I don't know what it is about these PDEs that make them behave like waves. ...
9
votes
1answer
191 views

Why do we care about normal matrices/operators?

We know that normal operators are "nice". In the finite dimensional case, the spectral theorem tells us everything we need to know. In the infinite dimensional case, we can define a continuous ...
9
votes
4answers
676 views

What is the physical meaning of fractional calculus?

What is the physical meaning of the fractional integral and fractional derivative? And many researchers deal with the fractional boundary value problems, and what is the physical background? What ...
8
votes
9answers
5k views

Why is the derivative important? [duplicate]

Derivatives, both ordinary and partial, appear often in my mathematics courses. However, my teachers have never really given a good example of why the derivative is useful. My questions: Other than ...
8
votes
10answers
2k views

What is the use of Calculus? [closed]

I know this may seem like a really broad question, but I will narrow it down. I really want to know the purpose of some of the things my teacher is emphasizing in my calc class. For example why it ...