# Tagged Questions

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.)

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### Are there real world applications of finite group theory?

I would like to know whether there are examples where finite group theory can be directly applied to solve real world problems outside of mathematics. (Sufficiently applied mathematics such as ...
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### 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 ...
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### Real life applications of Topology

The other day I and my friend were having an argument. He was saying that there is no real life application of Topology at all whatsoever. I want to disprove him, so posting the question here What ...
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### Real-world applications of prime numbers?

I am going through the problems from Project Euler and I notice a strong insistence on Primes and efficient algorithms to compute large primes efficiently. The problems are interesting per se, but I ...
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### Why does Benford's Law (or Zipf's Law) hold?

Both Benford's Law (if you take a list of values, the distribution of the most significant digit is rougly proportional to the logarithm of the digit) and Zipf's Law (given a corpus of natural ...
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### What is a simple example of a limit in the real world?

This morning, I read Wikipedia's informal definition of a limit: Informally, a function f assigns an output $f(x)$ to every input $x$. The function has a limit $L$ at an input $p$ if $f(x)$ is "...
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### What are some applications of elementary linear algebra outside of math?

I'm TAing linear algebra next quarter, and it strikes me that I only know one example of an application I can present to my students. I'm looking for applications of elementary linear algebra outside ...
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### 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 ...
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### Is the Law of Large Numbers empirically proven?

Does this reflect the real world and what is the empirical evidence behind this? Layman here so please avoid abstract math in your response. The Law of Large Numbers states that the average of the ...
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### Real life usage of Benford's Law

I recently discovered Benford's Law. I find it very fascinating. I'm wondering what are some of the real life uses of Benford's law. Specific examples would be great.
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### 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 ...
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### 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 ...
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### How do I sell out with abstract algebra?

My plan as an undergraduate was unequivocally to be a pure mathematician, working as an algebraist as a bigshot professor at a bigshot university. I'm graduating this month, and I didn't get into ...
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### Uses of quadratic reciprocity theorem

I want to motivate the quadratic reciprocity theorem, which at first glance does not look too important to justify it being one of Gauss' favorites. So far I can think of two uses that are basic ...
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### Real world applications of category theory

I was reading some basic information from Wiki about category theory and honestly speaking I have a very weak knowledge about it. As it sounds interesting, I will go into the theory to learn more if ...
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### Applications of algebraic topology

What are some nice applications of algebraic topology that can be presented to beginning students? To give examples of what I have in mind: Brouwer's fixed point theorem, Borsuk-Ulam theorem, Hairy ...
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### Surprising applications of cohomology

The concept of cohomology is one of the most subtle and powerful in modern mathematics. While its application to topology and integrability is immediate (it was probably how cohomology was born in the ...
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### How does linear algebra help with computer science

I'm a Computer Science student. I've just completed a linear algebra course. I got 75 points out of 100 points on the final exam. I know linear algebra well. As a programmer, I'm having a difficult ...
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### Applications of Gröbner Bases

I would like to present an application of GrÃ¶bner bases. The audience is a class of first year graduate students who are taking first year algebra. Anyone have suggestions on a specific ...
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### 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 ...
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### Applications of cardinal numbers

I know basic things about cardinality (I'm only in High School) like that since $\mathbb{Q}$ is countable, its cardinality is $\aleph_0$. Also that the cardinality of $\mathbb{R}$ is $2^{\aleph_0}$. ...
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### What is Cramer's rule used for?

I could have sworn I posted the question in the subject line somewhere on the internet, and I thought it was here. But I can't find it. It ought to be here in case anyone looks for it. Cramer's ...
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### What are the real-world applications of real analysis?

I've read the wikipedia article on mathematical analysis and this, but I can't exactly find an answer. Is real analysis just some pure math, or does it really have something to with physical ...
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### How are complex numbers useful to real number mathematics?

Suppose I have only real number problems, where I need to find solutions. By what means could knowledge about complex numbers be useful? Of course, the obviously applications are: contour ...
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### Calculate half life of esters

I'm trying to calculate the level of testosterone released from different testosterone esters. Here are some graphs of testosterone levels after single injections of 250mg of each ester. Testo U ...
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### Differential Equations Skydiver Problem

I've seen many variants of this problem online, but not quite the same as this, so I don't believe this is a duplicate. The famous differential equation problem models a skydiver jumping out of a ...
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### Can you provide me historical examples of pure mathematics becoming “useful”?

I'm trying to think/know about something but I don't know if my basis premise is plausible, here we go. Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because ...
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### What are some examples of mathematics that had unintended useful applications much later?

I would like to know some examples of interesting (to the layman or young student), easy-to-describe examples of mathematics that has had profound unanticipated useful applications in the real world. ...
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### Why do we still do symbolic math?

I just read that most practical problems (algebraic equations, differential equations) do not have a symbolic solution, but only a numerical one. Numerical computations, to my understanding, never ...
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### How do people apply the Lebesgue integration theory?

This question has puzzled me for a long time. It may be too vague to ask here. I hope I can narrow down the question well so that one can offer some ideas. In a lot of calculus textbooks, there is ...
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### Surprising applications of topology [closed]

Today in class we got to see how to use the Brouwer Fixed Point theorem for $D^2$ to prove that a $3 \times 3$ matrix $M$ with positive real entries has an eigenvector with a positive eigenvalue. The ...
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### What is the real life use of hyperbola? [closed]

The point of this question is to compile a list of applications of hyperbola because a lot of people are unknown to it and asks it frequently.
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### Real world uses of Quaternions?

I've recently started reading about Quaternions, and I keep reading that for example they're used in computer graphics and mechanics calculations to calculate movement and rotation, but without real ...
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### Factorial of a matrix: what could be the use of it?

Recently on this site, the question was raised how we might define the factorial operation $\mathsf{A}!$ on a square matrix $\mathsf{A}$. The answer, perhaps unsurprisingly, involves the Gamma ...
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### “Real”-life applications of algebraic geometry

Before you tell me that this question has been asked, give me a bit of your time please to read this question because it is not as simple as it sounds. I did my undergraduate degree in mathematics, ...
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### 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 much keen to have an elementary proof of the ...
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### Applications of Perfect Numbers

I'm preparing a talk on Mersenne primes, Perfect numbers and Fermat primes. In trying to provide motivation for it all I'd like to provide an application of these things. I came up with these: ...
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### Applications of the Fibonacci sequence

The Fibonacci sequence is very well known, and is often explained with a story about how many rabbits there are after $n$ generations if they each produce a new pair every generation. Is there any ...
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### Applications for Homology

The Question: Are there any ways that "applied" mathematicians can use Homology theory? Have you seen any good applications of it to the "real world" either directly or indirectly? Why do I care? ...
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### 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 ...
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### 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 ...
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### What are the applications of finite calculus

I'm reading through Concrete Mathematics [Graham, Knuth, Patashnik; 2nd edition], and in the section regarding Summation, they have a sub-section entitled "Finite and Infinite Calculus". In this ...
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### 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 ...
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### 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 ...
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### Biology: Wright-Fisher model of genetic drift

In evolutionary biology (in population genetics to be more accurate) exists the concept of genetic drift. It describes how an allele (gene variant) (that has no advantage or disadvantage in terms of ...
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### 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 ...
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### 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 ...
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### 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, ...