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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.)

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225 votes
11 answers
36k views

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 ...
170 votes
34 answers
31k views

Can you provide me historical examples of pure mathematics becoming "useful"?

I am trying to think/know about something, but I don't know if my base premise is plausible. Here we go. Sometimes when I'm talking with people about pure mathematics, they usually dismiss it because ...
133 votes
20 answers
102k views

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 ...
Bhargav's user avatar
  • 2,977
116 votes
8 answers
36k views

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 ...
Alexander Gruber's user avatar
  • 27.1k
112 votes
24 answers
19k views

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 ...
totalnoob's user avatar
  • 1,243
105 votes
20 answers
13k views

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. ...
Eric Tressler's user avatar
83 votes
12 answers
33k views

What are the applications of functional analysis?

I recently had a course on functional analysis. I was thinking of studying the mathematical applications of functional analysis. I came to know it had some applications on calculus of variations. I am ...
gamma's user avatar
  • 924
80 votes
7 answers
7k views

Algebraic Intuition for Homological Algebra and Applications to More Elementary Algebra

I am taking a course next term in homological algebra (using Weibel's classic text) and am having a hard time seeing some of the big picture of the idea behind homological algebra. Now, this sort of ...
Alex Youcis's user avatar
  • 54.3k
80 votes
2 answers
3k views

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 ...
Oliphaunt's user avatar
  • 933
73 votes
17 answers
174k views

What is a real world application of polynomial factoring?

The wife and I are sitting here on a Saturday night doing some algebra homework. We're factoring polynomials and had the same thought at the same time: when will we use this? I feel a bit silly ...
Dan's user avatar
  • 871
70 votes
4 answers
15k views

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 ...
user avatar
69 votes
20 answers
9k views

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 ...
64 votes
17 answers
23k views

Interesting "real life" applications of serious theorems [closed]

As student in mathematics, one sometimes encounters exercises which ask you to solve a rather funny "real life problem", e.g. I recall an exercise on the Krein-Milman theorem which was something like: ...
64 votes
17 answers
16k views

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 ...
vantage5353's user avatar
57 votes
26 answers
8k views

Applications of complex numbers to solve non-complex problems

Recently I asked a question regarding the diophantine equation $x^2+y^2=z^n$ for $x, y, z, n \in \mathbb{N}$, which to my surprise was answered with the help complex numbers. I find it fascinating ...
acernine's user avatar
  • 1,750
54 votes
13 answers
173k views

Real world application of Fourier series

What are some real world applications of Fourier series? Particularly the complex Fourier integrals?
Namit Sinha's user avatar
53 votes
7 answers
13k views

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 ...
Gadi A's user avatar
  • 19.3k
52 votes
9 answers
25k views

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 ...
Seyhmus Güngören's user avatar
49 votes
18 answers
99k views

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 ...
Sylverdrag's user avatar
  • 1,512
49 votes
10 answers
66k views

Real world uses of hyperbolic trigonometric functions

I covered hyperbolic trigonometric functions in a recent maths course. However I was never presented with any reasons as to why (or even if) they are useful. Is there any good examples of their uses ...
Jacob's user avatar
  • 1,009
49 votes
11 answers
22k views

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 ...
mau's user avatar
  • 9,794
47 votes
7 answers
22k views

"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, ...
user110285's user avatar
45 votes
10 answers
15k views

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.
Jin's user avatar
  • 701
45 votes
1 answer
10k views

Physical interpretation of Laplace transforms

One may define the derivative of $f$ at $x$ as $\lim\limits_{h\to0}\cdots\cdots\cdots$ etc., and show that that has certain properties, but it also has a "physical" interpretation: it is an ...
Michael Hardy's user avatar
44 votes
17 answers
9k views

What is a simple, physical situation where complex numbers emerge naturally? [duplicate]

I'm trying to teach middle schoolers about the emergence of complex numbers and I want to motivate this organically. By this, I mean some sort of real world problem that people were trying to solve ...
Joshua Frank's user avatar
44 votes
2 answers
9k views

What is the use of hyperreal numbers?

For sometime I have been trying to come to terms with the concept of hyperreal numbers. It appears that they were invented as an alternative to the $\epsilon-\delta$ definitions to put the processes ...
Paramanand Singh's user avatar
  • 87.8k
43 votes
18 answers
65k views

What is an example of real application of cubic equations?

I didn't yet encounter to a case that need to be solved by cubic equations (degree three) ! May you give me some information about the branches of science or criterion deal with such nature ?
Fereydoon Shekofte's user avatar
42 votes
11 answers
24k views

what are the different applications of group theory in CS? [closed]

What are some applications of abstract algebra in computer science an undergraduate could begin exploring after a first course? Gallian's text goes into Hamming distance, coding theory, etc., I ...
user avatar
42 votes
8 answers
26k views

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 ...
Paul B's user avatar
  • 808
38 votes
8 answers
9k views

Applications of the wreath product?

We recently went through the wreath product in my group theory class, but the definition still seems a bit unmotivated to me. The two reasons I can see for it are 1) it allows us to construct new ...
user avatar
36 votes
10 answers
4k views

Surprising applications of topology

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 ...
user141592's user avatar
  • 6,128
34 votes
3 answers
3k views

Mathematical preparation for postgraduate studies in Linguistics

I am an undergraduate student in Mathematics and I would like to continue my postgraduate studies in the harder, more mathematical aspects of Linguistics. What exactly would that include is unknown ...
Orest Xherija's user avatar
33 votes
5 answers
6k views

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 ...
geodude's user avatar
  • 8,097
33 votes
1 answer
2k views

Does complex dynamics offer any insights into real dynamics?

One of the most fascinating things about complex analysis is that it provides insights into real analysis. Here are two pictures from Needham's book Visual Complex Analysis (p. 65): Picture 1 (...
Leo's user avatar
  • 7,710
32 votes
7 answers
4k views

Honest application of category theory

I believe that category theory is one of the most fundamental theories of mathematics, and is becoming a fundamental theory for other sciences as well. It allows us to understand many concepts on a ...
Martin Brandenburg's user avatar
31 votes
2 answers
1k views

Statistics Primer for the Unwary Mathematician

I have a new position in a biology department (after being housed in a maths department) working on cognitive and population modeling. People in my lab are asking for help with applying statistical ...
Lyjat's user avatar
  • 363
30 votes
6 answers
10k views

Real life uses of prime numbers (in physics/engineering) [closed]

Prime numbers (or coprimes) have few well-known uses but interesting ones. The classical example is that prime numbers are used in asymmetric (or public key) cryptography. Prime numbers and coprimes ...
Morlock's user avatar
  • 449
30 votes
3 answers
3k views

Applications of model theory to analysis

Some of the more organic theories considered in model theory (other than set theory, which, from what I've seen, seems to be quite distinct from "mainstream" model theory) are those which arise from ...
tomasz's user avatar
  • 35.7k
29 votes
3 answers
2k views

Exceptional books on real world applications of graph theory.

What are some exceptional graph theory books geared explicitly towards real-world applications? I would be interested in both general books on the subject (essentially surveys of applied graph theory ...
Alexander Gruber's user avatar
  • 27.1k
28 votes
4 answers
4k views

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 ...
Thomas Russell's user avatar
28 votes
1 answer
1k views

St. Basil's cathedral, Moscow steeple shape

Onion-shaped dome cathedral architecture seen here appears to include in its lower part a geometry of positive, and in upper (steeple) part negative Gauss curvature. The corresponding elliptic and ...
Narasimham's user avatar
  • 40.7k
27 votes
9 answers
148k views

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 "...
Hal's user avatar
  • 3,416
27 votes
3 answers
6k views

Consider a man who travelled exactly 2 km in two hours. Is there a one-hour interval when he traveled exactly 1 km?

Consider a man who travelled exactly 2 km in two hours. Is there a one-hour interval when he traveled exactly 1 km? Can we make a mathematical argument? I have written my attempt in an answer below. ...
whoisit's user avatar
  • 3,208
27 votes
4 answers
6k views

Why does dust gather in corners?

I've noticed when sweeping the floor that dust gathers particularly in the corners. I assume there is a fluid mechanics reason for this. Does anyone know what it is? Edit: No, really, this is a ...
isomorphismes's user avatar
26 votes
18 answers
48k views

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 ...
25 votes
5 answers
4k 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{...
user2902293's user avatar
  • 2,669
25 votes
14 answers
27k views

What are some applications of Mathematics to the medical field?

This semester I'm charged with finding a senior capstone project for next year. I've given it a lot of thought and can't seem to find any interesting ideas that are appropriate for my level of ...
25 votes
5 answers
9k views

Why does the Elo rating system work?

The Elo rating system is used to rank players in games such as chess. I can find plenty of explanations online of how to compute someone's Elo rating, how to actually crunch the numbers in practice, ...
Jack M's user avatar
  • 27.9k
24 votes
1 answer
3k views

StarCraft II: Ladder math

At the Blizzcon 2010, StarCraft II multiplayer panel, this stuff was supposed to explain the ladder matchmaking system. I look at this and go eh? what!? Is any of this real? or are they just messing ...
John Leidegren's user avatar
23 votes
10 answers
3k views

What are the most prominent uses of transfinite induction outside of set theory?

What are the most prominent uses of transfinite induction in fields of mathematics other than set theory? (Was it used in Cantor's investigations of trigonometric series?)
Michael Hardy's user avatar

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