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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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6
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1answer
660 views

Topological book which covers applications in the Medical Field (Medicine/Bacteria/Cancer/Viruses)

To get to the point I'm looking for a book on Topology that covers specifically its uses in the medical field. I've seen a lot of book requests in Topology, but they are all about learning topology ...
6
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1answer
925 views

Why more than 3 dimensions in linear algebra?

This might seem a silly question, but I was wondering why mathematicians came out with more than 3 dimensions when studying vector spaces, matrices, etc. I cannot visualise more than 3 dimensions, so ...
6
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2answers
368 views

Which features would be interesting for a mathematician in a fractal program?

Many years ago I wrote this fractal generator: http://uberto.fractovia.org/ It was shareware but then I put it as open source. It's written in Delphi, a language that I don't use anymore. So I'm ...
6
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1answer
93 views

Are ordinals greater than $\varepsilon_0$ used outside Ordinal Analysis?

I know of Conway's use of ordinals to exhibit the algebraic closure of $\mathcal{F}_2$. I also read a document about the Cantor Bendixson rank of some family of groups. But I found no applications of ...
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0answers
34 views

Extending a common-neighbor statistic to more than two nodes

first time poster here (happy to edit if I am violating any guidelines, please just let me know) :) I am curious whether the following formula from this paper by Li and Liang for the probability of ...
6
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1answer
140 views

Show that the profile of the hill is a cycloid

I'm struggling with this problem: From George Simmons_ Differential Equations At sunset a man is standing at the base of a dome-shaped hill where if faces the setting sun. He throws a rock ...
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0answers
302 views

Applications of the Kuratowski closure-complement theorem

I crossed with the Kuratowski closure-complement theorem while learning Munkres's Topology (Problem 21 in Section 17; Page 102, 2nd edition). The following description is from B.J. Gardner and M. ...
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2answers
466 views

Why demonstrations are important in mathematics? [closed]

Good evening, I'm studying math and would like to know how important are mathematical proofs in the world and particularly in a school of mathematics Thanks for your help
5
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5answers
746 views

Decoding Every Top 100 Voting Ever

I need expert help on the math behind the following voting mechanism, any comment towards solutions are greatly appreciated! -- A country is holding a poll to determine the top 100 restaurants out ...
5
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3answers
11k views

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 ...
5
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3answers
1k views

Does “Big Data” Have a Ramsey Theory Problem?

I'm erring on the side of conservatism asking here rather than MO, as it is possible this is a complex question. "Big Data" is the Silicon Valley term for the issues surrounding the huge amounts of ...
5
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2answers
1k views

What's interesting in latus rectum?

I'm a maths teacher in Italian secondary school and I've been spending some time trying to construct "meaningful" problems about conic sections. I particularly like problems which focus on practical ...
5
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2answers
202 views

Who generates the prime numbers for encryption?

I was talking to a friend of mine yesterday about encryption. I was explaining RSA and how prime numbers are used - the product $N = pq$ is known to the public and used to encrypt, but to decrypt you ...
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2answers
2k views

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 $2^{\aleph_0}$. ...
5
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3answers
1k views

What is an application of the dual space?

Does somebody know any application of the dual space in physics, chemistry, biology, computer science or economics? (I would like to add that to the german wikipedia article about the dual space.)
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3answers
836 views

Second Order and Beyond for Multivariable Taylor Series

I am looking for reasons why an engineer might want to learn about multivariable Taylor Series beyond order one. I have no problem seeing the value of single variable Taylor Series. I have quite a ...
5
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4answers
967 views

Why use differentials to compute error?

I get how to use differentials to compute error, but why is it a "good" method? For example, a standard problem is something like: If the radius of a circle is $3 \pm 0.1$ cm, find the area with ...
5
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2answers
922 views

Mathematics for Graduate Political Science

I'm preparing to attend graduate school for political science here in Canada and I'm having something of a crisis. Midway through my degree program I chose to drop my first love (English) to focus on ...
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2answers
1k views

Applications of matroid theory.

I am considering learning about matroid thoery. I would like to know what the applications of matroid theory are before (if they exist). Regards
5
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2answers
719 views

Motivation for the study of the Chern connection

Given a Hermitian metric $H$ over a holomorphic vector bundle $E$ with holomorphic structure $\overline{\partial}$, there exists a unique connection $\nabla$ (named afer Chern) satisying the following ...
5
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2answers
376 views

Simple lowpass frequency response

Okay, so hopefully this isn't too hard or off-topic. Let's say I have a very simple lowpass filter (something that smooths out a signal), and the filter object has a position variable and a cutoff ...
5
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2answers
894 views

types of distances between points

I was just finished working on a project where we had to allocate facilities in a $2$-dimensional plane in order to satisfy certain demand restrictions while keeping the cost at minimum. I do NOT have ...
5
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2answers
1k views

Applications of algebraic graph theory

What are some subtle, or non-obvious applications of algebraic graph theory? Obviously it can be used to study anything directly involving graphs (for instance, the wikipedia page mentions ...
5
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1answer
1k views

Background for studying and understanding Stochastic differential equations

Assume I have back ground of the following knowledge based on the textbook as : ODE : ODE by Tenenbaum Baby probability : Ross 's baby probability Baby real anlysis : Bartle's introduction to real ...
5
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1answer
191 views

Applications of symplectic geometry in industry

I am wondering if symplectic geometry is being used anywhere outside of academia? Are there any current applications of symplectic geometry in industry?
5
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1answer
103 views

Concrete Applications of Lattices to Algebra

The importance of lattices to algebra (or any field of mathematics really) should be fairly obvious. Specifically, we always have a complete lattice of subobjects (and a lattice of strong subobjects ...
5
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1answer
71 views

applications of (topological and algebraic) commutative diagrams in organic synthesis

In algebraic topology, there are a lot of commutative diagrams and commutative diagrams up to homotopy. Different ways of compositions of maps in a commutative diagram are equal or homotopy equivalent....
5
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1answer
453 views

Solving Kepler's second law

Kepler's second law, about equal areas in equal times, is a differential equation: it gives velocity as a function of location. Where are the best expository accounts of the process of solving this ...
5
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1answer
2k views

Unexpected Practical Applications of Calculus

Calculus shows up in a lot of places in the world. Specifically, here are three areas where I see it used the most: Optimization problems. Anything involving rates of change (e.g. velocity $\...
5
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1answer
191 views

History and connecting math to real world

I am software developer with big interest in Mathematics and especially discrete mathematics (which is foundational for computer science). I am currently reading Discrete Mathematics and Its ...
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2answers
295 views

Powerful applications of linear algebra?

I'd like to see some neat, elegant applications of linear algebra. I'm a undergraduate student but I don't want to prevent people from posting things just because I won't understand them, but if it's ...
5
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1answer
1k views

What happens if you follow the sun?

Travelling around for quite a while and sometimes, well, just following the sun, today the question occurred to me: What happens if you really do this? So let's say some point is moving along the ...
5
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1answer
69 views

Math of Jury Sizes

If we go by the assumption that a Jury is a representation of the public at large, then is 12 people statistically signficant? When doing any scientific survey or poll, a sample of 12 people would be ...
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0answers
108 views

Derivation of 2D Korteweg-de-Vries equation

Coming from engineering rather than mathematics, I am recently dealing with non-linear partial differential equations e.g. like the well known Korteweg-de-Vries equation: $$u_{t} + uu_x + u_{xxx} = 0$$...
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482 views

The Mathematics of Skateboarding Tricks.

This question is just for fun and I apologise if it's too broad or off topic. The Details: As anyone who has played the Tony Hawk games can tell you, skateboarding - at least in part - can be scored ...
5
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0answers
58 views

What are some examples of algorithms besides crypto and integer factorization that use elliptic curves?

I've heard that elliptic curves have applications in strange places, due to their connection to elliptic functions and then elliptic integrals, which have nice algebraic addition formulas. I see ...
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0answers
154 views

Significance and application of Riesz Decomposition Theorem

The Riesz Decomposition Theorem in Operator Theory is given as: Let $a \in \mathcal{A}$ (for unital Banach algebra $\mathcal{A}$) Suppose $\sigma(a) = \sigma_1 \cup \sigma_2$ where $\sigma_1 \cap \...
5
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1answer
158 views

How is it possible to change the pitch and the tempo of an audio track independently of each other?

If you slow down a turntable or cassette-player, both pitch and tempo are decreased. How is it possible to change one without affecting the other?
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8answers
2k views

Practical application of matrices and determinants

I have learned recently about matrices and determinants and also about the geometrical interpretations, i.e, how the matrix is used for linear transformations and how determinants tell us about area/...
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5answers
562 views

Why - not how - do you solve Differential Equations? [closed]

I know HOW to mechanically solve basic diff. equations. To recap, you start out with the derivative $\frac{dy}{dx}=...$ and you aim to find out y=... To do this, you separate the variables, and ...
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3answers
3k views

Are questions of convergence important in real life?

In the real world, do we ever need to worry about convergence and what not? I am not talking about whether recursive functions and such terminate, but convergence in analysis. It seems like the ...
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3answers
2k views

What is the speed with which the shadow of the horse move along the fence at the moment when it covers $1/8$ of the circle in km/hr?

A horse runs along a circle with a speed of 20 km/hr.A lantern is at the center of the circle.A fence is along the tangent to the circle at the point at which the horse starts.What is the speed with ...
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4answers
254 views

Why are partial orderings important?

I was reviewing my old Discrete Mathematics notes, and I came across a section describing how Partial Orderings are identified. I understand this, but I can't seem to recall/find information on why ...
4
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1answer
184 views

Using Rolle's theorem to show $e^x=1+x$ has only one real root

Applying Rolle's Theorem, prove that the given equation has only one root: $$e^x=1+x$$ By inspection, we can say that $x=0$ is one root of the equation. But how can we use Rolle's theorem to prove ...
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2answers
358 views

What is the point of isomorphism concept?

In many courses, say Linear Algebra, Group Theory, Topology, instructors often say that knowing that certaing objects are isomorphic, sometimes makes life easier because we can work with more friendly ...
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5answers
3k views

Are there examples of third-(or higher)-order linear differential equations in physics or applied mathematics?

The classical second-order linear ordinary differential equation is that named after Sturm and Liouville: formally, \begin{equation} (pu')'=ru. \end{equation} It arises naturally in many physical ...
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3answers
3k views

Probability of 15 consecutive green lights

Introduction Upon a trip home, my mother and I were noticing a very peculiar occurrence: Traffic lights were almost continuously green. Indeed, exactly fifteen different traffic lights were green ...
4
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1answer
2k views

Usage of finite fields or Galois fields in real world

I'm currently studying the theory of Galois fields. And I have a question, what practical usage of this finite fields? As stated in Wikipedia: Finite fields are important in number theory, ...
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2answers
336 views

Real-world applications of fields, rings and groups in linear algebra.

Real-world applications of fields, rings and groups in linear algebra. A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact ...
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3answers
538 views

Need to find the equation of a curve from a Hand drawing [closed]

My uncle makes hand drawings of furniture on a large piece of chart paper at 1:1 scale. He has recently passed away. I have the task of converting those hand drawings into Autocad drawings. The ...