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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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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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
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 ...
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 ...
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 ...
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 ...
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 ...
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 $2^{\aleph_0}$. ...
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.)
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 ...
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 ...
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 ...
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
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 ...
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 ...
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 ...
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 ...
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 ...
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?
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 ...
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....
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 ...
2k views

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### 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?
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/...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, $$(pu')'=ru.$$ It arises naturally in many physical ...
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 ...
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, ...