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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1answer
226 views

Applying linear algebra to solve a problem in mechanical equilibrium

I came across the following problem in "Introduction to Applied Mechanics" by Gilbert Strang, and am a little confused about the solution to this problem. The following figure shows the problem. ...
0
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1answer
32 views

A prove for information restoration with 2 schedules that delete information

What kind of mathematics or technique do I need to use the following? Just pointing me in the right direction is also helpful as I love mathematics but I am not so good at it. It's a problem I have ...
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0answers
266 views

Does there exist some relations between Cryptography and Algebraic Topology?

We know that there are many application of Cryptography in our real life. Are there any relation between Cryptography and Algebraic Topology? If yes, please suggest me some link or books. Thanks ...
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1answer
108 views

What are some applications of real analysis? [duplicate]

What are some applications of real analysis? Can someone post a simple example of how real analysis can solve such problems?
0
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1answer
130 views

what are some applications of group theory [duplicate]

what are some applications of group theory? Group theory seems to be rather abstract.
54
votes
19answers
5k 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 ...
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4answers
107 views

If $2000 m^{2}$ of material is used to to construct a box…,then what is the largest possible volume of the box?

If $2000 m^{2}$ of material is used to to construct a rectangular box with a square base and an open top,then what is the largest possible volume of the box? I put an equation for the volume : $V = ...
1
vote
0answers
82 views

Water Flow Rate

I am doing a software development code to dispense water for which I need to find the its flow rate. The tank can hold around $300$ liters of water and has only a $1/2$" inch ($.75$ cm inch diameter) ...
3
votes
1answer
181 views

Examples of applications of category theory to chemistry

What is some simple application of category theory to chemistry, namely, something that is much easier to do in chemistry with category theory than without. It does not need to be bleeding edge, or to ...
4
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0answers
68 views

Applications of resolution of singularities

I would to know applications of Resolution of Singularities, this means what is profits of having a resolution of singularities of a variety both in and out of mathematics and both in positive and ...
4
votes
1answer
119 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 ...
2
votes
0answers
74 views

What did homogeneous coordinates allow 19th century mathematicians to do?

I read about Mobius developing Barycentric and homogeneous coordinates, and I read about homogeneous coordinates and what they are and I'm totally on board with taking a line from the origin and ...
0
votes
1answer
45 views

An $\Bbb{R}\to\Bbb{R}$ function with two plateaus of different heights and a valley

I am looking for a $\Bbb{R}\to\Bbb{R}$ function $f$ with two plateaus of different heights and a valley. The function has a minimum for $x=a$ and $f(a)=b$. The first (the one for smaller $x$) ...
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0answers
35 views

Pairing Two Point Clouds

So I have two point clouds $X$ and $Y$ each with $N$ points in the familiar $\mathbb{R}^3$ euclidian 3D space. I then have an inter-point distance $d(\vec x_i,\vec y_j)$ which is zero if $\vec x_i$ is ...
0
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1answer
225 views

Application for interpolating periodic B-spline

I need to draw a cubic C^2 continous, closed (periodic boundary conditions) B-spline which should interpolate a set of control points. If possible it would be great if I could specify the knot vector. ...
2
votes
2answers
458 views

A comprehensive book on Applied Mathematics for beginners

The Princeton Companion To Mathematics is described on Wikipedia thus: The book concentrates primarily on modern pure mathematics rather than applied mathematics, although it does also cover both ...
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1answer
75 views

What is an elementary yet important application of matrix in finance?

What is an elementary yet important application of matrix in finance? I have difficulty to read anything intermediate/advanced associated with this topics, hopefully I can find something interesting ...
2
votes
1answer
145 views

Question about homotopy equivalence

I have this proof but I don't understand why $i\circ j$ induces a homotopy equivalence, and how to see $j_*$ is injective at the level of homology? $X$ is a Banach space
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0answers
39 views

Classifying growth as percent increase.

So I have been thinking about resource consumption a lot after watching the most important video you will ever see. It is pretty long so I will summarize it as follows, the professor makes a strong ...
1
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3answers
132 views

Applications of derivatives outside mathematics and physics

I've been teaching calculus for several years and have some doubts about whether derivatives (and integration techniques) of common functions are useful and important outside mathematics and physics. ...
3
votes
1answer
74 views

(Possible) application of Sarason interpolation theorem

This question is related to the following Wikipedia article on Nevanlinna–Pick interpolation. At the end it has been written as Pick–Nevanlinna interpolation was introduced into robust control by ...
5
votes
1answer
238 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 ...
0
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3answers
78 views

competitive math

I hope everyone knows about competitive programming. There are so many sites where you can solve programming tasks and increase your rating. I am curious, does site about something like this for math ...
0
votes
1answer
83 views

Matrix diagonalization example

I want a real world example or simply a good example that explains the use of a diagonal matrix, and when to prefer to use a diagonal matrix? any other important information about diagonal matrix or ...
0
votes
1answer
50 views

Uses of Mersenne primes in math

There is an international search for Mersenne primes. The project is huge. But what are the uses of Mersenne Primes in math? Do they have any other properties other than being of the form $2^n-1$?
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1answer
49 views

Android application like mathjax

I am looking for an application like mathjax for android so I can type equations with my cellphone in the correct format
2
votes
1answer
17 views

Problem on Finding the speed using Intertia

I did the first part (using parallel axis theorem) and showed that intertia. The problem is in the second part, I know that $C=I\frac{d^2\theta}{dt^2}$ , where C is the moment. So in this case it ...
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0answers
110 views

Mathematics only with physics? What about biology and chemistry?

In The Mathematical Mechanic, the author "reveals how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways ...
3
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1answer
141 views

Is Linear Algebra the foundation of Applied Mathematics?

I've lately taken an interest in foundations of my field. While there are many important areas that contribute to Applied Mathematics (differential equations, probability & statistics, numerical ...
7
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3answers
521 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 ...
0
votes
2answers
225 views

Optimization of a rectangular container

A rectangular sheet of tinplate is $2k$ cm by $k$ cm. Four squares, each with sides $x$ cm, are cut from its corners. The remainder is bent into the shape of an open rectangular container. Find the ...
0
votes
1answer
166 views

Using differentials with volume of a cube

my question is The volume of a cube is increased from 1000 cubic centimeters to 1156 cubic centimeters. Use differentials to determine. the side length of the cube increases by? the surface area ...
1
vote
1answer
31 views

Finding the angle of elevation in a projectile

Let $\theta$ be the angle of elevation $x(t) = x_0 + u_0t + \frac{1}{2} at^2$ where $x(t)=0$ and $x_0=50m$ , And $u_0$ is vertically resolved initial component of the velocity I applied ...
0
votes
0answers
61 views

Usefulness of $\frac{ac}{b}<a-b+c$

For $$a<b<0<c$$ I have a proof that shows that $$\frac{ac}{b}>a-b+c$$ But if $$a<0<b<c$$ Then $$\frac{ac}{b}<a-b+c$$ What I was wondering is how useful are these ...
0
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1answer
24 views

How I can find the inverse function $F⁻¹$?

Let $$F:U⊂ℝ^{r+1}→ℝ^{r+1}$$ $$(s₁,s₂,...,s_{r},s_{r+1})→F(s₁,s₂,...,s_{r},s_{r+1})=(f(s₁),f(s₂),....,f(s_{r}),f(s_{r+1}))$$ be a continuously differentiable function defined from an open set ...
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2answers
130 views

Finding more than one root using Newton's Method

The problem is stated as follows: Find the two roots of $x^{4}-8x^{2}-x+16 \:\:in \: [1,3].$ What is a good first guess / a good way to make a first guess when more than one root is involved, if one ...
11
votes
2answers
867 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 ...
2
votes
0answers
95 views

Application of integrating $\cos^4 x$?

A student asked a colleague the other day for a practical application that involved needing to integrate the fourth power of cosine, but no one here could think of one off-hand other than some volume ...
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0answers
109 views

Has knot theory led to the development of better knots?

Knot theory was likely originally motivated by the study of real-world knots such as these: Indeed, mathematical knot tables to this day look not too dissimilar from the familiar "age of ...
0
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1answer
96 views

Including non-markovian processes in a birth-death process

Current model I want to model a stochastic system with a birth-death (Markovian) model. I therefore have this kind of $n$ times $n$ (where $n$ is the number of possible states) transition matrix: ...
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1answer
67 views

Variance in offspring genotypes. Binomial distribution

Background Here is first some vocabulary: Diploid: phase in the life cycle where the individuals carry two chromosomes of each type, just like in humans (exception of the sexual chromosomes). ...
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2answers
140 views

Applications of infinite cardinalities in real analysis

What are some topics in real analysis that make use of infinite cardinalities larger than that of the real numbers themselves, preferably [edit: but not necessarily] topics that are widely applied in ...
1
vote
1answer
142 views

Engineer searching for calculus and complex analysis books without limits

I am an engineer and I need to study calculus and complex analysis without too much limits or Riemann sums or proofs. I mean on the differentiation and integration levels and higher (not digging ...
0
votes
2answers
100 views

Vector space without a scalar product

In linear algebra the terms vector space and scalar product always (at least for me) appear together. Can you give me an example of a vector space without a scalar product? Does the senescence Let V ...
0
votes
2answers
407 views

Is Real Analysis an Applied Subject?

I am doing my graduate study in Applied Statistics. This semester my professor told me to take Real Analysis and the professor who is teaching Real Analysis is using Folland's Book entitled "Real ...
3
votes
1answer
78 views

How to draw Congressional districts to mirror the Popular Vote

Let me preface this by saying that I'm not sure whether this is fundamentally a mathematical question or not, but I think it is. In the United States, the House of Representatives is elected roughly ...
3
votes
0answers
123 views

What is the motivation behind the study of pattern-avoiding permutations?

There is a ton of research on pattern-avoiding permutations (permutations that do not contain some designated permutation pattern). We're figuring out how to enumerate them, what random ones are ...
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vote
2answers
3k views

What is the usage of Permuation and Combination in the real life or Computer Programming world?

I have never understood the application of P & C, even in the software programming. I know, the principle behind P&C is counting. So, basically it makes the counting quicker. However, I could ...
2
votes
2answers
76 views

What is the line integral in higher dimensions?

Given a function $\ f:\mathbb{R}^2\to\mathbb{R}$ and some curve $\ \gamma:[a,b]\to\mathbb{R}^2$ it is my understanding that the integral of $\ f$ over $\ \gamma$ is the area of the region "between" $\ ...
5
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0answers
86 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 ...