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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26 views

What is the application of dimension $6$ representation of $SU(3)$ in particle physics? [migrated]

As we know, the uds transforms in fundamental representations of $SU(3)$. It has the antifundamental partner. According to representation theory, $$ \mathbf{3} \otimes \mathbf{\bar{3}}= \mathbf{8} \...
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Is it useful for an engineer to study projective geometry? [closed]

I'm an engineering student, is there any application of projective geometry that can be a useful skill to have?
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Justifying the use of an unconventional metric to rate accuracy of predictions

I was having a discussion with friends and at some point we decided to make predictions on a quantity (value of daily new covid cases in a specific area). We all made our predictions and then we ...
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1answer
95 views

Are there applications of martingales other than in finance?

I’ve only had a brief introduction to martingales and was wondering if there are applications of the theory in other areas of mathematics and in real world applications other than in finance (finance ...
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1answer
38 views

Topological groups vs regular groups [duplicate]

I know group theory and I'm familiar with the concept and definition of Group. Today I was reading an article about topology and discoverer the concept of "topological group". I read the ...
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2answers
71 views

How should I learn from proofs in Applied Mathematics?

I am aware that similar questions have been asked here and elsewhere about how to learn from proofs. Some common advice is: Most proofs are written in a polished form, not how they were first ...
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What are differences between Geometric, Logarithmic and Exponential Growth?

At past I have read in some ecology text that geometrical, logarithmic and exponential growths are not exactly the same thing; and there were various equations for them. (The book is not available to ...
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Show an equilibrium state at $x = 1$, considering a small perturbation determine if it is a stable/unstable state…

A population is governed by the nonlinear equation $\dot x= x^4 − 3x^3 + 2$. Show that there is an equilibrium state at $x = 1$ and by considering a small perturbation determine whether it is a stable ...
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Reed Solomon codes and RAID-6

I have the following definition of Reed Solomon (RS) code. For $q = 2^t$, let $α$ be a primitive root of unity in the field $GF(q)$. An RS code with parameters $q$, $δ$, $α$, $a$ ($a ≥ 0$, $2 ≤ δ ≤ q-...
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Interpretation and use of the logarithmic scale for high school students

Often when we discuss on the logarithms in high school we also talk about a scale called logarithmic. In the he logarithmic scale: the distance from $1$ to $2$ is the same as the distance from $2$ to ...
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1answer
43 views

Maximum volume of a cuboid box

A rectangular sheet of a fixed perimeter with sides having their lengths in the ratio 8: 15 is converted into an open rectangular box by folding after removing squares of equal areas from all four ...
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Does weak convergence imply some kind of approximation?

Let $X$ be a Banach space and $x_n$ be a sequence in $X$ converging weakly to $x \in X$. Then can we say $x$ 'approximates' $x_n$ in some sense? This question is motivated from the homogenization ...
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Intuition for why we can apply complex analysis to solving 2D cases in applied science problems

In fluid dynamics and elasticity theory (and probably many other theories Im not familiar with) , when we consider a 2D "flat" case, we summon complex analysis for help. It usually starts ...
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28 views

Time needed to check all possible combinations

Suppose we want to find the time needed to write down all possible combinations of 58 characters. With a string of size n the possible combinations are 58^n. We pick random characters every time we ...
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Differential equation undamped system

Question image How can I solve this question? An object weighting 8 pounds is suspended from a spring stretching it 0.5 feet. The weight, which is at rest in the equilibrium position, is struck an ...
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25 views

Information about Mathematical Neuroscience

I would like some advices about my career. I'm an undergraduate student of math and I was looking for some interesting fields I could choose for my advanced studies. A field that caught my attention ...
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2answers
52 views

Finding the surface area of a greenhouse

I was given the following problem, which I feel should be simple but I seem to be getting the wrong answer: Determine the surface area of the greenhouse with the dimensions below. Round to the ...
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What are the applications of proving some results related to number theory like the one given below?

I had this problem in my Mathematics textbook. Here's how it goes : $$\text{For any two positive integers, } a \text{ and } b \text{, prove that } \sqrt{2} \text{ always lies between } \dfrac{a}{b} \...
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92 views

Invertible polynomial that approaches linearity at large x

I need to approximate a function $y=f(x)$ using a small set of constants $a_0…a_n$, ideally where the number of constants can be arbitrarily increased to improve accuracy. $x$ and $y$ are both real ...
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1answer
65 views

Is there any theorem that can only be proven using the axiom of choice and that is actually used in real-world applications?

I don't have a strong background in mathematics but I am interested in it from a philosophical perspective and I was wondering: is there any theorem or mathematical tool that is used in real-world ...
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1answer
42 views

Applications of a theorem on certain dense subgraphs?

In my introductory course on graph theory the following statement was proven. Any finite graph $G$ with at least one edge contains an induced subgraph $H$ such that $\delta(H) > \frac{d(H)}{2}\...
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153 views

Real-world application where strong LLN is needed (weak LLN is not enough) [closed]

Do you know of any real world (algorithm, physics, ...) application of the law of large numbers where we need the strong LLN and the weak LLN by itself is not enough to prove that the application is ...
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108 views

Is there any mathematical conjecture that is successfully applied in the real world in spite of being yet unproven? [closed]

I'm a philosophy student and I'm writing a thesis that makes a few comparisons between ethics and mathematics. My knowledge of mathematics is limited, however, and in the process of making my ...
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Is there a simple reduction from permutations of {1, … 2M} to {1, … M}?

Suppose I have a random permutation uniformly chosen from the set of all permutations of $M N$ elements; often in the contexts that I am interested in, this is going to be $2^{m+n}$ elements. And let ...
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75 views

Applying mathematics to police killing data

I want to analyze, albeit loosely, the rate at which black and white offender populations are killed by police (because often people argue disproportionate killings by police are explained by ...
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Application of Levy's Continuity Theorem. How is it applied herebelow?

THEOREM (Levy's Continuity Theorem) Let $(\mu_n)_{n\geq1}$ be a sequence of probability measures on $\mathbb{R}^d$, and let $(\hat{\mu}_n)_{n\geq1}$ denote their characteristic functions (or Fourier ...
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Solving an application with linear transformations

I have sawed this application below on this forum and I wondered If we are looking for a period like "who get the flu after 2 years". We are going to have n=2. And if we don't use eigenvectors. How ...
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337 views

Swinging factorial and swinging constant

The Swinging factorial $n≀$ defined as $$n≀=\frac{n!}{\left\lfloor{n/2}\right\rfloor!^2}$$ is relatively common and I found some results on Google. But when $$\sum_{n=0}^{\infty}\frac{1}{n≀}$$is ...
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Are histograms with varying class widths ever used in the real world?

It seems that every math textbook that teaches histograms teaches how to calculate frequency density, which is needed for cases where class widths (i.e. range of data covered by each bar in the ...
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1answer
41 views

A real life example for the linear transformations [duplicate]

This was what I wanted to say in my previews questions. I need a real life example that can be solved only with linear transformation. I will be verry grateful if you can give me a problem and it' s ...
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Can someone please explain me what a marked Poisson process is, and give an example of an application for this process.

Can someone please explain what a marked Poisson process is, and give an example of an application for which a marked Poisson process might be a useful model. I've been looking for explanations on the ...
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Approximate my grade in a class, based on knowledge of the curve that was used

Suppose I took an exam in a class and I know the raw percentage I scored. The average of the class was low, so the professor decides to curve the scores. Now, the professor provides a list of letter ...
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Applications of equations $B\partial_t u=Au$ where $B$ and $A$ are differential operators and $B$ invertible.

I was wondering if there are any nice applications of equations of the flavour $$ B\partial_t u=Au, $$ where $A$ and $B$ are differential operators and $B$ is invertible. E.g. On suitable domains such ...
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I was wondering if someone could explain me the concept of the norm of a linear application or a matrix.

I was wondering if someone could explain me the concept of norm. For example, if I have a linear application from $\mathbb{R}^2 \to \mathbb{R}$, I understand that the norm is the maximum slope of the ...
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1answer
58 views

Using the Principle of Least Action to find the Constant/Equation of Motion

Suppose that we have a particle with mass $m$ which moves in its plane with its position at time $t$ defined by the planar polar co-ordinated $r, \theta$ (with the notation $r=r(t)$ and $\theta = \...
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46 views

Find a function

It's a cuttout from Rempe article "A mathematical model of the sleep/wake cycle" about a function which I don't understand how to describe: $h(t)$ decays exponentially while the system is asleep and ...
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3answers
79 views

Practical application for linear transformations

Can anyone help me with a practical application of linear transformations? I am very curious about how can be an application in real life that can be solved with a linear transformation.
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1answer
32 views

How Singular Integrals Theory is applied on Partial Differential Equations

Currently I'm interested in Singular Integrals Theory (I'm a beginner). I have read that this theory has deep relations with PDE's. For that reason I would like to know if there exists some web page, ...
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31 views

Is gaining enough understanding of SVD/QR factorization until you have their formulas memorized useful?

Is knowing how to compute SVD/QRfactorization,Power iteration/power method by hand without notes useful in applications such as Statistics? Now adays, we can do everytime by Mathematica/computer ...
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Nowcasting, what is it?

I stumbled upon this word in the context of corona virus forecasting. As far as I understand it is some kind of extrapolation method that is also used in economics and meteorolgy, but am struggling ...
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33 views

Application of PDE for solving steady state heat problem.

A thin rectangular homogeneous thermally conducting plate occupies the region $0 \leq x \leq a$, $0 \leq y \leq b$. The edge $y = 0$ is held at temperature $Tx(x − a)$, where T is a constant and the ...
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67 views

Leveraging pure math knowledge to learn applied math

The long and short of this questions is that I’m someone with a pure mathematics background (albeit at a junior-undergrad level) who wants to learn a set of applied math topics in a way leverages what ...
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1answer
52 views

First class mathematics that is useful

In Oksendal's Stochastic Differential Equations he writes in the first few pages: The Kalman-Bucy filter is an example of a recent mathematical discovery that has proved to be useful - it is not just ...
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1answer
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Area and Volumes of revolution using disc method

(1) The disk method to determine the volume of revolution uses the volume of a cylinder of width dx a proof of this involves showing cylinders (disks) above the curve and those below the curve ...
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35 views

Differential Equation Application of Physics-Sliding Block

Where I can I start to solve this question? A block is released with an initial velocity v0 = 20 m/s from the bottom of an inclined plane making an angle of 30◦ with the horizontal. If the constant ...
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43 views

Physical significance of 3rd derivative [duplicate]

I am new to calculus and currently learning differentiation. I understood that the first derivative indicates the slope of the function and the second derivative indicates the rate at which the slope ...
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1answer
51 views

Basic ODE story - tank with pumps

Full tank has $500$ liter of water containing $0.2\%$ of salt. One pipe pumps clear water in ($100$ liters per minute) and the other gets the mixture from the tank ($100$ liters per minute too). ...
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378 views

Simple understanding of advanced math

Title might be a bit vague, so I will explain further here. I am compiling a list of examples of how a person may realize some mathematical result is either obvious or unsurprising from the ...
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More applications on Integral [closed]

Formula for calculating mass of earth
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Are there examples persistent homology being used to study non-linear data?

You can compute the persistent homology of any point cloud embedded in a metric space. In the real-world applications of persistent homology I've come across so far, the data points all have (...

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