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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Pascal's Identity and Trees

Pascal's Identity states that $n \choose k$ = $n-1 \choose k-1$ + $n-1 \choose k$ since if one element is separated from the rest we can claim that either it is chosen (resulting in $k-1$ elements ...
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Percent profits and base costs: Word problems.

A table is bought for $23.50$, which includes a profit of $17.5 \%$. I need to calculate the amount of profit. I tried finding $17.5\%$ of $23.5$, but I don't think that's what's being asked ...
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Iterations of Pascal's Identity

Pascal's Identity states that $n \choose k$ = $n-1 \choose k-1$ + $n-1 \choose k$ since if one element is separated from the rest we can claim that either it is chosen (resulting in $k-1$ elements ...
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Applied Math Foundational Books

I have a BA in mathematics from a pretty good school, where I effectively exhausted the mathematics sequence. The sequence mostly focused on pure math (including measure theoretic real analysis and ...
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23 views

collision of two bodies

Two cars A and B, each 5 m in length, travel with constant velocity 20 m/s along a straight level road. The front of car A is 15 m directly behind the rear of car B. Immediately on reaching a point P ...
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41 views

“Real world” applications of rational functions

I need a rational function/equation beyond the contrived d=rt and work problems typically given in beginner algebra. I am teaching such a class and would like to motivate the study of techniques for ...
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How can the R3 vertices of a 4-dimensional object be generated?

After learning a bit of OpenGL, I was hoping to find a way to project a 4-dimensional object into 3-space to visually study them. However, I'm not even sure how I would begin to do this. What kind ...
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Determining diameter of strands of twisted rope

Twisted ropes are made by taking 3 strands of smaller rope and twisting them together tightly, by coiling the strands in the same direction, as opposed to braided rope, which requires strands to be ...
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70 views

Ancient calculus or thorough observation

Integration. It's the simplest way on earth with which we can derive any formula like surface area or volume of symmetrical shapes and solids (square, circle, cube etc.). But what I've been hearing is ...
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Can we transform bijectionally each element in $C(ℚ)$?

Let $C$ be an elliptic curve over $ℚ$. The group $C(ℚ)$ is a finitely generated Abelian group and we have $C(ℚ)≃ℤ^{r}⊕C(ℚ)^\mathrm{tors}$, where $C(ℚ)^\mathrm{tors}$ is a finite abelian group. ...
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What does “symbolically tractable” mean?

What does "symbolically tractable" mean in the following quote? "Traditional treatments of mechanics concentrate most of their effort on the extremely small class of symbolically tractable dynamical ...
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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. Numerical computations, to my understanding, never deal ...
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Fibonacci Numbers in Nature

Supposedly the Fibonacci sequence appears naturally in nature, and my question is how, where and I guess why? I read that one way this is so is that it models the population of honey bees under ideal ...
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Basis representation for non-negative, compact support, reasonably smooth spectral function

I was wondering if anyone has ideas on representing a non-negative, compact support (from x=-1 to 1 on the real axis) spectral function as a superposition of basis elements. Ideally, the basis ...
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1answer
46 views

Prerequisite of Dynamical system and applied PDE

For the further research interest, I want to focus on the application of Dynamical systems and PDE in the field of robotics and neuroscience, particularly from a mathematical points of view. ...
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159 views

Applications of Geometry to Computer Science

How is differential geometry (or any type of theoretical math) related to computer graphics and/or computer programming? A friend of mine has only a bachelors degree in pure math and got hired by ...
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1answer
26 views

Show solution to ODE's fourier series is a series of sines only

This question was given in an exam in applied mathematics, on the subject of Fourier series: Observe the following ODE: $u\left ( x \right) ^{\prime \prime}+Q \left ( x \right) u\left ( x \right) ...
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1answer
26 views

Calculate remaining space of a box/cube

Im developing an eCommerce system where items are 'logically' placed into boxes. Rather than the shipping system calculating the shipping of each item individually. The shipping will be calculated by ...
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1answer
73 views

Books in mathematics based on problem solving

Hi I'm looking for mathematical books that try to teach mathematical concepts by motivating and solving real life problems. For example a book in topology that is motivated by problems of planetary ...
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User of a System

Given a system with n users and each user will only use the system once (for an hour) during a year. The user will only access the system during business hours (so ...
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1answer
30 views

What are some other applied advanced probability sub-field relevant to finance?

What are some other applied advanced probability sub-field relevant to finance? I have heard Martingale, stochastic process, stochastic calculus, monte-carlo statistics I've been searching other ...
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Mathematical field theory Application in real world and other branches of Mathematics

I need to write work about applications of Mathematical field theory in real world and in other branches of Mathematics. Can someone guide me to an appropriate book, resource? Thanks, Denis.
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distance between A and B. solve with pythagorean theorem

distance between two person. person A like to watch movie by 3 unit. person B like to watch movie by 4 unit. in this case we can tell the distance between person A and B. person A is 1 unit away ...
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1answer
51 views

How many answers can be created using the elementary arithmetic operators?

If I gave you an amount of $n$ numbers, how many anwswer will you be able to create using the elementary arithmetic operators ($+, -, \times, /$)? These are the rules: All numbers ...
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1answer
21 views

Question regarding simple harmonic motion?

Hi guys, I was just wondering what the answers are for this question, as it says it's B, and I'm only getting C as an answer (attempted multiple times). Could anyone please just clarify what the ...
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PDE modeling (heat conduction and flow)

The heat conduction is expressed by a classic heat equation like $p(x) u_t + div (A(x) u) = f(x,t) $. If I look at a porous medium like this (solid+gas) the heat equation should apply too (in a ...
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39 views

I want an intutive/theoretical understanding of the $\sin(\omega t +f)$

What is the meaning of $x(t)=x_0\cos(\omega t+f)$, where $x_0$ is the amplitude, $\omega$ the angular frequency, $t$ time and $f$ phase constant? I know how to solve the mathematical problems which ...
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42 views

Are the following functions also surjective?

Let $f\colon\mathbb R\to\mathbb R$ be a surjective function. Assume that $f'$ is also surjective. Assume also that $f$ vanishe on $s=1$ of order $m$. My question is: Are the following functions also ...
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1answer
25 views

Looking to assign percentage contribution among 4 variables in a simple equation

I have a seemingly simple problem, that is giving me some trouble in solving. I have a 4 variable equation and want to determine the contribution of each variable in moving the dependent variable from ...
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1answer
140 views

Applications of Countable Infinite Sets and Power Sets

What are the possible applications of Countable Infinite Sets and Power Sets in areas that are not strictly mathematical? Also I want to know the significance they carry. What was not possible ...
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94 views

What are the other methods used to prove that a homomorphism is bijective?

The motivation can be found in: Show that $ℤ^{m}$ is a subgroup (and a free abelian group) of $ℤ^{n}$ for all $m≤n$. In a specified problem related to a dynamical system the only possibility is ...
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1answer
17 views

Bessell function of the first kind $J_v$ of the Bessel equation $x^2y''+xy'+(\lambda^2 x^2-v^2)y=0$

If we have an equation $x^2y''+xy'+(x^2-v^2)y=0$ then the solution of the first kind $J_v(x)=x^v\sum_{m=0}^{\infty}\frac{(-1)^mx^{2m}}{2^{2m+v}m!(m+v)!}$. Then how would you find the solution of ...
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Number of collisions of particles in a box. Application to epidemiology

I was surprised to see in this biology article a model assuming that the number of newly infected cells is a linear function of the number of (healthy) cells and of the number of viruses. I am not ...
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1answer
31 views

What is the practical application of local linearization

Whenever I'm studying a new topic in mathematics, the question of potential practical application is the one that matters to me the most. While it's relatively easy to come up with hypothetical cases ...
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1answer
56 views

what is difference between open and mixed queue

please consider this image: In this picture that I got it from Here write said that Network C is Open,B is Mixed and A is Closed. I want to know why C isn't mixed? ...
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Help with a game design function.

I'm working on building a 'result table' for an RPG. In said table, you compare an effect rating to a resistance rating, to find a whole number result. Essentially, for each cell I need to find Z, ...
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1answer
26 views

Meaning of multiplication by $\sin$ in $\omega$-domain

Multiplying some signal, a function of time, $m(t)$ by a cosine $\cos{\omega' t}$ causes a shift in frequency of $m(t)$, by $\pm\omega'$. But what about multiplication by a sine wave, such ...
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1answer
93 views

numerical update rule for discretized hawkes excitation process

So I think I am just misunderstanding some simple notation or something and would appreciate some help. I am trying to replicate this model in an agent based model, but I cannot seem to figure out the ...
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1answer
59 views

Analyzing the stability of equilibria

There's a model with a condition $r>\mu$: $$\begin{align} S'&=r(S+I)-\beta SI-\mu S \\ I'&=\beta SI-(\mu +\alpha)I \end{align}$$ I can easily see that the equilibria of the second ...
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Applied problem of multivariable calculus with integrals.

How to solve this problem: A medal has the shape of the portion of the plane $x + z = 1$ lying inside the cylinder $$x^2 + \frac{y^2}{2} = 1.$$ The edge of the medal is covered in cold and it costs ...
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86 views

Questions about the field scientific computing

I have heard about the field of Applied and Computational Mathematics, Scientific Computing and want to get some information. Is this a combination of computer science and mathematics? What subjects ...
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Representative value of non-square matrix

First of all, I apologise if this question is inappropriate, I wish I could be more specific - but due to the nature of it, as I am actually asking for a suggestion of some technique, that's hard to ...
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Polynomials and NSA

I'm looking for some applications of criteria of irreducibility of integer polynomials inside and outside mathematics. I was reading the CV of Filaseta, a great researcher in this area and he has ...
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108 views

Derivative application question

A girl of height $120 $cm is walking towards a light on the ground at a speed of $0.6$ m/s. Her shadow is being cast on a wall behind her that is $5 $m from the light. How is the size of her shadow ...
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40 views

Show that there exist a bijection between $ℤ$ and $A$

Let $A$ be the set of points of the form $(s,0)$ (the second component is still zero) where $s∈B⊂ℝ$ and $B$ is an infinite discrete set. My question: Show that there exist a bijection between $ℤ$ ...
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How I can construct this bijection?

Assume that there is a bijection between $ℤ/2mℤ$ and the set $\{1,2,...,2m\}$ and there is a bijection between $ℤ/2ℤ$ and the set $\{1,2\}$, so it is possible to construct a bijection from the set ...
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24 views

polynomial word problem?

My answer is wrong... I understand what I did was found the volume of the pool (cubic feet) I am supposed to get square feet.
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What is Radius of Convergence used for?

What is the applications for "Radius of convergence"? I haven't been successful in finding any information about the applications, just a lot of information about how to calculate and what it is... ...
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1answer
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Finding the basic reproduction number of a particular model

I have been reading a paper about a host-parasites models and for the model: $$\begin{array}{rll} \displaystyle{\frac{dx}{dt}}&=\lambda -dx -\beta v x & \text{Susceptible host} \\ ...
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1answer
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Matrices in Linear Algebra

Let: $ u: R^2 --> R^3$ be defined by: $$ u(x,y)=(x+2y, 2x-y, 2x+ 3y)$$ Give the matrix $M[u]$ in the canonical base of its definition space. This question might seem sort of stupid, but it was ...