# Tagged Questions

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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### How can Bayesian and Frequentist approach be different?

Let's say I am trying to add numbers, like say one to ten. I can either add them in order, or I can notice that I can group them into five groups of eleven, so I suppose which method to use depends on ...
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### Interesting calculus problems for beginner

Recently I started learning calculus and I think I have grasped the basics. However when calculating examples I tend to drift away and not put much effort in it. When I was learning programming in ...
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### Moment of inertia : How to find out perpendicular distance?

The boundary of a thin plate is an ellipse with semiaxes a and b. Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis of length ...
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### System of equations and the Brouwer's Fixed-Point Theorem.

Let's consider the following system of equations: \begin{eqnarray}{ e^{xyz} = \frac{x}{\sqrt{e^{2xyz}+1}}\\ \cos(x+y+z) = \frac{y}{\sqrt{e^{2xyz}+1}}\\ \sin(x+y+z) = \frac{z}{\sqrt{e^{2xyz}+1}} ...
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### Honest application of category theory

I believe that category theory is one of the most fundamental theories of mathematics, and is becoming a fundamental theory for other sciences as well. It allows us to understand many concepts on a ...
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### What are some real life applications of least squares problem?

I'm looking for some applications that require solving the least square problem. I know polynomial fitting is one of them, but sure there are many others. Thanks
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### Learning to Apply Mathematical Concepts ( i.e. function modelling, etc.)

Firsty, I want to state my situation clearly. I am one of those students who are incredibly good at absorbing mathematical concepts but without knowing how to apply them. I get A's but it is growing ...
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### Kahler-Einstein Metrics in Physics - Topic Suggestions

I am hoping to get some topic suggestions for a presentation I have to give in a couple of weeks. The course the presentation is for is called Kahler-Einstein metrics. I would really like the ...
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### partial differential equation applicational problem

As a Maths student with not much knowledge in physics, I dont understand how the "string" can be "cut" into half at x=L/2. Also, how many initial conditions(data) does this question have apart from ...
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### Why are noetherian and artinian modules important?

As a TA I was recently asked to give the students an introduction to two (quite related) concepts that are new to me, noetherian and artinian modules. I intend to prove the characterisation theorem ...
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### Determine the multi-dimensional relationship given the data

I have a dependent variable - A and 3 independent variables, H,V and N I have a data for all the variables and dependency relationship is based on my operational knowledge. I'd like to know what ...
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### application of kinematics and the rates of change

A ladder 20 feet long leans against a vertical building. If the bottom of the ladder slides away from the building horizontally at a rate of 3ft/sec, how fast is the ladder sliding down the building ...
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### Finding the rate of rising water. [duplicate]

Water is pouring into a conical tank at a rate of 8 cubic feet per minute. If the height of the tank is 12ft, and the radius of its circular opening is 6ft, how fast is the water level rising when ...
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### Show that the cubic equation has one real roots

Show that $x^3+ax+b=0$ has a) only one real root when $a>0$ b) at most only one of it's roots are in $(-\sqrt{-a/3},\sqrt{-a/3})$ when $a<0$. For a) I supposed that it had two real roots ...
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### book to learn calculus by examples and real world applications

Don't know if it's the right question in this section I'll ask it anyway. When I study math I barely understand theorems, but after being given the examples I can understand the theory behind it. The ...
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### The wave equation with forcing function

What would the solution to this problem be? $\frac{1}{x} u _t - (x u_x )_x = \frac{1}{x} \ln{x} \quad 1<x<e \quad t>0$ $u(x,0) = \sin{(\frac{\pi}{2}\ln{x})} \quad (1<x<e)$ ...
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### Is Principal Component Analysis applicable to this type of situation?

I'm trying to model the response of ant populations to pheromones in this way: The ants are simulated as Self Propelled Particles with internal energy. They undergo acceleration due to their internal ...
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### Determining how long a body has been dead using the number e

I have recently seen a quote about determining how long a body has been dead: “Dead bodies lose heat exponentially, and therefore e can be used in an appropriate equation to determine how long ...
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### Mathematical Formulas for Game Battle Calculations

I am from a programming background and trying to write a game for fun. I am trying to write a battle calculator and which ever way I think about it I seem to run into trouble. Basically the scenario ...
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### Solve for the charge on a discharging capacitor in an RC circuit using Laplace Transforms. (5.3-61)

Please check my work. I need to solve the following problem but my answer varies from that of the book by a factor of $C$ for capacitance. A print screen of the problem is given below. Problem to ...
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### House allocation with existing tenants

In a house allocation with existing tenants model using the TTC mechanism, consider the incentive of an agent to misreport his/her preferences. Can it ever be that misreporting the true preferences by ...
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### Time taken to empty a hemispherical shaped tank

The tank has a radius of $2$m when initially filled and has an outlet of cross section $12$ cm2 Outlet flow as I calculated goes according to the law $V(t)=0.6\sqrt{2gh(t)}$. Having found out the ...
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### Rate of change question involving velocity, displacement and acceleration

I have been having trouble understanding questions c)-e) and am in need of some help: An object is moving in a straight line from a fixed point. The displacement $s$ in metres is given by ...
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### Is the Law of Large Numbers empirically proven?

Does this reflect the real world and what is the empirical evidence behind this? Layman here so please avoid abstract math in your response. The Law of Large Numbers states that the average of the ...
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### Finding maximum of convex function (appliance of derivatives)

The task goes as following: Divide the length of $14$ into parts $a$ and $b$, in a way that the sum of surfaces of two squares (which sizes are $a$ and $b$), is minimal. $14=a+b => b=14-a$ ...
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### Creating a weighted score

I have an audit where there are six criteria, each can be scored Excellent (E), Satisfactory (S), Needs improvement (N) or Unsatisfactory (U). I know that if someone scores Excellent in all six areas ...
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### How to calculate a monthly mortality rate?

If the instantaneous mortality rate for a species (or a group of humans) is 0.1/year, what is the mortality rate per month? Can you just divide $0.1/12$? This seems too simple and incorrect because ...
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### Surprising applications of topology [closed]

Today in class we got to see how to use the Brouwer Fixed Point theorem for $D^2$ to prove that a $3 \times 3$ matrix $M$ with positive real entries has an eigenvector with a positive eigenvalue. The ...
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### Finding the height of a bouncing ball. (Using the geometric series in an applied setting)

I am doing a problem in a textbook (Boas' Mathematical Methods in the Physical Sciences) where a ball is dropped from a height of one yard and the sum of vertical distance in each drop is the series: ...
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### Application of Dimensional Analysis Problem

It is given that the radius $R$, in meters, of the expansion of a liquid in the soil is given by $t$ (time elapsed since the liquid was released), the mass $M$ of the liquid released and of the ...
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### Is LU decomposition of matrices efficient for today's standards?

This is in the spirit of a previous question of mine about the efficiency of the QR algorithm. The reason for asking is that I want to motivate some students, and I'm also curious. I do understand ...
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### Why stronger norm defines weak local minimizer? [closed]

Why the stronger norm defines weak local minimizer, while the weaker norm defines strong local minimizer? For example, when minimizing a functional on $C^1[a,b]$, one can also consider the weaker ...
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### 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. ...
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### 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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### 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 ...