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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3answers
253 views

Golden ratio rectangles

I'm designing a layout and I would like to use four golden ratio rectangles. The total width of the layout is 960px. How do I find the height (x)? Below is a diagram of the layout.
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What Uses Does Lagrange's Interpolation See Today?

More concretely, in what situations are the predictions made by Lagrange's Interpolation accurate? Say, if we have 4 known values of some country's populations, would the unknown value predicted by ...
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3answers
99 views

Oceans and volume [closed]

What would be the math formulas to calculate the increase in the height of the ocean if one drop of water were released into it. Assuming that everything is static. How would you solve that question....
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1answer
3k views

Ideas for a Applications of Calculus Video

Note: I am not sure if this should be posted here, but, after looking through the other sites, I felt this was the best fit for the question. For class, I have to make a video with applications of ...
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3answers
2k views

Modelling with exact differential equations?

I'm teaching some very elementary differential equations to engineering students, and their constant question to me is "What's the use of this?" or alternatively "Where would we use this?" Now, I'm ...
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2answers
78 views

Where is the choice of orthogonal basis being made in the human auditory system?

I have a vague question which I have trouble googling an answer to. Let $X$ be a circle. I want to think of $L^2(X)$ as embedded into the space of periodic functions on the real line, with period 1, ...
4
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1answer
120 views

Mathematician approach to mathematical sociology

I've always been fascinated by sociology, from the philosophical and psychological theories to the study of mass social phenomena, e.g. such as crowds, the dynamics of the crowds, key triggers of mass ...
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1answer
379 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 ...
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1answer
10k views

Confused about Effective Rate of Discount- Theory of Interest

I'm currently reading Kellison's book, The Theory of Interest. I've reached the chapter on Effective Rate of Discount and it's somewhat confusing. The book explains it as a loan where interest is paid ...
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3answers
71 views

Use of the fact that $e^{i\pi}=-1$?

Yesterday, my son asked me of what use was the fact that $e^{i \pi}=-1$. I told him that he could use it to impress a girl, which is true but probably an incomplete response. So, I ask you, is there ...
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1answer
127 views

What mathematics topics pertain more towards applied mathematics?

I'm entering my second year of undergrad (majoring in mathematics), and I've found that I am really bad at Linear Algebra, but very good at Calculus and Differential Equations. I'm hoping to venture ...
4
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1answer
219 views

Graph theory application of homology

I am struggling with the idea of local homology groups and would like to see an example of how to go about finding them in general. I'm thinking of the most trivial case to apply the theory of local ...
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1answer
1k views

Transpose a square matrix code

I know it's not programming area , but I think it's more related to math. I have the following function: ...
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1answer
17k views

How to convert interest rate to discount factor

I'm studying on Kellison's Theory of Interest and I'm stuck on the exercise 20/a of the 1st chapter. If the $i=0.1$ then $d = 0.0901$ $d_5=\frac{A_5-A_4}{A_5}$ when I insert $d$ into this equation,...
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1answer
180 views

What are the use cases related to cluster analysis of different distance metrics?

I'm trying to use different distance metrics like Euclidean, Manhattan, cosine, chebyshev among other distance metrics in my k-means algorithm to calculate distances between the data points and the ...
4
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1answer
214 views

Motivation for the Basel problem

I realized that I know of several ways how to prove that $\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$, but I have no idea why I would want to know the answer in the first place. Answers I have ...
4
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1answer
411 views

Applications of First Order Differential Equations

Can I get help for this question please? Suppose that a tank containing a liquid is vented to the air at the top and has an outlet at the bottom through which the liquid can drain. It follows from ...
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2answers
126 views

Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs

Suppose one wants to transition from the study of certain theoretical aspects of PDEs (say, regularity theory for elliptic operators) to a career in industry solving real-world problems about PDEs and ...
4
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1answer
281 views

Mathematical rigor for engineers

An engineer with a master's degree, I would like to improve my level of mathematical rigor. For example, I would like to come to grasp what measure theory has to do with the Fourier series and what ...
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2answers
3k views

Applications of Linear Algebra in software engineering.

I'm a software engineering and mathematics student, I was searching for disciplines of mathematics that would go well with my engineering degree, and found a lot of people recommended that software ...
4
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1answer
355 views

[Levenberg-Marquardt]What is the link between positive-definiteness and well-conditioning?

Working on optimization problems through neural networks, I use the Levenberg-Marquardt algorithm. I have read this assertion that I do not understand : A positive definite diagonal matrix is added ...
4
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1answer
130 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 ...
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1answer
749 views

Problem with a dipstick

The problem: Some houses are heated by burning oil. The oil is stored in a horizontal elliptical cylinder that is lying underground. To measure the residual volume, one has to use a dipstick that ...
4
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1answer
623 views

What are applications of Lagrange's identity?

I recently proved for homework the following identity on $\mathbb{C}$: if $a_1, \ldots , a_n, b_1, \ldots, b_n\in\mathbb{C}$, then $$ \left|\sum_{i=1}^na_ib_i\right|^2 = \left(\sum_{i=1}^n|a_i|^2\...
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380 views

Cryptocurrency Math

I'm looking for any relevant books/articles on the maths of cryptocurrency transactions. Also open to any resources that may have some cryptocurrency transactions but not it may not be the main bite. ...
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76 views

Calculating half life from proteins

I have no idea if this would be the right place to post. I am a biologist by trade so mathematics is not my forte. I am having problems calculating the degradation/synthesis constants and protein ...
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1k views

Are there practical applications of Mersenne primes?

Mersenne primes are prime numbers which are one less than a power of two, i.e. primes expressible as $M_n=2^n-1$. They are notoriously far apart and unpredictable, which is indicated by the fact that ...
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268 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 like,...
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925 views

Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
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254 views

Applications of a theorem of Cartier and Gabriel

In a representation theory course I took we stated and proved the following Theorem due to Cartier and Gabriel: Theorem: Suppose $H$ is a cocommutative Hopf algebra over a field $k$ such that $ \...
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1answer
409 views

dynamic mean: measurement of randomly distributed events

Aim is to estimate an error on a stochastic event rate. I read out the event counter second-wise, every black $1$ is a counted event (new events over time, see the plot below). During the measurement ...
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3answers
1k views

Minimum distance between the curves $f(x) =e^x$ and $g(x) =\ln x$ [closed]

What is the minimum distance between the curves $f(x) =e^x$ and $g(x) = \ln x$? I didn't understand how to solve the problem. Please help me.
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What branch of mathematics is most needed in the industry or how one can make living with mathematics (apart from teaching)?

If you learn carpentry or programming you have the clear options of becoming a carpenter or programmer. But what if you learn mathematics? I know that there are some financial institutions out there, ...
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4answers
2k views

Applications of group theory to geometry

What are the applications of group theory to geometry? Where can I know more about these applications?
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2answers
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Interpretation of definite integrals [closed]

It is known from the Fundamental Theorem of Calculus that $$\int_a^b f(x)=F(b)-F(a).$$ This has the geometric interpretation of the net area between $f(x)$ and the $x-$axis. I suspect that there are ...
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2answers
290 views

Resources to understand real world usage of linear algebra

I've learned linear algebra basics at university and really liked it, so I decided to learn it more deeply. Secondly, I want to work in computer science and I think linear algebra knowledge could be ...
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3answers
164 views

Puzzle: leaning a ladder at $45^\circ$ to a wall using only yourself

This question was asked to my friend in an interview. You are provided a ladder and are led to a wall. The ladder must be kept against the wall making an angle of $45^\circ$ with the floor. You are ...
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1answer
346 views

Closed form of $I(a)=\int_{0}^a {(e^{-x²})}^{\operatorname{erf}(x)}dx $ and is it behave similar with error function?

$\newcommand{\erf}{\operatorname{erf}}$ The computation of $\int_{0}^{a}{(e^{-x²})}^{\erf(x)}dx$ for large $a$ gives $0.972106...$ by wolfram alpha, but according to JJacquelin comments which ...
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1answer
546 views

Time reversal in Robertson's chemical reaction

I am studying the behavior of the Robertson chemical reaction, $$\begin{array}{rl} \dot{x} &= -0.04 x + 10^4 y z\\ \dot{y} &= 0.04 x - 10^4 y z - 3 \times 10^7 y^2\\ \dot{z} &= 3 \times ...
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2answers
91 views

Examples of non-commutative rings in nature

So this may sound kinda vague but my point is: mathematics can be applied in several ways to our understanding of nature and often even things that seems to be totally abstract can be, more or less ...
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3answers
1k views

What are the most obscure or advanced mathematics with practical application

Throughout my engineering studies there were jokes made by my professors (mostly mathematics professors) that referenced the fact that pure mathematicians strive to create mathematics with no ...
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4answers
2k views

Sports that use Mathematics

What kind of sports and games use mathematics beyond simple arithmetic? How is math applied to build strategies for these games? Sailing could use mathematics in terms of astronavigation, tying knots,...
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2answers
1k views

Application of maths in economics

What are the branches of maths where we can see undoubtful connections with economics? Where can we use mathematical methods or models and apply them to analyze economic concepts?
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3answers
488 views

What is the use of remainders in polynomial division?

My class has just been taught about polynomial division, and how it can be used to see if something is a factor (although remainder theorem is quicker), if the remainder = 0. But what is the use of ...
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2answers
112 views

Partial Differentiation of an equation using implicit differentiation confusion

I wanted to ask a question about implicit differentiation in partial differentiation. When I was at school, I remember partial differentiation as something like this: When you have a function ...
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4answers
77 views

Finding the formula for acceleration from $v=2s^3+5s$, where $s$ is the displacement at time $t$

This is the question: I first found $\frac{dv}{ds}=6s^2+5$, then I tried to find $\frac{ds}{dt}$ by messing about a little with implicit differentiation, but I had no luck and I therefore couldn't ...
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2answers
1k views

Curve on a basketball

The sewing pattern on a basketball is composed of two great circles and a single curve that intersects each great circle twice. Does this curve have a name? Are there any parametric descriptions of ...
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5answers
3k views

How are complex numbers useful to real number mathematics?

Suppose I have only real number problems, where I need to find solutions. By what means could knowledge about complex numbers be useful? Of course, the obviously applications are: contour ...
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3answers
35 views

Ratio and Proportion Concept clarity.

The milk and water in two vessels $A$ and $B$ are in ratio of $4:3$ and $2:3 $ respectively. In what ratio should the liquids in both vessels be mixed to obtain a new mixture in vessel $C$ consisting ...
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2answers
64 views

Can we motivate mathematically why wind turbines almost always have 3 flappers and aeroplane propellers can have any number of flappers?

Firstly I know some might frown upon a question so very broad and applied as this one. It really may not be a well defined mathematical question as some people would prefer on the site. I am okay with ...