Diophantine equations are polynomial equations over the integers. These are useful in many fields of mathematics such as group theory and operations research.
Mathematics
Discovering the Frequencies in Financial Markets
Wavelet analysis stems from the 19th century when Joseph Fourier studied the heat equation. From his work, a foundation was set for Fourier transformations (FT). However, FT requires conditions such as stationarity of the data set and it only gives frequency...
Is math discovered or invented?
Mathematics has been used and researched since ancient times. The point of view on what mathematics is shifts from being an invention, a discovery to an artefact, by the influence of time and people. -Britt Brugts
Zeno’s paradox
It’s a calm and sunny day as Achilles is walking through the city when he comes across a tortoise that approaches him. “Hi Achilles, I have a rather interesting question for you.”, says the tortoise. “Would you like to have a sprint race against me? I will get a head...
A road to mathematics
Remember when you were young and you were too excited to sleep because you were going on vacation the next day? Your parents would wake you up very early the next morning because they wanted to drive all the way to the south of France in one day. Then, sometime during...
The raven paradox
The raven paradox Econometricians face difficult problems. One of the hardest problems one can encounter is a paradox. The raven paradox is such a problem and was first proposed by logician Carl Gustav Hempel. The paradox has its basis in statististics. In this...
The math conference
Two mathematicians, Simon and Blume, are at a conference dinner, fighting over the last few pieces of lobster and steak, when another mathematician walks up to them. Having heard about the brilliance of the two, he decides to present them a riddle. After thinking for...
The World of Sports Betting
It’s Saturday evening and you’re watching a football game with a couple of friends. Unfortunately, the game is between mediocre teams, so you don’t expect to see a great match. However, one of your friends has an idea to spice it all a bit up and to make the game more...
Newcomb’s paradox
Let's suppose that we have a game with two players. One is a person that will make a decision and the other is a supercomputer that will try and predict that decision beforehand. This computer has been tested many times and the testers have worked out that the...
The conundrum of perpetual motion
It is no surprise that the 19th century was a time of scientific breakthroughs and wondrous inventions. However, for the people of Philadelphia, this meant that for only one dollar they could admire the most amazing machine in the world: a machine that stayed in...
Is OLS a thing of the past?
[latexpage] One of the most popular regression methods an econometrician learns is the Ordinary Least Squares (OLS). It is a simple and elegant way of estimating parameters in linear regression. However, there is another technique to perform linear regression using...
Will your family name ever go extinct?
[latexpage] Nowadays, in most countries, everyone has a surname. Some names are very common, like “de Jong” in the Netherlands, or for example “Nguyễn” in Vietnam, where almost 40% of the population has this surname. On the other hand, some surnames are extremely...
Are jugglers actually math enthusiasts?
Juggling, something we have all tried at least once in our life. For some, it resulted in the great satisfaction of three balls flying in perfect harmony through the air. For others, it was a traumatic experience of balls flying everywhere except for the right place....
Christmas with a mathematical touch
At first, you may think that mathematics has nothing to do with Christmas. The only link I could think of was calculating whether you have enough budget to buy that all those present for your family. However, mathematicians will always think of a way to integrate...
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