What is your favorite function?
If your answer is not the gamma function, then I’ll ask you again after you have read this article.
Your answer might have changed…
In the late 1720s, Leonhard Euler was thinking about how to extend the factorial to non-integer values.
This was the start of a rich theory used all over the scientific world. A theory of one of the most important functions in mathematics.
Leonhard Euler is, without doubt, one of the greatest mathematicians in history. To give you an idea of Euler’s powers here follows some examples that show his brilliance.
It has been called “The Holy Grail of Mathematics” and it is, without doubt, one of the hardest and most famous problems in mathematics.
The inaccessibility in terms of mathematical complexity doesn’t exactly help in understanding the problem.
In this article, I will start by giving you the classical problem description. Later I will state the problem without using complex numbers and the theory of analytic continuation hoping to make this beautiful problem accessible to more people.
There’s no reason to hide the beauty of this mathematical pearl and reserve it only to people with specialized mathematical knowledge.
Oftentimes I hear people stating that Heisenberg’s uncertainty principle is about observers interacting with electrons through photons and thereby affecting the momenta of the photons.
It might be true that an observer has to affect the momentum (or some quantum state) of an electron in order to observe it but that is not the reason behind the uncertainty principle!
Before jumping headfirst into this topic, let us define Heisenberg’s uncertainty principle so we are all on the same page.
In quantum mechanics, the uncertainty principle (also known as Heisenberg’s uncertainty principle) is any of a variety of mathematical inequalities asserting…
The theory of Fourier series is in my opinion one of the most powerful and beautiful theories in all of mathematics.
Not only is it beautiful, but it is useful as well. From electrical engineering and quantum physics to pure mathematics and number theory, the usefulness and importance of this tool cannot be overstated.
In order to fully understand this topic, we need to understand the origin and the broader picture. It all started with waves.
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Imagine you are the lead developer on some project. One day your boss tells you that you and your team have to make sure that all the functions and methods have logging and type checking protocols implemented and it needs to be tested by the end of the week.
You know that the project consists of 100’s of callable objects: functions, classes, generators, etc., and here you are, being asked by your boss when you can have this enormous task done and implemented.
You take a sip of your coffee, look at your boss, and say: “In a few hours”…
Python is an object-oriented programming language. In fact, it is often said that everything in Python is an object.
So in order to fully understand Python, you really need to understand the underlying structures like objects and classes to be able to understand what is really happening under the hood.
This article is about the concept of metaprogramming in Python and we will see how to manipulate classes and the instantiation of them.
Metaprogramming can be loosely defined as code that manipulates code.
An object is of course an instantiation of a class and as the curious beings that we…
In 1859 Bernhard Riemann published one of the most influential papers in analytic number theory concerning the distribution of the prime numbers by use of analytic methods.
It was titled Eber die Anzahl der Primzahlen unter einer gegebenen Grösse. It translates to something like On the Number of Primes Less than a Given Magnitude.
In particular, he investigated the zeta function (now called the Riemann zeta function in his honor) and proved that the zeta function encoded information about the distribution of the prime numbers through its zeros.
In this rather short article, I will give you some of my…
In this article, I will train a deep neural network to classify images, but I will also give you an understanding of what is happening inside the neural network itself and how convolutions really work.
We will explore the following sections.
I will show you the network in action by displaying to you what it is actually “seeing” when it makes the decisions by diving into its “brain” — the layers of the…
There are tons of great theoretical articles out there on the anatomy and mathematics of artificial neural networks, so I am going to take another approach to writing about and teaching this subject. In this article, we are going to get our hands dirty right away!
Let’s jump right in. You can choose a section below if you want to skip the installation section.
If you already have the requirements installed, then you can skip this section.
You are sitting in a bar with drinks on the table. Unfortunately, the table has four legs making it susceptible to wobbling.
People are folding napkins and paper plates to make them fit under the supposedly too-short leg.
But none of these attempts will really work and you have to perform a small circus act of carrying all your stuff while dancing around with the table. Oh, and the whole bar is watching you perform this act…
Allow me to let you in on a little secret.
Mathematicians don’t have wobbly tables. Why? …
Mathematician and Data Scientist interested in the mysteries of the Universe, fascinated by the human mind, music and things that I don’t understand.