Mathematics

Symbolic Math in Python

Yes, you can do symbolic math in Python! The library to take a look at is SymPy. This article is not a SymPy tutorial, as I only want to walk you through some examples to show you the kinds of things that it can do. A good place to start… read more

Submitted on 22 May 2018

What is a Hadamard Matrix?

A Hadamard matrix is a matrix with all elements equal to \(+1\) or \(-1\), and for which the rows are mutually orthogonal. If you pick two rows from the matrix and write it as vectors \(\bf x\) and \(\bf y\), then these are orthogonal if… read more

Submitted on 6 December 2017

Jerk

What is jerk? Jerk is to acceleration as acceleration is to velocity. And, acceleration is to velocity as velocity is to position. So let’s start there. The instantaneous velocity at which you travel tells you… read more

Submitted on 20 November 2017

The Birthday Paradox

How many people do you need before the probability that two of them have the same birthday is 50%? The answer to this question is, amazingly, 23. This surprising result is known as the birthday paradox. The word paradox is used here in the sense that… read more

Submitted on 5 March 2017

Exponentiation by Squaring

In this article, I present the simple idea of exponentiation by squaring. This idea saves computation time in determining the value of large integer powers by “splitting” the exponentiation in a clever way into a series of squaring operations. The technique is based on the fact that… read more

Submitted on 12 February 2017

Some Mathematics Behind "Catching Them All"

Pokémon Go logo

Mathematics is everywhere. In this article, I present some of the mathematics behind “Catching Them All”. Say that a rare Pokémon pops up in your Sightings, and that you walk in a straight line until it disappears again. What have you then learned about the position of that Pokémon? Well, since the… read more

Submitted on 28 September 2016

Are there Infinitely Many Twin Primes?

Recently, there has been much progress towards proving the twin prime conjecture, one of the great open questions in number theory. There are infinitely many primes, a fact that was already known by the ancient Greek. A short proof, although not the… read more

Submitted on 25 May 2015

Exponential Growth

Linear vs. exponential

The term “exponential growth” strongly implies quick growth. However, something that grows exponentially will seem to grow quite slowly at first. In practice, there is a good chance that you won’t notice it at all until it suddenly “pops into view”. Take the adoption of… read more

Submitted on 26 May 2013

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