From finance to route planning, the reflection principle is an incredibly versatile technique, capable of transforming seemingly fiendish problems into elegant systems. In this post, I walk through three example applications of the principle.
The efficient frontier is a ubiquitous tool in quantative finance, yet it is often calculated using incredibly inefficient methods. Can we do better using a healthy helping of analysis and linear algebra.
One week ago today, we lost one of the most inspirational mathematicians of this generation. In this post, we take a brief look at the incredible legacy that John Conway left behind. On top of that we will discuss one of the many problems he tackled during his career; one that, to this day, occupies a special place in my heart. We close by discussing an intriguing puzzle that I am yet to find a solution to—can you?
Deciding the winner of a round-robin tournament is no simple task. The most naïve approach can easily be faltered by the existence of $k$-paradoxical tournaments. But what are these tournaments and what do we know about them? There is surprisingly little discussion on the topic and so, in this post, I plan to collate various pieces of knowledge on the subject into one succinct guide.
Not all integrals are created equally. In this post we look at a particular class of integrals which can be highly troublesome to evaluate. Thankfully, probability theory provides us with a framework that allows us to avoid the standard method of evaluation and by doing so makes our working far less error-prone.