What is a Markov Process?

A few students that have great interest in going into financial mathematics, be in JC students or Uni students that were taught by me before, asked me where to start. So I often recommend them to [...]

Let’s talk about Zipf’s Law

Zipf’s law /ˈzɪf/, an empirical law formulated using mathematical statistics, refers to the fact that many types of data studied in the physical and social sciences can be approximated with [...]

Pascal’s Triangle

This is a really good video that introduces students to Pascal Triangle’s. A-levels Students should be able to relate to the binomial expansion coefficients that are found in the triangle! [...]

Why we need to be close to zero?

Many students have asked me why it is important to for to be close to zero for the Maclaurin’s expansion to be a good approximation. So here, I plot it in the 4 curves: which is our actual [...]

Mathematical Computing #1

With regards to a recent post, I shall share further on Mathematical Computing and how we can start on it. So to assist me in not over-simplifying the journey, I’ve personally signed up for [...]

Prime Numbers and their uses

Prime Numbers are numbers that are only divisible by itself and 1. However, you will be amazed that the pursuit of prime numbers has gifted us a number that is 17 million digits long. So what is [...]

Taylor’s Series of a Polynomial

Remember the working on Taylor Series from your A-level Math MF15? This video walks you through what would be the Taylor’s Series of a polynomial. Surprised? Can you figure out why this is [...]

How many chess games are possible?

The Shannon number, named after Claude Shannon, is an estimated lower bound on the game-tree complexity of chess of 10120, based on about 103 initial moves for White and Black and a typical game [...]

Why is it all triangles in 3D

We see objects all the time and our brains decode the 3D shapes, but how do computers model these shapes and why break it all down to triangles?

Patterns in prime numbers

So you still think prime numbers are random? Take a look at this really cool project, it kinda reminds me of the sieve of Eratosthenes: El Patrón de los Números Primos: Prime Number Patterns [...]