I’m really excited to share my completed honours thesis! I’m honoured that my supervisors (and apparently the examiners too haha) were pleased with the result, and I’m humbled that my effort this y...

Make sure you have read the last post on generating functions first, else proceed at your own risk! Recall that for \(k,n \in \mathbb{N}\), the binomial coefficient is defined by [\binom{k}{n} = ...

Recall from high school that a geometric sequence is a sequence \((a_n)_{n \geq 0}\) that satisfies the recurrence relation \(a_{n + 1} = r a_n\) for some fixed \(r \in \mathbb{R}\), and an arithme...

Make sure you read part 1 first! Recall that we were exploring integrating rational functions, and to do so, we needed to look at partial fraction decompositions. As we now begin to discuss that in...

You know how to integrate a polynomial: [\int (a_0 + a_1x + \dotsb + a_nx^n) \,dx = C + a_0x + \frac{a_1}{2}x^2 + \dotsb + \frac{a_n}{n + 1}x^{n + 1},] where \(C \in \mathbb R\) is a real constan...

Note: this article is currently a WIP. Some examples of surface visualisations Here are a couple of versions of the Desmos save file with different cool pre-loaded plots: The default: a hemis...

If you haven’t already read part 1, make sure you read it here first! Or else, much of the below will not make sense! Random variables: neither random, nor a variable What is a random variable? ...

Introduction to the problem You may have encountered continuous probability distributions such as the normal distribution. It’s often used to model things in the real world, and has nice statistic...