Mathematicians have constructed a small but diverse ecosystem of number systems, ranging from the integers (whole numbers) to the complex numbers and beyond. Even long after university (and now thr...

Dear reader… I’m excited that this blog is back after a 3-year pause. Formerly Epic Maths Time, it’s now called Forms and Formation: a space for me to share some new reflections about faith, music ...

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...

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...

The below was submitted as my essay for the final assignment in the unit MTH3110 – Differential Geometry, at Monash University, in Semester 1, 2021. I’ve chosen to upload it here for those who may ...

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...