Enjoy the thirteenth group of essays from the 2024 TRM Essay Competition, now proudly held in partnership with the Oxford University Department for Continuing Education. The showcase will take place throughout June and July with the winners being announced in August.

If you enjoy reading any of the essays, be sure to leave a comment to let the author know!

This essay explains how the many paradoxes of Zeno can be explained with modern mathematics.

This essay looks at a range of different ways maths is used in Economics, including the infamous Black-Scholes equation.

This essay investigates the birthday paradox which states that only 23 people need to be present in a room for there to be a >50% chance that two of them share a birthday.

This essay looks back at the history of chaos theory, fro the three body problem to weather forecasting.

This essay outlines the many facets of chaos theory, including how it is used to understand the rhythm of the human heart.

This essay discusses the history and the eventual solution of the world’s most famous maths problem.

This essay demonstrates how fractals similar to the Mandelbrot set can be generated using number systems other than the complex numbers.

This essay provides an overview of catastrophe theory and how it can be used to predict event such as prison riots.

This essay provides an in-depth analysis of sound waves generated by musical instruments.

This essay reads as an ode to remainders, in their many forms.

This essay explains the theory of optimal control, and how it is used alongside Brownian motion to model financial systems.

This essay carefully defines the terms ‘odds’ and ‘probability’ and analyses the many ways in which they are easily confused.

This essay provides an in-depth analysis of the maths of skateboarding, from the force balance of an ‘ollie’, to the rotation axis of an ‘impossible’.

This essay explores the range of different types of infinity from Hilbert’s Hotel to Cantor’s Diagonal argument.

This essay introduces the Newton-Raphson fractal and explores its similarities to the Mandelbrot set.