Enjoy the first 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 looks at the maths behind some of the most popular casino games (Blackjack, Roulette, Craps) and calculates the ‘house edge’.

This essay uncovers a surprising connection between the Cantor’s study of infinity and the topic of computational complexity in Computer Science.

This essay investigates prime numbers and the many visual patterns that they form when looked at in different coordinate systems.

This essay explores the topic of chaos through the example of the Lorenz equations and the infamous butterfly-shaped visualisation of a Lorenz attractor.

This essay explores the detailed mathematics that leads to the ‘Homer Simpson Function’ – an animated drawing of the cartoon character.

This essay provides a graphical solution to the ‘Red Square Problem’ of whether or not two people will meet in Moscow.

This essay uncovers some interesting patterns in the prime numbers when analysed using modular arithmetic base 180.

This essay charts the history of Imaginary Numbers from their humble beginning in mathematical duels to underpinning our understanding of the universe.

This essay compares and contrasts the use of Euler Angles and Quaternions in Computer Graphics.

This essay provides a succinct overview of the theory of constructivism and illustrates its importance through the example of Godel’s Incompleteness Theorems.

This essay introduces the topic of Non-Euclidean Geometry through spherical trigonometry and great circles.

This essay derives the Black-Scholes Equation commonly used in finance, whilst explaining the meaning and origin of each term.

This essay looks more closely at table salt – and with more maths – than anyone has ever done before…

This essay discusses vectors and their usefulness to solve a wide range of problems.

This essay succinctly summarises the history and mathematics of cryptography.