Enjoy the sixteenth – and final – 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 introduces the axioms of group theory and uses them to prove some of the fundamental properties of a group.

This essay uses statistics to analyse the accuracy of predicting the points total of Premier League football teams using data from previous seasons.

This essay explains the notion of the Euler characteristic and the important role it plays in the subject of topology.

This essay looks back at the counting systems used throughout history and asks what advantages they each had.

This essay begins with a discussion of the golden ratio, before progressing onto other numbers defined by similar sequences.

This essay explores how matrices are used in developing accurate perspectives in video games, and for understanding special relativity.

This essay conducts an entertaining experiment to determine the optimal walking speed for a journey to school which also allows your coffee to cool sufficiently.

This essay provides a brief overview of the history of mathematics, from ancient times to the modern world.

This essay identifies the many occurrences of the golden ratio in the natural world.

This essay describes some of the many mathematical paradoxes, and how the work of Godel helps us to understand them.

This essay champions the Mobius strip through its history and many useful peoperties and applications.

This essay explains how to use the Chinese Remainder Theorem to solve problems involving the identification of a number from its remainders.

This essay introduces the core concepts of the subject of graph theory and how it can be applied to help to understand social networks.

This essay defines the Gaussian distribution for a single variable, multiple variables, and even a general supporting domain.