Enjoy the eleventh 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 tells the story of secret messages from ancient civilisations to modern-day computers.

This essay outlines some of the key results involving the distribution of prime numbers and the authors own investigations on the matter.

This essay summarises the key mathematical results used in modern encryption methods when sending secure messages online.

This essay provides an introduction to the topic of category theory and how it can be thought of as the study of the language of mathematics.

This essay applies the techniques of fluid mechanics and calculus to explain the shape of the jugs used in Ancient Greece to measure time.

This essay introduces a wide range of problems where the techniques and tools of combinatorics can be used to provide insight.

This essay gives a brief introduction to the ideas of Georg Cantor and the classification of different sizes of infinity.

This essay details the compression techniques used in medical imaging, and the mathematical principles that underpin them.

This essay discusses the Gamma function, including its extension to the complex numbers and a derivation of the integral formula.

This essay presents mathematics as a tool for understanding the universe.

This essay goes into great detail to explain how the mathematical tools of group theory can be used to solve a Rubik’s cube.

This essay explores how ratios defined by simple sequences are used throughout the world in architecture.

This essay presents the many faces of infinity through the lens of Hilbert’s Hotel.

This essay describes the beauty and mathematical complexity of the art of origami.

This essay introduces the concept of dual numbers and explains how they are used in the process of automatic differentiation.