Enjoy the fourth 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 constructs a prime counting formula which whilst theoretically correct, is unfortunately impractical for use in real-life.

This essay conducts a statistical analysis of the relationship between the number of tackles made by a team in a game of football, and the number of goals they concede.

This essay uses dimensional analysis – and the work of G.I. Taylor at the Trinity Atomic Test – to estimate the power of the Death Star used in Star Wars.

This essay calculates the perimeter, area, and fractional dimension of a range of famous fractals, including the Koch Snowflake, the Sierpinski Gasket, and the Menger Sponge.

This essay explains the concept of Fourier Analysis through the popular app ‘Shazam’ which is able to identify the song you are listening to from a short piece of audio.

This essay outlines the key concepts used in Neural Networks, from Optimisation and Loss, to Gradient Descent.

This essay explores the topic of ‘Generating Functions’ and their application to a range of mathematical topics such as Binomial Coefficients, the Golden Ratio and Geometry.

This essay investigates the topic of infinite integrals and asks when they can – and cannot – be calculated.

This essay discusses the fractional dimension of fractals, including how and why it is calculated as such.

This essay introduces the topic of Transcendental Numbers, through their history, definition and application to some famous mathematical constants.

This essay derives a formula for the brachistochrone – the curve which gives the shortest travel time under gravity.

This essay highlights the ubiquitous nature of symmetry in the world around us.

This essay applies mathematical modelling to the actions of Spiderman to determine just how strong he must be.

This essay introduces a wide range of mathematical models used in Physics, Biology and Chemistry.

This essay looks at the Fibonacci sequence and why we are so fascinated by it as human beings.