Enjoy the twelfth 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 whether the Fibonacci numbers, and associated sequences, can be used for cryptography.

This essay explores the concept of infinity starting from the fundamentals of set theory and building up to the continuum hypothesis.

This essay explains the maths behind Buffon’s Needle – a method to estimate the value of pi by dropping needles onto equally spaced lines.

This essays looks at how a range of dynamical phenomena can be applied to the motion of a cricket bat as it makes contact with a cricket ball.

This essay derives the Taylor series for the sine function from first principles.

This essay outlines some of the main applications of the topic of linear algebra.

This essay discusses the mathematical and architectural techniques that are required when constructing a dome-shaped building.

This essay looks back through history at the variety of methods that have been used to calculate the digits of pi.

This essay investigates the patterns and properties of prime numbers and looks at how they can be applied to aid our understanding of the universe.

This essay explains the mathematical concept of a convolution – a method of combining two functions which is commonly used in graphics and audio processing.

This essay explores the importance of the number zero in a wide range of mathematical topics, from algebra and calculus, to paradoxes and logic.

This essay outlines the infamous Collatz conjecture before playing around with visualisations of some of the results obtained in Python.

This essay explains some of the key mathematical concepts used in Economics, from game theory to optimisation.

This essay investigates a mysterious occurrence of pi as a seemingly rational number on all Casio calculators.

This essay introduces the concept of a fractal through their history, famous examples, and applications in the real world.