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TRM Essay Competition 2024 Showcase: Group 9

Enjoy the ninth 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!

The 100 prisoners problemDownload

This essay presents the ingenious solution to a famous problem involving prisoners selecting numbers from 100 boxes.

Bifurcation theory: when does extinction become a threat?Download

This essay uses the tools of mathematical biology to investigate population growth and the threat of extinction.

Essence of CalculusDownload

This essay explains some of the basics of calculus, from differentiation to integration.

Newton and LeibnizDownload

This essay tells the history of the rivalry between Newton and Leibniz as they each tried to understand the techniques underpinning calculus.

Deciphering the Equations Behind Animal Size and Speed EvolutionDownload

This essay discusses the relationship between an animals size and its maximum speed.

How does mathematics protect your privacy online?Download

This essay discusses the past, present, and future of encryption.

Bringing biological evolution into artificial intelligenceDownload

This essay introduces the concept of genetic algorithms and how they can be used to generate more efficient forms of artificial intelligence.

RSA Encryption, How Maths Keeps Us SafeDownload

This essay provides a detailed overview of RSA encryption, including several proofs of key theorems that underpin the technique.

Principles in Building Giant DomesDownload

This essay looks at dome-shaped buildings and how mathematics is combined with engineering and architecture to create these marvellous structures.

Scratching the surface of infinityDownload

This essay explores the treatment of the infinite at various points in history, from the Ancient Greek paradoxes, to Cauchy’s definition of a limit.

Stepping to the world of Eigenvalues and EigenvectorsDownload

This essay explains the concepts of eigenvalues and eigenvectors, and how they are applied to face recognition software.

The Königsberg bridge problem and graph theoryDownload

This essay details the history of the subject of graph theory, beginning with its origin as a method of solution to the Königsberg bridge problem.

Will computer systems remain secure with advancements in technology?Download

This essay outlines the current methods used for encryption and looks at how they will fare should the development of quantum computers be successful.

Unravelling the secrets of musical tones with Fourier’s methodsDownload

This essay explains how the techniques of the Fourier transform and Fourier series are used to analyse music.

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