Constraints drive creativity. I consider that solving mathematical problems
within the constraints of computer hardware is a fascinating challenge with
practical application. The tension between the abstract field of mathematics
and the tangible hardware of computers is at the core of computer science.

For my first EPQ, I wrote a chess engine using Rust. I found that by storing
chess positions adjacently in memory and evaluating them sequentially, cache
lines are used more effectively thus reducing the frequency of slow main memory
reads. The book 'Numerical Recipes: Third Edition' by Press et al helped me
realise other subtle ways in which hardware can affect the efficiency and
precision of mathematical algorithms and how software can account for and
overcome these limitations.

To learn more about hardware, I built my own 8-bit computer using a 6502
microprocessor. At present, it consists of the 6502, 32KiB ROM and an output
interface register connected to an LCD character display. To reduce cost, I
made logic gates from transistors, used multiple clock signals to overcome
hardware limitations and built my own ROM programmer. This project developed
problem solving skills and inspired a lasting interest in hardware which I
continue to pursue by modifying and improving the computer.

For my second EPQ, I created a guide for how to cross-compile a Linux based
operating system from scratch. Understanding how a Linux system works
internally gave me the ability to customise and experiment with my desktop OS.
It satisfies a desire to better understand the software I use every day. I plan
to build my next primary desktop OS from scratch so that I will not rely on a
distribution to hide how my system works internally. I enjoy the academic
nature of EPQs and feel ready for the challenge of degree level study.

In 2020, I participated in GCHQ's 'Cyber Discovery' course where cyber security
concepts were taught through a series of varied challenges. I was one of 500
students to progress to the final 'Elite' phase where we participated in a
2-day capture the flag competition and learnt from industry experts about
binary exploitation. I developed a particular interest in cryptography and
invented an algorithm to generate secure Vernam cipher one-time-pads of
arbitrary length from a short passphrase.

I enjoy designing and testing novel methods for 3D rendering and lighting. My
latest experiment approximates a 3D scene with voxels. The first pass in my
deferred render pipeline draws the gbuffer using a unique combination of
rasterisation and ray casting. Because the scene is made up of voxels, ray
traced lighting for the second pass can use an algorithm similar to 3D-DDA for
ray-scene intersection. Monte Carlo light samples are accumulated over multiple
frames using a method of my own invention which combines the advantages of
screen space and world space irradiance caching. In this project, I was able to
apply concepts learnt in my A-Level further mathematics class: trigonometry for
generating weighted random ray directions, statistics for approximating
irradiance from finite samples and matrices for transforming 3D vectors.

To see through a compiler's abstractions, I wrote a clone of the game 'pong'
using x86-64 assembly; understanding software at a low level reignited my
interest in binary exploitation. I wrote a C program and exploited it by
overflowing a buffer on the stack and manipulating the call stack to return
into libc and open an interactive shell.

I enjoy using my skills for the benefit of my local and wider community. For
example, in 2020 I made an Android and IOS app for my local food bank; staff
can use it to update a list of which products are needed most. I have also
contributed significantly to the open source 'cglm' 3D maths library. I look
forward to continuing my studies at university, meeting like-minded people and
joining a chess society.