William Wylde

Personal projects & academic work


Academic Study

I am in the fourth year of a mathematics degree at the University of Bath on track for a first.
I am interested in studying topics in representation theory of Lie algebras in positive characteristic and ring theory.


Personal Projects

LMS Project - Simple Lie algebras in positive characteristic: Summer 2025

I was awarded the London Mathematical Society Undergraduate Reserach Bursary to study the Jacobson Witt algebras under the supervision of Professor Lewis Topley. Our aim was to study central elements in their enveloping algeras.
As part of the project, I developed a computer algebra program using SAGE with Python to work with elements of the Jacobson Witt algebras and the center of their enveloping algebras.
Reading for this project included Modular Lie Algebras and their Representations by Strade & Farnsteiner.
We are continuing this project for my master's thesis.

Backstage Committee: 2024 - 2026

In the 2024-2025 academic year I took up the role of Secretary, and for 2025-2026 Chair, on the Backstage Technical Services committee. As a committee member, I was responsible for the day-to-day running of the society and as Chair I was also responsible for the society's relationships within the University of Bath, as well as society finances.


University Modules

Fourth-year (2025 - 2026, Currently Studying):

Algebraic Curves
Algebraic Topology
Representation Theory of Finite Groups
Differential Geometry of Curves and Surfaces
Differential and Geometric Analysis
Theory of PDEs
Graph Theory
Modelling with Randomness

Third-year (2024 - 2025):

Group Theory - 82%
Galois Theory - 88%
Number Theory - 83%
Measure Theory and Integration - 75%
Introduction to Topology - 80%
Analysis of Nonlinear ODEs - 82%
Mathematical Methods 1 - 87%
Mathematical Methods 2 - 70%
Probability 2 - 76%

Second-year (2023 - 2024):

Algebra 2A Advanced Linear Algebra - 80%
Algebra 2B Groups, Rings, and Fields - 82%
Analysis 2A Metric Spaces and Topology - 90%
Analysis 2B Complex and Multivariable Analysis - 78%
Numerical Analysis - 75%
ODEs and Control - 89%
Vector Calculus and PDEs - 87%
Modelling and Dynamical Systems - 65%
Introduction to Data Science - 64%
Machine Learning - 71%

First-year (2022 - 2023):

Algebra 1A - 95%
Algebra 1B Linear Algebra - 95%
Analysis 1 - 79%
Multivariable Calculus and Differential Equations - 83%
Vectors, Vector Calculus, and Mechanics - 92%
Programming, Foundations, and Connections - 75%
Probability & Statistics 1A - 81%
Probability & Statistics 1B - 81%

A-Levels

Brookfield Community School (2020 - 2022)

Further Mathematics - A*
Mathematics - A*
Physics - A*
Product Design - A*

Additional Qualifications

Goethe Institut

CEFR German
Writing - B2
Listening - B2
Speaking - B2
Reading - B1 (Youth)


Work Experience

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