Teaching

Teaching is one of the most enjoyable parts of my job, and I am committed to teaching to the highest standard possible; my teaching statement outlines my teaching philosophy in more detail. Below are some materials related to courses I have taught and developed. Typos and corrections in any course materials are always welcome!

Durham University

Computational Mathematics II (MATH2731) — Winter 2025

A hands-on introduction to numerical analysis and scientific computing, covering algorithms for root-finding, interpolation, numerical integration, and the numerical solution of ordinary and partial differential equations.

This course is assessed by weekly computational lab reports and e-assessments (50%), and a computational project grounded in one of the research areas of the department (50%).

Fractal boundaries between convergence regions of Newton’s root-finding method.

Advanced Mathematical Biology IV (MATH4411) — Winter 2023, 2024, 2025

An advanced course in the mathematical modelling of biological systems. Michaelmas term covers stochastic models, including simulating and analysing discrete-state Markov processes, reaction-diffusion processes, and stochastic differential equations.

Epiphany term covers continuum-mechanical models of biological media, including non-Newtonian fluids, solids, and viscoelastic media.

Stochastic Turing patterns in a Schnakenberg reaction-diffusion system.

Brandeis University

Differential Equations — Summer 2020

An introduction to ordinary differential equations from a dynamical systems perspective, covering qualitative methods, phase plane analysis, and applications.

Text: Blanchard, P., Devaney, R. L., & Hall, G. R. (2012). Differential Equations (4th ed.). Brooks/Cole.

Probability — Fall 2019

A rigorous introduction to probability theory, covering sample spaces, random variables, distributions, expectation, limit theorems, and applications.

Text: Ross, S. M. (2012). A First Course in Probability. Pearson.

Multivariable Calculus — Spring 2019

An introduction to calculus in several variables, covering partial differentiation, multiple integration, vector fields, and the theorems of Green, Stokes, and Gauss.

Text: Marsden, J. E., & Tromba, A. (2011). Vector Calculus. W. H. Freeman.

Dublin City University

Simulation for Finance (MS455) — 2017

An introduction to probabilistic simulation methods and their applications in quantitative finance, covering Monte Carlo methods, stochastic processes, and the pricing of financial derivatives.