$$ \def\ab{\boldsymbol{a}} \def\bb{\boldsymbol{b}} \def\cb{\boldsymbol{c}} \def\db{\boldsymbol{d}} \def\eb{\boldsymbol{e}} \def\fb{\boldsymbol{f}} \def\gb{\boldsymbol{g}} \def\hb{\boldsymbol{h}} \def\kb{\boldsymbol{k}} \def\nb{\boldsymbol{n}} \def\pb{\boldsymbol{p}} \def\qb{\boldsymbol{q}} \def\rb{\boldsymbol{r}} \def\tb{\boldsymbol{t}} \def\ub{\boldsymbol{u}} \def\vb{\boldsymbol{v}} \def\xb{\boldsymbol{x}} \def\yb{\boldsymbol{y}} \def\zb{\boldsymbol{z}} \def\Ab{\boldsymbol{A}} \def\Bb{\boldsymbol{B}} \def\Eb{\boldsymbol{E}} \def\Fb{\boldsymbol{F}} \def\Jb{\boldsymbol{J}} \def\Ub{\boldsymbol{U}} \def\xib{\boldsymbol{\xi}} \def\evx{\boldsymbol{e}_x} \def\evy{\boldsymbol{e}_y} \def\evz{\boldsymbol{e}_z} \def\evr{\boldsymbol{e}_r} \def\evt{\boldsymbol{e}_\theta} \def\evp{\boldsymbol{e}_r} \def\evf{\boldsymbol{e}_\phi} \def\evb{\boldsymbol{e}_\parallel} \def\omb{\boldsymbol{\omega}} \def\dA{\;\mathrm{d}\Ab} \def\dS{\;\mathrm{d}\boldsymbol{S}} \def\dV{\;\mathrm{d}V} \def\dl{\mathrm{d}\boldsymbol{l}} \def\bfzero{\boldsymbol{0}} \def\Rey{\mathrm{Re}} \def\Real{\mathbb{R}} \def\grad{\boldsymbol\nabla} \newcommand{\dds}[1]{\frac{\mathrm{d}{#1}}{\mathrm{d}s}} \newcommand{\ddy}[2]{\frac{\partial{#1}}{\partial{#2}}} \newcommand{\ddt}[1]{\frac{\mathrm{d}{#1}}{\mathrm{d}t}} \newcommand{\DDt}[1]{\frac{\mathrm{D}{#1}}{\mathrm{D}t}} $$
Teaching
Lecture notes
Here is a collection of lecture notes for (some of the) undergraduate courses I have taught:
MATH 2031 Analysis in Many Variables II (HTML) (Michaelmas 2024-25) – mostly vector calculus including index notation and some functions from \(\mathbb{R}^n\to\mathbb{R}^m\). This is core second-year material, 25 lectures. Note that despite the name, this is a non-rigorous methods course.
MATH 4381 Topics in Applied Mathematics IV (HTML) (Michaelmas 2022-23) – a 20-lecture introduction to MHD (magnetohydrodynamics) given to fourth-year (MMath) students. (The course now forms Epiphany Term of MATH 4421 Geophysical and Astrophysical Fluids.)
MATH 3101 Fluid Mechanics III (PDF) (Epiphany 2021-22) – the second term of our third year fluids course, covering compressible flow, instabilities and viscosity.
MATH 2051 Numerical Analysis II (PDF) (2017-18) – this is an optional 40-lecture second-year course introducing Numerical Analysis (everything except differential equations!). The course is running for the last time in its current form in 2024-25, due to restructuring of the second year. It will be replaced by a more hands-on Computational Mathematics course.
MATH 3081 Approximation Theory III (HTML) (Epiphany 2014-15) – this was an optional third-year course that no longer exists. It followed on from Numerical Analysis II to cover splines, minimax approximation and trigonometric interpolation (including the FFT).
And at graduate level:
Magnetohydrodynamics (PDF) – slides from the STFC Introductory Course in Solar and Solar-Terrestrial Physics for new PhD students, Durham, 23-Aug-2021.
Magnetohydrodynamic Relaxation Theory (PDF) – a short series of graduate lectures given at CISM in 2019. Published as a book chapter by Springer:
Other resources
A Quick introduction to parallel computing with MPI, with examples in both C++ and Fortran – from a practical computing seminar given in Durham on 2017-Mar-15.
Conway’s Army – a talk designed for A Level maths students, given to prospective students at the university open day.