During this thrid-year course, which is part of the Advanced Theoretical Techniques and Modelling Matter module, we study the mathematical tools which underpin modern theoretical physics. With these powerful techniques, my students are able to solve advanced problems in theoretical physics and beyond. The course consists of 22 lectures in which we study

- Integral transforms (such as Fourier and Laplace) and Green functions, and how they can be used to solve linear differential equations
- An introduction to non-linear differential equations
- The calculus of variations, which is used in classical and quantum mechanics, optics, field theories and more
- Tensors and how they are used to transform physical laws between reference frames, for example within Special and General Relativity.

All my lecture notes are available to students via the virtual learning environment (VLE).

I teach linear algebra to the second-year undergraduates as part of the following modules Mathematics, Professional Skills & Experimental Laboratories, Computational Laboratories and Introduction to Laboratories. During my class, my students learn the mathematics that is crucial to fields such as quantum mechanics, electronics and circuit theory and optics, among many others.

All lecture notes are available through the VLE.

I teach applied mathematics to the first-year undergraduates as part of the module Mathematical, Computational & Professional Skills 2. My class is core to the students' learning and covers some of the most important areas of mathematical physics, for example

- Vector calculus, which is essential for studying electromagnetism, fluid dynamics, quantum mechanics and more
- Solving second-order differential equations that describe the behaviour and dynamics of many systems in physics
- Fourier series and transform, both of which are key tools for signal analysis, imaging and tomography, quantum mechanics and beyond.

I lecture advanced mechanics as part of the modules Advanced Mechanics, Computational Laboratories, Astrophysical Laboratories, Physics Laboratories & Skills. The Lagrangian and Hamiltonian approaches to classical mechanics allow my students to describe complex physical phenomena, from mechanical systems to the motion of planets.

All lecture notes are available through the VLE.

In this second-year theoretical physics class, which is now part of the module Mathematical Techniques & Machine Learning, I covered

- Finite difference methods
- Complex analysis
- The calculus of variations
- Special functions.

I was head of the third-year Advanced Computational Lab. During my lab, students used the skills they had developed in computational and theoretical physics over their 3 years of study to tackle challenging, research-style physics problems. The current head of the Advanced Comp Lab is Dr Yvette Hancock.