Courses that I’ve lectured in Oxford over the past few years are listed below, along with their official synopses. If you’d like copies of the notes please get in touch.
Prelims – Fourier Series and Partial Differential Equations
Fourier Series and Partial Differential Equations begins by introducing students to Fourier series, concentrating on their practical application rather than proofs of convergence. Students will then be shown how the heat equation, the wave equation and Laplace’s equation arise in physical models. They will learn basic techniques for solving each of these equations in several independent variables, and will be introduced to elementary uniqueness theorems.
Part A – Modelling in Mathematical Biology
Modelling in Mathematical Biology introduces the applied mathematician to practical applications in an area that is growing very rapidly. The course focuses on examples from population biology that can be analysed using deterministic discrete- and continuous-time non-spatial models, and demonstrates how mathematical techniques such as linear stability analysis and phase planes can enable us to predict the behaviour of living systems.
Part B – Mathematical Biology and Ecology
Mathematical Biology and Ecology introduces the applied mathematician to practical applications in an area that is growing very rapidly. The course mainly focusses on situations where continuous models are appropriate and where these may be modelled by deterministic ordinary and partial differential equations. By using particular modelling examples in ecology, chemistry, biology, physiology and epidemiology, the course demonstrates how various applied mathematical techniques, such as those describing linear stability, phase planes, singular perturbation and travelling waves, can yield important information about the behaviour of complex models.
Part B – Stochastic Modelling of Biological Processes
Stochastic Modelling of Biological Processes provides an introduction to stochastic methods for modelling biological systems. The course starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods which can be used for analysis of stochastic models. Different models of molecular diffusion (on-lattice and off-lattice models, velocity-jump processes) and their properties are studied, before moving to stochastic reaction-diffusion models. Compartment-based and molecular-based approaches to stochastic reaction-diffusion modelling (Brownian dynamics) are discussed together with stochastic spatially-distributed models (pattern formation).