To introduce some hot problems of contemporary mathematical biology, including analysis of developmental processes, networks and biological mechanics.

To further develop mathematical skills in the areas of difference equations and ordinary and partial differential equations.

To explore biological applications of fluid dynamics in the limit of low and high Reynolds number.

(LO1) Understand mathematical modelling methodology used in contemporary mathematical biology.

(LO2) Be able to use techniques from difference equations and ordinary and partial differential equations in tackling problems in biology.

Weeks 1-4: Biological fluid dynamics: low Re flow - flow field around sphere (sinking speed of marine particles, hydrodynamic signalling, circulation, lift, drag); high Re flow (inviscid flow), steady flight (Bernoulli's theory, Kutta-Joukowski hypothesis, circulation, lift, drag)

Weeks 5-8: Epidemic dynamics on Networks: introduction to epidemic models on graphs, particularly Markovian SIS and SIR dynamics;  overview of recent results and methods (e.g. pair-approximation, long-term behaviour of the dynamics)

Weeks 9-12: Modelling developmental processes: cell-cell signalling and cellular differentiation in biological tissues; scaling of biological patterns, noise and fluctuations in biological systems; movement of cells in tissues.