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) To familiarise with 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.

(S1) Numeracy/computational skills - Problem solving

•4 weeks - 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.

•4 weeks - Epidemic dynamics on Networks: introduction to random graphs (e.g. generating functions, configuration models, giant component, clustering coefficient); introduction to epidemic models on graphs, particularly Markovian SIS and SIR dynamics; overview of recent results and methods (e.g. bond-percolation, pair-approximation, long-term behaviour of the dynamics, duality in the contact process, Volz model).

•4 weeks - Biogical 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).