MATH3565/5566M

In Semester 1 of the academic year 2024/25, I taught MATH3565/5566M: (Advanced) Mathematical Biology along with Martı́n López-Garcı́a: Martı́n delivered the first 4 weeks of the course, and I lectured in the following 7 weeks.

Course Resources: Lecture notes, videos and lecture recordings, examples and solutions, past exam papers will be available on Minerva  to students enrolled on MATH3565/5566M.

Objectives of the course: All the major developments in the physical sciences are underpinned by mathematics, both as a structure or language for the concise statement of the laws of nature, and as a tool for developing an understanding of new phenomena by modelling analysis. The introduction of mathematics in biology is still at a rather early stage, but it is becoming increasingly important in many areas. This module aims to introduce the student to some areas of mathematical biology that give rise to exciting new developments and top some current challenges for mathematical biology.

Topics covered in MATH3565/5566M in 2024/25:

• Modelling biological phenomena from several areas of biology and medicine (MATH3565/5566M)

• Ordinary differential equations in biology: population growth and molecular reactions (MATH3565/5566M)

• Steady states and stability in one and multiple dimensions (MATH3565/5566M).

• Probability generating functions, random variables and stochastic processes (MATH3565/5566M). Poisson process (MATH5566M)

• Discrete and continuous time Markov chains: extinction (MATH3565/5566M).

• Branching processes in discrete time (MATH3565/5566M)

• Birth-and-death processes (MATH3565/5566M)

• Branching processes continuous time (MATH5566M)

• Brownian motion in one and more spatial dimensions, hitting properties and associated differential

equations (MATH3565/5566M)

• Aged-structured populations (MATH5566M)

• Spatially extended systems: Turing phenomenon (MATH5566M), travelling waves and spread of epidemics (MATH3565/5566M)