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New course: Mathematical Biology

Posted on 2 mins read

Together with Sam Jelbart, I have been developing a new course on Mathematical Biology (MATHX309). The information on the course outline page is currently incorrect, so I have added more information below for students. It will first be taught in semester 2, 2026. These details are not final, but represent our best plan as of the time of writing.

Overview

This course develops mathematical models for understanding biological systems across a wide range of settings, from populations and chemical reactions through to neurons, spatial processes, and stochastic dynamics. A central goal is to show how relatively simple mathematical structures can generate complex biological behaviour.

The first half of the course focuses on deterministic modelling using ordinary and partial differential equations. We begin with population dynamics, where differential equations describe growth, interaction, and disease spread. We then move to chemical reaction systems and enzyme kinetics, developing tools for simplifying and analysing nonlinear models. This builds towards modelling electrical activity in neurons, where we derive the Hodgkin–Huxley equations and use them to describe how action potentials arise from ionic currents. We then extend these ideas to spatial systems, deriving reaction–diffusion and advection equations using conservation laws. This leads naturally to pattern formation, where we study how spatial structure can emerge spontaneously through Turing’s mechanism.

The second half of the course shifts focus to stochastic modelling and the role of randomness in biology. We introduce discrete, individual-based descriptions of biological systems and develop simulation methods for reaction networks. We then analyse birth–death processes, before showing how deterministic models can emerge as approximations of underlying stochastic dynamics. Finally, we connect random motion at the individual level to diffusion and spatial stochastic processes, building a unified view of space, movement, and noise.

Module 1: Deterministic models
  1. Population Dynamics
  2. Chemical reactions
  3. Excitable systems - Neurons
  4. Spatial variation
  5. Pattern formation
Module 2: Stochastic models
  1. Stochastic models and simulation
  2. Birth-death processes
  3. Approximations and deterministic limits
  4. Movement and diffusion
  5. Spatial dynamics and emergent patterns