Lecture Notes and Articles
The first 5-6 weeks of the term will be devoted to what one might describe as mathematical biology in the classical style and the lectures will follow sections of Jim Murray's famous text, Mathematical Biology I: An Introduction. This book is available online, though only from within the University's network (e.g. in the campus clusters or in the halls), but if you want to access it from off campus, you can install software that will allow you to use all the Library's services via the University's excellent Virtual Private Network (VPN).
Notes such as the ones below will be available for the whole term. Additionally, there will be links to some articles we'll discuss.
Opportunities for feedback
The main channel for formal, written feedback in this module is the coursework. It will be a problem set similar to the ones provided below, but devoted to a novel application that uses the ideas from the course. You'll prepare written solutions and I'll mark them over the Easter Break, providing both written comments and a mark. In addition, the weekly examples classes provide further opportunities for verbal feedback and—for students who bring written solutions to the exercises—on-the-spot marking and written feedback as well.
Problem Sets & Solutions
|The problems below are intended as a guide for students considering taking the course in 2017-18. Once the term starts, there will be new problems most weeks and I will publish the solutions at the same time as the problems.|
Coursework & Exams
Intended Learning Outcomes
- Interpret differential equation models for populations, relating the expression appearing in the model to processes that affect the population.
- Formulate and analyse ordinary differential equation (ODE) models for the population of a single species, finding equilibrium populations and determining how their stability depends on parameters.
- Analyse delay-differential equation (DDE) models for the population of a single species and use linear stability analysis to determine which values of the parameters induce oscillatory instabilities.
- Analyse ODE models for the populations of two interacting species, finding equilibria and using information about their linear stability to characterise the long-term behaviour of the system.
- Define a conserved quantity for a system of ODEs and, where possible, use such quantities to determine the long-term behaviour of both two-species ODE models and single-species models population models include diffusion.
- Construct the ODEs associated with a system of chemical reactions subject to mass-action kinetics and analyse them to discover conserved quantities.
- Construct the Markov process associated with a system of chemical reactions and, for small numbers of reactions, analyse it to determine the long-term behaviour of the system.
- Analyse two key models, Wolpert's Frech flag model and Turing's reaction-diffusion model, relating the solutions of the associated PDEs to the processes of pattern-formation in developing organisms.
- Explain the notion of a motif in a genetic regulatory network and, for small examples, compute the probability of seeing k instances of a given motif in a randomly-assembled network.
A hyperlinked version of the lists below is available from Manchester University Library's Link2Lists system.
I studied the following—more or less mathematically-minded—books while preparing this course.
I also looked at the books below for biological background.