Taught Component

The MSc aims to train and educate mathematics graduates in mathematical and statistical techniques together with a range of biological systems and processes so that they can engage in interdisciplinary research in mathematical/theoretical biology in the university sector, or in industry. The MSc is a 90 credit course of which the taught component comprises 60 credits (10 units of 6 credits each), divided evenly over two semesters. The remaining 30 credits come from a summer research project. Taught units are offered in biology, mathematical biology and mathematics.

Biology Units

Four biology units are offered. These units provide an overview of both the classical concepts and theoretical approaches in the biological sciences and the recent developments and current research interests within the field. In addition to the theory, students take part in field work as part of a second semester unit to expose them to the procedures and challenges associated with data collection and analysis. In Semester 1, students register for Biology/Biochemistry for Mathematical Biologists and The Evolution of Genetic Systems. In Semester 2, students will register for the Field Course.

The Evolution of Genetic Systems This course trains students in the techniques of mathematical population genetics and its role in exploring problems related to the organisation and structure of genetic systems. It introduces concepts in genetic and molecular evolution and methods for testing evolutionary hypotheses.

Biology and Biochemistry for Mathematical Biologists This course provides students with an overview of a wide variety of biological concepts from areas including chemotaxis, developmental biology, ecology and population biology, enzyme kinetics, epidemiology, evolution, genome science, immunology, neuroscience, structural biology, and trafficking and signalling. Ten staff members from the department of Biology and Biochemistry will present the students with an overview of their subject, including a discussion of key concepts, current research and commentary on the role of mathematical modelling to address key questions within the subject.

Field Course This unit introduces students to the protocols and problems of data collection and analysis. During the field course, students will collect data and carry out some statistical analysis of that data. As a follow up, the students will work in teams to produce a mathematical model based on their field study.

Mathematical Biology Units

Three mathematical biology units are offered. In semester 1 students register for Mathematical Modelling in Ecology, Evolution and Epidemiology. In semester 2 they register for Statistics for Biological Dynamic Modelling and Mathematical Biology Topic Review. Embedded within these units is a training strand which will include the use of a range of scientific software: LaTeX, R, Matlab, Maple; communication skills: presenting a poster, giving a seminar, providing constructive criticism of other students' seminars; research methods: summarising a research paper, literature review, library databases, peer assessment.

Mathematical Modelling in Ecology, Evolution and Epidemiology This course introduces students to a range of current problems in ecology, evolution and epidemiology through a mixture of seminars, lectures and directed reading. Subject could include: co-operative behaviour, evolution of metabolic pathways, contact networks, disease resistance and co-infection or infection control. Students are taught how to produce, analyse and validate mathematical models using a predictive biology approach. Model structures could include: dynamical systems, control systems, reaction-diffusion equations, network models or cellular automata. Analysis techniques could include perturbation theory, numerical solution, bifurcation theory, bounds and stability.

Statistics for Biological Dynamic Modelling This course provides students with an introduction to some of the key quantitative methods available for combining models of biological mechanisms with data, in order to make inferences and predictions about the system that data and model relate to. Students learn about models in which the major stochastic component is measurement error and ones in which process error also exists. They are trained in the use of R, a software package for statistical analysis.

Mathematical Biology Topic Review. For this course students choose a single topic from the biological sciences (for example, ecology, enzymology, epidemiology, evolution, development, neuroscience, signalling, structural biology) where mathematical modelling has made an important contribution and engage in a unit of supported self-study. The research takes the form of a literature review and provides opportunities to learn about basic biological concepts and to study some of the recent and/or seminal mathematical models used to enhance understanding of these concepts. Students engage in peer assessment of oral presentations and written reports.

Mathematics Units

Four mathematics units are offered. The units provide students with the essential tools and skills to analyse models used to describe biological processes. In Semester 1 students register for Advanced Numerical Methods and Advanced Mathematical Methods. In Semester 2 students register for Topics in Differential Equations and Case Studies in Mathematical Modelling.

Advanced Numerical Methods. This unit provides an introduction to the numerical solution of differential equations and how they arise in applications. Students become familiar with mathematical software packages Matlab and Maple and their potential for solving differential equations which arise in a wide variety of applied (including biological) problems. The unit also provides background material on aspects of linear algebra.

Advanced Mathematical Methods. This unit presents methods and techniques relevant to solving problems which arise in applications modelled by differential equations (both ordinary and partial) and integral equations. It provides students with a set of techniques with which they can solve a problem or construct an accurate approximation to the solution. Students are encouraged to develop an understanding of the theory and range of applications of each technique.

Topics in Differential Equations. This unit explores the use of mathematical models to describe processes occurring on multiple scales. Examples are taken from the physical sciences but the phenomenon is also core to systems biology. Students are given additional materials to motivate the problems and their analysis such as phase transitions and the formation of microstructures.

Case Studies in Mathematical Modelling. In this unit, students learn about the nature of the modelling process, starting with a physical problem, representing it mathematically, simplifying and solving the resulting model and interpreting their results. Case studies could include microwave cooking and tests for elasticity. In addition, the unit provides training in key research skills and working in teams.