Taught Component

The MSc aims to train and educate mathematics graduates in mathematical and statistical techniques and a range of biological processes and systems so that they can engage in interdisciplinary research in systems biology or Mathematical/Theoretical Biology either as MPhil/PhD students 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 and a summer supervised research project of 30 credits. Taught units will be offered in biology, mathematical biology and mathematics.

Biology units

There will be three biology units offered. These units will 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 will 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, the students will register for the two units, Biology/Biochemistry for mathematical biologists and The evolution of genetic systems. In Semester 2, the students will register for the Field Course.

The evolution of genetic systems This course will train students in the techniques of mathematical population genetics and its role in exploring problems related to the organisation and structure of genetic systems. They will be introduced to concepts in genetic and molecular evolution and will be trained in the methods for testing evolutionary hypotheses.

Biology and Biochemistry for mathematical biologists This course will provide students with an overview of a wide variety of biological concepts taken 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 in which will include a discussion of key concepts, current research interest and commentary on the role of mathematical modelling to address key questions within the subject. Supplementary reading material will be suggested. One session will be given to techniques of essay writing.

Field Course This unit will introduce 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 as teams to produce a mathematical model based on their field study which they will use to address important biological questions such as the development and maintenance of community or niche structure.

Mathematical Biology units

There will be three units; in semester 1, students will attend Mathematical modelling in ecology, evolution and epidemiology and in semester 2, they will attend Statistics for biological dynamic modelling and Mathematical Biology Topic Review. Embedded within these units will be a training strand which will include:

• The use of a range of scientific computing 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.

This training will be run jointly with the Students Union SORTED programme following a successful bid to the University Teaching and Learning Fund to work with SORTED on undergraduate generic training.

Mathematical modelling in ecology, evolution and epidemiology will introduce students to a range of current problems in ecology, evolution and epidemiology through a mixture of seminars, lectures and directed reading.

These could include: co-operative behaviour, evolution of metabolic pathways, contact networks, disease resistance and co-infection, infection control. Students will be taught how to produce, analyse and validate mathematical models using a predictive biology approach. Model structures will include: dynamical systems, control systems, reaction-diffusion equations, network models and Cellular Automata/simulation. Students will be introduced to a variety of analysis techniques including perturbation theory, numerical solution, bifurcation theory, bounds and stability.

Statistics for biological dynamic modelling will provide 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 will learn about models in which the major stochastic component is measurement error and ones in which process error also exists. They will be trained in the use of R, a software package for statistical analysis.

Mathematical Biology Topic Review. Students will 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. A list of possible topics together with corresponding reading lists and key concepts will be issued to students during the previous semester. Students will each choose one topic in consultation with the Director of Studies. The research will take the form of a literature review and will provide 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 will engage in peer assessment of an oral presentation and summary review document.

Mathematics units

We will make use of the highly successful taught units in Mathematical Methods currently offered to students on the MSc in Modern Applications of Mathematics. The units will provide students with the essential tools and skills to analyse models used to describe biological processes. In Semester 1, students will register for the two units Advanced Numerical Methods and Advanced Mathematical Methods. In Semester 2, the units offered will be Topics in Differential Equations and Case Studies in Mathematical Modelling.

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

Advanced Mathematical Methods. This unit will present methods and techniques relevant to solving problems which arise in applications modelled by differential equations (both ordinary and partial) and integral equations. It will provide students with a set of techniques with which they can solve a problem or construct an accurate approximation to the solution. Students will be encouraged to develop an understanding of both 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 and students will be 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 will 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 will include microwave cooking and tests for elasticity. In addition, the unit will provide training in key research skills and working in teams.

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