This course aims to ensure that the successful student has an understanding of the core mathematical concepts and techniques used in mathematical modelling of biological systems; is able to express in mathematical terms simple representations of a biological system, manipulate and develop simplifying approximations of those representations in order to gain insight into the behaviour of the mathematical model and hence the real biological system; has a basic understanding of how parameters within a mathematical model are inferred from or fitted to experimental data, and the basic issues and pitfalls of model fitting.

It is designed to prepare participants for our core modelling course in computational simulation and analysis of biochemical networks.

An introduction to the basic mathematical skills, concepts and ideas that underpin the modelling of biological systems.

This module is entirely web-based, so a reliable internet connection is essential.

This module will provide an introduction to the basic mathematical skills, concepts and ideas that underpin the modelling of biological systems. In particular the unit will use as an exemplar mathematical techniques for use in Systems Biology and for analysis and simulation of biochemical networks. It will cover :

• basic algebraic manipulations;
• elementary differential and integral calculus;
• ordinary differential equations;
• the foundations of probability and statistics;
• basics of inference and fitting mathematical models to experimental data;
• intermediate computational techniques, e.g. Monte Carlo sampling for Bayesian inference;
• examples of basic mathematical analysis informing modelling procedures for biochemical networks.

The assessment methods:

1. There will be a tutorial exercise for each section of the course.  These exercises will be brief: they are included as one means of maintaining a dialogue between all those participating in the course. This exchange is particularly important for Systems Biology, which spans traditional academic disciplines.
2. There will be two written assessments.  At the discretion of the examiners, you may also be required to attend a viva voce examination.

All the course materials are provided within the Moodle virtual learning environment (VLE). The tools provided will allow you to navigate and search through the course textbook, practical exercises and references to other useful texts and URLs. The course textbook is provided as a set of web pages. It will be used to provide the necessary background to the focus of the course, which is problem-based learning.

You will interact with the members of the course team, and with other learners, through course bulletin boards. Our students and graduates can use the programme bulletin boards after a course has ended, so we now have a large and supportive online community.

Mathematics for Biological Scientists, Aitken, M., Broadhurst, B. and Hladky, S., Garland Science, Taylor and Francis

An Introduction to Differential Equations and their Applications, Farlow, S. J., Dover

This book is recommended for further readings on ODEs

An Introduction to R : Notes on R: A Programming Environment for Data Analysis and Graphics, Version 2.10.1 (2009-12-14), W. N. Venables, D. M. Smith and the R Development Core Team