See also ...

Course provider:

University of Manchester 
Course contact:

Heather Vincent (heather.vincent@manchester.ac.uk)

Summary:

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 can be studied as an individual module, for professional development. In the context of our Masters programme, it is designed to prepare participants for our core modelling course in computational simulation and analysis of biochemical networks.

Syllabus:

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.

Assessment:

The assessment methods:
 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.
 There will be two written assessments. At the discretion of the examiners, you may also be required to attend a viva voce examination.

Further details:

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 problembased 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. 
Technical requirements:

This module is entirely webbased, so a reliable internet connection is essential. 
References:

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 (20091214), W. N. Venables, D. M. Smith and the R Development Core Team
This text is available from the R site.

