Unit name | Modern Mathematical Biology |
---|---|

Unit code | MATH30004 |

Credit points | 10 |

Level of study | H/6 |

Teaching block(s) |
Teaching Block 2C (weeks 13 - 18) |

Unit director | Professor. Liverpool |

Open unit status | Not open |

Pre-requisites |
Mechanics 1, Calculus 1, Calculus 2. |

Co-requisites |
None |

School/department | School of Mathematics |

Faculty | Faculty of Science |

Unit aims

To provide students with the mathematical tools used to study and solve a variety of problems in biology at different scales. Examples will be taken from problems at different length and timescales - from the scale of the cell, tissue to organisms.

General Description of the Unit

Mathematical Biology is one of the most rapidly growing and exciting areas of Applied Mathematics. This is because recently developed experimental techniques in the biological sciences, are generating an unprecedented amount of quantitative data. This new 'quantitative revolution' is changing the way biology is done - requiring methods of generating hypotheses and then testing them that rely heavily on sophisticated mathematical analyses. Biological systems are complex systems and the modern process of studying them requires an iterative process of communication between mathematicians (modellers) and biologists. This starts with making quantitative measurements; second, this biological data is used to develop mathematical models; third, approximate solutions of the models are obtained; and fourth, these solutions are used to make new predictions which can be further tested by new measurements - thus starting the cycle anew. Professionals in the biomedical sector are increasingly using technology that is reliant on sophisticated mathematics. Examples include ECG readings of the heart, MRI brain scans, blood flow through arteries, tumor invasion, drug design and immunology. Therefore research in this area has the promise of quickly finding real world applications with a positive impact on society. Mathematical Biology also encompasses other interesting phenomena observed in nature, such as the swimming of micro-organisms, spread of infectious diseases, and the emergence of patterns in the development and growth.

In this unit we shall use a number of fundamental biological problems as the motivation and starting point for developing mathematical models, explore methods for solving these models and discuss the implications of the predictions that can be made based on them.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

Learning Objectives

By the end of the unit the students will be familiar with (1) the applications of ODE models in a variety of biological systems, (2)Reaction-Diffusion equations and their applications in biology, (3) the use of linear and nonlinear stability analysis to study the dynamics of complex systems, (4) the dynamical systems approach to describing excitable media.

A standard chalk-and-talk lecture unit of about 15 lectures, with occasional problems classes or informal discussion to meet the needs of individual students. Regular homework problems set and marked. Homework will include simple numerical exercises using Maple and MATLAB.

100% Examination

on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

- R. Philips, J. Kondev , J. Theriot and H. Garcia, "Physical Biology of the Cell", Garland Science, ISBN 0815341636;

- J.D. Murray, "Mathematical Biology I. An Introduction", Springer, ISBN 0387952233;

- J.D. Murray, "Mathematical Biology II. Spatial models and biomedical applications", Springer, ISBN 0387952284;

- L.A. Segel, "Modelling dynamic phenomena in molecular and cellular biology", Cambridge University Press, ISBN 052127477X;

- P. Nelson, "Biological Physics : Energy, Information, Life" , W. H. Freeman, ISBN 0716798972

- U Alon, "An Introduction to Systems Biology: Design Principles of Biological Circuits", CRC press, ISBN-13: 978-1584886426