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

Unit code | MATH30004 |

Credit points | 10 |

Level of study | H/6 |

Teaching block(s) |
Teaching Block 1A (weeks 1 - 6) |

Unit director | Professor. Liverpool |

Open unit status | Not open |

Pre-requisites |
MATH11300 Probability 1 (MATH10013 Probability and Statistics), MATH11009 Mechanics 1 and MATH11007 Calculus 1 (or MATH10012 ODEs, Curves and Dynamics), MATH20901 Multivariable Calculus, and MATH20001 Methods of Complex Functions |

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.

**Unit Description**

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.

**Relation to Other Units**

This is a Level H/6 version of Modern Mathematical Biology 34, sharing the lectures but with differentiated problems and exam. Students may not take both units.

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.

**Recommended**

- Uri Alon,
*An Introduction to Systems Biology: Design Principles of Biological Circuits*, CRC Press, 2007 - J.D. Murray,
*Mathematical Biology I. An Introduction*, Springer, 1989 - J.D. Murray,
*Mathematical Biology II. Spatial models and biomedical applications*, Springer, 2002 - Philip Charles Nelson,
*Biological Physics: Energy, Information, Life*, W. H. Freeman, 2008 - Rob Philips, Jane Kondev , Julie Theriot and Hernan G. Garcia,
*Physical Biology of the Cell*, Garland Science, 2009 - Lee A. Segel,
*Modelling Dynamic Phenomena in Molecular and Cellular Biology*, Cambridge University Press, 1984