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

Unit code | MATH30004 |

Credit points | 10 |

Level of study | H/6 |

Teaching block(s) |
Teaching Block 2D (weeks 19 - 24) |

Unit director | Professor. Liverpool |

Open unit status | Not open |

Pre-requisites |
Year 2 Theoretical Physics (for Physics students) OR MATH10013 Probability and Statistics, MATH10012 ODEs, Curves and Dynamics, MATH20015 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.

The unit will be taught through a combination of

- synchronous online and, if subsequently possible, face-to-face lectures
- asynchronous online materials, including narrated presentations and worked examples
- guided asynchronous independent activities such as problem sheets and/or other exercises
- synchronous weekly group problem/example classes, workshops and/or tutorials
- synchronous weekly group tutorials
- synchronous weekly office hours

90% Timed, open-book examination 10% Coursework

Raw scores on the examinations will be determined according to the marking scheme written 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.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH30004).

**How much time the unit requires**

Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.

See the Faculty workload statement relating to this unit for more information.

**Assessment**

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study.
If you have self-certificated your absence from an assessment, you will normally be required to complete it the next time it runs
(this is usually in the next assessment period).

The Board of Examiners will take into account any extenuating circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.