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Module details

MA333-6-SP: MATHEMATICAL BIOLOGY

Year: 2014/15
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to year(s) of study:
Available to Study Abroad / Exchange Students: Yes
Full Year Module Available to Study Abroad / Exchange Students for a Single Term: No
Co-requisites: MA303-6-AU

Staff
Supervisor: Prof Edd Codling, email: ecodling@essex.ac.uk  
Teaching Staff: Prof Edd Codling, email: ecodling@essex.ac.uk  
Contact details: Miss Claire Watts, Departmental Administrator, Tel. 01206 873040, email cmwatts (Non essex users should add @essex.ac.uk to create the full email address) 

Module is taught during the following terms
AutumnnoSpringyesSummerno

Module Description

The course will concentrate on selected case studies in which knowledge of mathematical processes helps to explain biological phenomena.

The topics considered will be:

Random walks and the movement of animals and cells leading to diffusion and dispersal patterns; Population dynamics, harvesting and spatial interactions; Morphogenesis, pattern formation and the Turing Instability.

The mathematical methods used are varied and include: probability, limits, phase plane analysis, travelling waves, reaction-diffusion equations and ODE's with moving boundaries.

Syllabus

Introduction

The range of problems in mathematical biology and general principles in constructing mathematical models.

Random walks and movement

Simple random walk in 1 and 2 dimensions. Biased movement. Derivation of Diffusion Equation and solution. Correlated movement in 1 dimension and the Telegraph Equation. Mean Squared Dispersal Distance in 2 dimensions.

Population dynamics

Discrete and continuous systems. Birth, death, growth. Predator-prey and competing populations. Harvesting and optimal yields. Spatial interactions.

Morphogenesis, the Turing Instability, random walks and diffusion

Morphogenesis and the concept of pre-patterning. Reaction-diffusion equations. The Law of Mass Balance. Linearisation and the analysis of Turing instabilities. Examples of pattern formation in animals.

Learning and Teaching Methods

This course runs at 3 hours per week. There are 5 lectures and one class in every fortnight.

In the Summer term 3 revision lectures are given.

Assessment

10 per cent Coursework Mark, 90 per cent Exam Mark

Other details:
Information about coursework deadlines can be found in the "Coursework Information" section of the Current Students, Useful Information Maths web pages: Coursework and Test Information

Exam Duration and Period

2:00 hour exam during Summer Examination period.

Other information

Available to Socrates/IP students spending all relevant terms at Essex.

Bibliography

  • Recommended Reading:
  • J.D. Murray, Mathematical Biology, Springer-Verlag (1989)
  • M. Kot, Elements of Mathematical Ecology, Cambridge (2001)
  • Supplementary Reading:
  • Okubo & S. Levin, Diffusion and Ecological Problems: Modern Perspectives, Springer-Verlag (2001)

Further information

External Examiner Information

  • Name: Prof John Matthews
  • Institution: THE UNIVERSITY OF NEWCASTLE-UPON-TYNE
  • Academic Role: Professor of Medical Statistics

Should you have any queries about the Module Directory pages, please contact the Course Record Team, Systems Administration Office, Academic Section; email: crt (non Essex users should add @essex.ac.uk)