MA333-6-SP: MATHEMATICAL BIOLOGY
Year: 2013/14
Department: Mathematical Sciences
Essex credit: 15
ECTS credit: 7.5
Available to year(s) of study:
Available to Study Abroad / Exchange Students: Yes Co-requisites: MA303-6-AU
| Module is taught during the following terms |
| Autumn |  | Spring |  | Summer | |
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 & 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 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:
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J.D. Murray, Mathematical Biology, Springer-Verlag, 1989.
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M. Kot, Elements of Mathematical Ecology, Cambridge, 2001.
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Supplementary reading:
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A. Okubo & S. Levin, Diffusion and Ecological Problems: Modern Perspectives, Springer-Verlag, 2001.
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