MA333-6-SP: MATHEMATICAL BIOLOGY
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
|Module is taught during the following terms
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.
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.
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.
10 per cent Coursework Mark, 90 per cent Exam Mark
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.
Available to Socrates/IP students spending all relevant terms at Essex.
- Recommended Reading:
J.D. Murray, Mathematical Biology, Springer-Verlag (1989)
M. Kot, Elements of Mathematical Ecology, Cambridge (2001)
Okubo & S. Levin, Diffusion and Ecological Problems: Modern Perspectives, Springer-Verlag (2001)