Department of Mathematical Sciences, Unit Catalogue 2007/08 |
MA40146 Mathematical & statistical modelling for biological sciences |
| Credits: 6 |
| Level: Masters |
| Semester: 2 |
| Assessment: CW 50%, EX 50% |
| Requisites: |
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Pre-requisite: A-level Mathematics
Aims & Learning Objectives: This unit aims to study, by example, practical aspects of mathematical and statistical modelling, focussing on the biological sciences. Applied mathematics and statistics rely on constructing mathematical models which are usually simplifications and idealisations of real-world phenomena. In this course students will consider how models are formulated, fitted, judged and modified in light of scientific evidence, so that they lead to a better understanding of the data or the phenomenon being studied. the approach will be case-study-based and will involve the use of computer packages. Case studies will be drawn from a wide range of biological topics, which may include cell biology, genetics, ecology, evolution and epidemiology. After taking this unit, the student should be able to * Construct an initial mathematical model for a real-world process and assess this model critically; and * Suggest alterations or elaborations of a proposed model in light of discrepancies between model predictions and observed data, or failures of the model to exhibit correct quantitative behaviour. Content: * Modelling and the scientific method. Objectives of mathematical and statistical modelling; the iterative nature of modelling; falsifiability and predictive accuracy. * The three stages of modelling. (1) Model formulation, including the art of consultation and the use of empirical information. (2) Model fitting. (3) Model validation. * Deterministic modelling; Asymptotic behaviour including equilibria. Dynamic behaviour. Optimum behaviour for a system. * The interpretation of probability. Symmetry, relative frequency, and degree of belief. * Stochastic modelling. Probalistic models for complex systems. Modelling mean response and variability. The effects of model uncertainty on statistical interference. The dangers of multiple testing and data dredging. |