MATU9MC - Experimental Design and Mathematical Modelling

SCQF Level: 10
Availability: Spring
Course Prerequisite: MAT9K4
Credit Value: 20 (1 module)

Aims

This module will be motivated by real-life examples from Biology and Medicine. In part A the concepts underlying the design of experiments and their analysis will be explored. In particular, multivariate methods for describing and analysing many dimensional data will be presented and applied. In part B different mathematical modelling techniques will be studied and applied.

Learning Outcomes

Students should be able to:

• interpret a correlation matrix, carry out appropriate tests and describe underlying assumptions; discuss different types of experimental designs, different methods of random sampling and factors involved in clinical trials; construct and implement appropriate models for simple and multiway analysis of variance, interpret output from such tests and validate the assumptions; list factors that might be important in a model; discuss methods of reducing dimensionality of multivariate data; interpret the output from factor analysis, principal components analysis and cluster analysis;
• analyse the long term behaviour of sets of nonlinear differential equations; write down and analyse the Leslie matrix of a system; solve recurrence relations, find equilibria and test stability of recurrence relations and describe the nature of relationships between different species.

Content

A1. Introduction and Sampling Techniques
A2. Linear Models and Analysis of Variance
A3. Crossed & Nested Designs
A4. Multivariate Data
A5. Multivariate Normal Distribution
A6. Principal Components Analysis
A7. Discriminant Analysis
B1. Mathematical modelling: introduction
B2. Discrete time models; equilibria, time delays
B3. Matrices in modelling; Leslie matrix
B4. Continuous time models; equilibria
B5. Multi-species models; symbiotics, predator-prey, SIR model

Transferable Skills

The ability to formulate problems in statistical terms, to design and then to present, analyse and interpret data. Problem solving; information retrieval; computing; analytical skills; group working; presentational skills; report writing.

Teaching Format

There will be three 1-hour lectures and one 1 hour practical per week.

Assessment

1/3 coursework (2 practical projects) and 2/3 examination.

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