MATH35032 - 2007/2008

 

Specification

Aims

Brief Description of the unit

The life sciences are arguably the greatest scientific adventure of the age. Over the last few decades a series of revolutions in experimental technique have made it possible to ask very detailed questions about how life works, ranging from the smallest, sub-cellular scales up through the organisation of tissues and the functioning of the brain and, on the very largest scales, the evolution of species and ecosystems. Mathematics has so far played a small, but honourable part in this development, especially by providing simple models designed to illuminate principles and test broad hypotheses.

Although this course is still being written, it is likely to touch on several of the following topics.

• Population models and broad questions of ecological and evolutionary stability: these topics are normally treated with ODEs or, when one wants to include spatial organisation, PDEs. This area a good introduction to the "illustrative model" school of mathematical biology.
• Pattern selection and development of body plan in early life: here I would like to have the class read a famous old paper Alan Turing's and then look at the sorts of things that modern work - both experimental and theoretical - has to say about the same questions. The main tools here are, again, differential equations.
• Analysis of regulatory networks: this follows naturally from the previous topic and begins to bring in some new mathematical methods and ideas, especially from graph theory and probability. This is mathematical biology at its closest to experimental data.
• Molecular evolution and phylogenetics: this subject takes as its starting point biological sequence data (DNA or protein) and asks questions such as: "How closely related are mice and men and when did they last have a common ancestor?". Here the models are probabilistic and the questions have a statistical flavour.

The mathematics required for biology is not generally all that hard or deep (though there are exceptions: some of the most exciting recent work in phylogenetics requires tools from algebraic geometry), but as the sketches above suggest the range of tools is extremely broad. The point is that modern mathematical biology is genuinely applied maths: its techniques are chosen to suit the biological problems, not the traditional disciplinary subdivisions. Although some previous acquaintance with graph theory and probability would be helpful, this course is meant to be self-contained and will only assume knowledge of differential equations.

Learning Outcomes

Future topics requiring this course unit

None.

Syllabus

Textbooks

Teaching and learning methods

Two lectures and one examples class each week.

Assessment

Coursework: 15%

End of semester examination: two hours weighting 85%

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Arrangements