# Mathematics for the Life Sciences

## Course summary

Course code: MATH1134
Level: 6
Credits: 15
School: Architecture, Computing and Hums
Department: Mathematical Sciences
Course Coordinator(s): Erwin George

## Specification

### Pre and co requisites

MATH1105 Linear Algebra and its Applications.

### Aims

Mathematics is increasingly used in the life sciences to give insights into, for example, population modelling, the spread and control of diseases, and understanding human behaviour. The leading mathematical writer Ian Stewart has recently said "Biology will be the great mathematical frontier of the twenty-first century". This course gives students an overview of the mathematical ideas and methods used in twenty-first century biology and enhances their employability in this area.

### Learning outcomes

On successful completion of this course a student will be able to:

1. Construct continuous models of population dynamics and analyse the behaviour predicted by the models.
2. Use game-theoretic techniques to model co-operative and non-co-operative behaviour.

### Indicative content

Population modelling - predator-prey models, dynamic modelling, simulation, analysis of behaviours. Lotka-Volterra equations and other population models. Modelling the spread of disease.

The mathematics of DNA. The topology of viruses.

Evolutionary concepts: kin selection, group selection.

Mathematics of evolution: game theory, Hawk-dove models, evolutionary steady states.

The Prisoner's Dilemma as a model for the evolution of altruism. Tit for tat and other strategies for the Iterated Prisoner's Dilemma. The Tragedy of the Commons. Modelling co-operative behaviour. Cycles of behaviour patterns. Punishment and reward. Trust and reputation.

"Game Theory can save the world" (Nowak and Highfield). Climate change as a case study.

### Teaching and learning activity

Lectures, workshops, tutorials, student investigation. The student investigation might involve computing and simulation.

### Assessment

Summative assessment:
Coursework - 100%
3000 words
Investigative coursework covering both learning outcomes (1-2)

Formative assessment: weekly tutorial exercises