# 2020/21 Taught Postgraduate Module Catalogue

### 20 creditsClass Size: 60

Module manager: Professor Grant Lythe
Email: G.D.Lythe@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2020/21

### Pre-requisite qualifications

MATH2391 or MATH2375 or equivalent.

### This module is mutually exclusive with

 MATH3565 Mathematical Biology

This module is approved as an Elective

### Module summary

All the major developments in the physical sciences are underpinned by mathematics, both as a structure or language for the concise statement of the laws of nature, and as a tool for developing an understanding of new phenomena by modelling analysis. The introduction of mathematics to the biological and the medical sciences is still at anearly stage, but it is becoming increasingly important in many areas. This module aims to introduce the student to some areas of mathematical biology and medicine that give rise to exciting new developments and top some current challenges for mathematical biology.

### Objectives

On completion of this module, students should be able to

a) model certain biological phenomena described by:

- ordinary differential equations;
- difference equations;
- discrete time Markov chains;
- continuous time Markov chains;
- discrete-time and continuous-time branching processes
- Brownian motion;
- partial differential equations.

b) model phenomena in infectious diseases.

### Syllabus

- Modelling biological phenomena from several areas of biology and medicine.
- Ordinary differential equations in biology: population growth and molecular reactions.
- Steady states and stability in one and multiple dimensions.
- Probability, random variables and stochastic processes.
- Discrete and continuous time Markov chains: extinction.
- Branching processes in discrete time and continuous time.
- Brownian motion and associated differential equations.
- Spatially extended systems, Turing phenomenon, travelling waves and spread of epidemics.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Private study hours 178.00 Total Contact hours 22.00 Total hours (100hr per 10 credits) 200.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

### Opportunities for Formative Feedback

Example sheets and quizzes.

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Exams
 Exam type Exam duration % of formal assessment Open Book exam 3 hr 00 mins 100.00 Total percentage (Assessment Exams) 100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated