Module code: MATM040

Module provider


Module Leader

DUNLOP C Dr (Maths)

Number of Credits


ECTS Credits



FHEQ Level 7

JACs code


Module cap (Maximum number of students)


Module Availability

Semester 1

Overall student workload

Independent Study Hours: 117

Lecture Hours: 33

Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION (2 HOURS) 75
School-timetabled exam/test IN-SEMESTER TEST (50 MINS) 10

Alternative Assessment


Prerequisites / Co-requisites


Module overview

Mathematical biology is concerned with using mathematical techniques and models to shed light on the fundamental processes that underly biology. By abstracting biological detail into a formal mathematical setting we can identify what the mechanisms are that drive the observed phenomena, and can make predictions about system behaviour. Looking at a concrete example in cancer biology, it can be shown that tumour growth can be well-described using a simple system of linear partial differential equations. From this system we can then ascertain that tumour growth is initially limited by the availability of nutrients and can predict the result of different treatment methodologies.

To work in this field the mathematical biologist must develop a broad library of models, techniques and experience and be willing to engage with biological detail. They must learn to be conversant with e.g. systems of ordinary differential equations, partial differential equations and discrete models, and to analyse these systems using techniques ranging from stability analysis and phase plane diagrams, to looking for travelling wave solutions and applying asymptotic methods. A key aspect of the work is validating the derived models using experimental results.

Module aims

To show the power of applying mathematical techniques to biological and physiological problems, illustrating how such an approach can produce results that contribute significantly to biological understanding and thus enable the development of new therapies and technologies.

To develop the necessary biological and physiological modelling skills for real-world situations.

Introduce a range of biological models and techniques, and developing an understanding of their applicability in any given context.

Learning outcomes

Attributes Developed
Understand the process of modelling as applied to biological problems including model validation by comparison with experimental data;  KCT
Critically select from a range of mathematical techniques as appropriate to the biological application; KCT
Apply techniques such as dimensional analysis, asymptotic analysis and stability analysis to problems in biology; KC
Analyse and solve a range of biological models including signal-response dynamics, discrete biologically inspired models, diffusion-based models, and models for tumour progression.  KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

Indicative content includes:

Introduction to mathematical modelling of biological and physiological problems. This will include basic modelling methodology, dimensional analysis and the need for data analysis and model validation.

Models without spatial dependence including: discrete models for population genetics; signal-response dynamics and enzyme kinetics; oscillators and excitable systems with application to neurons (Fitzhugh-Nagumo models).

Spatially dependent models. Diffusion and reaction-diffusion equations: derivation and interpretation. Application including some of morphogenesis, tumour modelling, cell motility and taxis.

Selection of advanced techniques such as parameter estimation, asymptotic analysis and modelling case studies.

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Provide a detailed introduction to mathematical biological and physiological modelling.

Develop the ability to critically select appropriate models and mathematical techniques for use in this field.

Provide experience of applying advanced methods to analyse and solve biologically inspired models.


The learning and teaching methods include:

3 x 1 hour contact hours per week for 11 weeks split between lectures and modelling classes.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

Understanding of the modelling process applied to biological problems.

The ability to critically select and apply appropriate models and techniques.

Subject knowledge through the discussion of standard models, their derivations and key parameters.

Analytical ability through the solution of unseen problems.


Thus, the summative assessment for this module consists of:

One two hour examination worth 75% of the module mark.

One in-semester test and

One piece of assessed coursework


Formative assessment and feedback

Students will receive written feedback via a number of marked coursework assignments over the 11 week period. Students will also receive verbal feedback during modelling classes, and during small group work activities that will take place as integral parts of the lecture.

Reading list


Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics and Physics MPhys 1 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics MMath 1 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics MSc 1 Optional A weighted aggregate mark of 50% is required to pass the module
Mathematics and Physics MMath 1 Optional A weighted aggregate mark of 50% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2017/8 academic year.