MAS316 - Mathematical Modelling of Natural Systems

This is the course webpage for MAS316 Mathematical Modelling of Natural Systems. If you are taking the level 4 course MAS414 Advanced Mathematical Modelling of Natural Systems, please see the separate webpage as some of the details are different.

In this course you will learn the art of mathematical modelling, building on mathematical and computational skills learned earlier in your degree to gain insight in to the behaviour of natural systems from the biological and environmental sciences.

This is a 10-credit module running in semester 2.

MAS212 Scientific Programming and MAS222 Differential Equations are both pre-requisites for this course.

What is mathematical modelling?
If you were to build a model of anything - a model aeroplane, for example - you would want it to be recognisable as the real thing, but small and simple enough to play with or test. The same goes for a mathematical model. Natural systems in the biological or environmental sciences are fundamentally complicated phenomena that we could never hope to model in their entirity. We want to include enough realism in our model that it clearly represents the system we are interested in, yet be simple enough to use some of the many mathematical and computational tools at our disposal to gain understanding and make predictions about the system. In this course you will understand how to choose what parts of the system to include in your model, how to apply the most appropriate mathematical and computational methods, and how to relate the technical results back to the original question.

Course structure
Each week there is one lecture (Tuesday 12 LT3) and one computer class (Tuesday 4 G25). Attendance at both sessions is essential. There are three lecturers for this course, who will each introduce the students to a topic from their own research interests:
  • Weeks 1-4: Dr Alex Best (
    Evolution in ecological populations.
    Office hour: Tuesday 1-3 (G27b)

  • Weeks 5-8: Dr Jonathan Potts (
    Spatial pattern formation in biology.
    Office hour: Tuesday 1-3 (G27c)

  • Weeks 9-12: Dr Alex Fletcher (
    Stochastic modelling of biochemical reactions.
    Office hour: Tuesday 1-3 (G15)

The computing element of the course will be in Python. Following on from MAS212, in the practical sessions we will be using the Anaconda distribution, using both Jupyter (iPython notebooks) and Spyder.

Help with python
There are likely to be times in this module where you need some help remembering or working out how to produce some code in python. We suggest you work through the following stages until you can find an answer:
  • 1: Try and break the task up in to different stages and work through them one by one.

  • 2: Ask a friend or lecturer for suggestions (but you should not copy other people's code verbatim!).

  • 3: Look at the course notes from MAS212.

  • 4: Search on the internet.
You will note that searching on the internet is the last resort. While full of helpful information, advice given on forums can be very tailored to a specific problem that may not necessarily be helpful to you.

Assessment is by three written assignments, with no examination. Each lecturer will set one assignment on the topic they have been teaching. Each assignment counts equally (33.3% each) and all three assignments must be submitted by the given deadlines.

The assignments will appear below when they are released. The assignments are different for MAS316 and MAS414; if you are taking MAS414 please go to the separate webpage.

No. Assignment Deadline
1 Assignment 1 4pm Friday 3rd March
2 Released week 5 4pm Friday 31st March
3 Released week 9 4pm Friday 19th May

Marking guidelines
A general markscheme for the assignments can be found here. Each assignment may have a more specific markscheme which will be used in conjunction with this document.