MAS414 Mathematical Modelling of Natural Systems

Semester 2, 2021/22 10 Credits
Lecturer: Dr Ashley Willis Home page Timetable Reading List
Aims Outcomes Assessment

Mathematical modelling enables insight in to a wide range of scientific problems. This module will provide a practical introduction to techniques for modelling natural systems. Students will learn how to construct, analyse and interpret mathematical models, using a combination of differential equations, scientific computing and mathematical reasoning. Students will learn the art of mathematical modelling: translating a scientific problem into a mathematical model, identifying and using appropriate mathematical tools to analyse the model, and finally relating the significance of the mathematical results back to the original problem. Study systems will be drawn from throughout the environmental and life sciences.

Prerequisites: MAS212 (Scientific Computing and Simulation) Please contact lecturers if you did not take this module; MAS222 (Differential Equations)
Not with: MAS316 (Mathematical modelling of natural systems)
No other modules have this module as a prerequisite.

Outline syllabus

  • An introduction to chaotic dynamics.
  • Machine learning methods to retrieve forest biophysical parameters.
  • A stochastic approach to modelling disease spread.


  • develop students’ skills in comprehending problems, formulating them mathematically and obtaining solutions by appropriate methods;
  • provide practical demonstrations of how mathematical modelling may be used to gain insight in to the dynamics of natural systems;
  • build on mathematical methods (ordinary/partial differential equations, linear stability analysis, scientific computing in Python) learned at earlier levels, and expose students to how they can be used to model natural systems.

Learning outcomes

By the end of the unit, a candidate will 1. be familiar with the ideas of mathematical modelling and understand the utility of mathematical modelling to understand natural phenomena (QAA benchmark for mathematics, 5.4v); 2. be able to formulate a mathematical model that represents the dynamics of a natural system and apply appropriate methods to obtain solutions (QAA benchmark for mathematics, 5.4v); 3. be able to gain insight in to a natural system through the application of mathematical modelling techniques; 4. recognise how mathematical methods learned at earlier levels may be used to model natural systems.

12 lectures, no tutorials, 9 practicals


Three pieces of coursework and one oral presentation, with no examination.

Reading list

Type Author(s) Title Library Blackwells Amazon
B Hastie T, Tibshirani R, Friedman JH The Elements of Statistical Learning: Data Mining, Inference, and Prediction 006.31 (H) Blackwells Amazon
B Murray JD Mathematical Biology I and II 570.15118 (M) Blackwells Amazon
B Strogatz SH Nonlinear dynamics and chaos: with applications to physics, physics, biology, chemistry, and engineering 531.3 (S) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.