Modelling and Simulation

Overview

In this module, students will analyse real-life situations, build a mathematical model, solve it using analytical and/or numerical techniques, and analyse and interpret the results and the validity of the model by comparing to actual data. The emphasis will be on the construction and analysis of the model rather than on solution methods. Two group projects will fix the key ideas and incorporate the methodology. This will take 7-8 weeks of term and will be supported with seminars and workshops on the modelling process. Then students will focus on a solo project (relevant to their pathways) with real-life application and work individually on this for the remaining weeks of term. They will present their results in seminars with open discussion, and on a Webpage.
The starting group project will be focused, and offer a limited number of specific modelling problems. For the other projects, students will build on these initial problems by addressing a wider problem taken from, but not exclusively, the following areas: classical mechanics, biological models, finance, quantum mechanics, traffic flow, fluid dynamics, and agent-based models, including modelling linked to problems of relevance to the UN sustainable development goals. A pool of options will be offered, but students will also have the opportunity to propose a problem of their own choice.

Learning Objectives

On successful completion of the module, it is intended that students will be able to:

1. Develop mathematical models of different kinds of systems using multiple kinds of appropriate abstractions
2. Explain basic relevant numerical approaches
3. Implement their models in Python and use analytical tools when appropriate
4. Apply their models to make predictions, interpret behaviour, and make decisions
5. Validate the predictions of their models against real data.

Skills

1. Creative mathematical thinking
2. Formulation of models, the modelling process and interpretation of results
3. Teamwork
4. Problem-solving
5. Effective verbal and written communication skills

Assessment

None