After following this course, the student is able to:
- formulate a research question based on a real-life problem, and formulate a relevant and consistent mathematical model;
- conduct a mathematical analysis in relation to the other courses of this module;
- present the project results in written and verbal form;
- reflect on the modelling process;
- write efficient and well-documented code in Python;
- give a clear and structured presentation making adequate use of media;
- explain the mathematical content clearly, adapted to the mathematical background of the audience, and react appropriately to the questions from the audience;
- reflect on his own presentation and give relevant feedback to another’s presentation.
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Mathematical models are used in many applications such as population dynamics, mechanical systems, electrical circuits, infectious diseases, climate dynamics and weather forecasts. Mathematical modelling involves formulating and analysing such models. This is one of the key topics of the Bachelor programme Applied Mathematics, as an applied mathematician often encounters this in his/her profession.
In this project, we focus on dynamical system models applying knowledge of the courses on differential equations and numerical analysis. Within a small group of students, you first revisit the iterative modelling cycle taught in earlier AM modules: formulating, analysing, interpreting and refining until convergence. Initially, all groups work on the same elementary problem. Several mandatory plenary sessions are organized to acquire the relevant techniques as well as to provide feedback.
Afterwards, the students continue on a more extensive challenge of their own choice. During this part, the modelling is mainly done within the groups under the supervision of a tutor. There is special attention to the following new aspects:
- Delimit the assignment to one that is executable.
- Formulate a research question.
- Make a time plan for executing this assignment.
Besides the modelling (roughly 60% of the course) there will be programming in Python (roughly 20% of the course) and presentation skills (roughly 20% of the course).
Programming focuses on:
- Implementing complex algorithms from a textual description.
- Advanced data structures.
- Properly documenting and writing efficient code.
- Using Python to find solutions for dynamic systems using standard libraries and by implementing specified numerical algorithms.
As a mathematician, you will regularly face situations in your professional environment where you have to present to others, for example, the chosen model, your (mathematical) analysis and conclusions. You already did so in the course Modelling and Programming 2. Besides the general skills for a successful presentation, presenting material of a mathematical nature requires some specific attention. This is because, for ‘laymen’, mathematical concepts are often difficult to grasp, due to the abstract nature of the concepts and sometimes, due to the lack of proper background knowledge. In the part Presenting a Mathematical Subject, you will learn some skills needed for a good mathematical presentation.
Assessment
Modelling assignment (100%)
Programming assignment (pass/fail)
Presentation (pass/fail)
The modelling component is a group assignment, but each student must actively participate and show their understanding of all aspects of the assignment. The deliverables are a group report on the obtained results and a presentation where each individual student has to participate and will be evaluated. The programming skills will be assessed individually for every student by means of several programming tasks.
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