The course has only half the usual number of exercise classes. In addition to the homework problems discussed in these classes, each participant chooses two computational projects to be solved by independent work and written up in a report. Any software (e.g. MatLab, Maple, Mathematica, C++, Python, etc) can be used, but no technical help is provided with the chosen software.
The course has one open-book exam at the end (notes, books etc can be used). During the semester, progress is monitored via closed-book quick test, which focus on the basics and take only 5-10 min during lectures. For the dates of the quick tests, see the end of the introductory text above.
The final grade is from the exam (80%) and the two projects (20%). The quick tests and the homework exercises are meant primarily for self-evaluation, but good quick tests and good exercise class activity will improve marginal grades.
Master's Programme in Mathematics and Statistics is responsible for the course.
The course belongs to the Mathematics and Applied mathematics module.
The course is available to students from other degree programmes.
BSc courses on differential equations, linear algebra, probability theory; basic computer programming for project work
Mathematical modelling or Introduction to mathematical biology
Familiarity with a range of different models applicable to spatially structured systems, including partial differential equations, probabilistic cellular automata, coupled map lattices and structured metapopulation models.
Recommended time/stage of studies for completion: 1. or 2. year
Term/teaching period when the course will be offered: varying
This course will explore how to model the dynamics and evolution of populations with spatial movement, spatial constraints and spatial interactions between organisms. We study diffusion, travelling waves, pattern formation and Turing instability, stochastic patch occupancy models, structured metapopulation models, probabilistic cellular automata and coupled map lattices. We also discuss topical issues of evolutionary biology where spatial structure plays a crucial role, e.g. the evolution of mobility (dispersal), specialisation to different environments, and the evolution of altruistic behaviour. This is a course in applied mathematics. Instead of choosing the problem to suit a method, we emphasize the use of versatile techniques. We introduce/review methods for ordinary differential equations and difference equations, partial differential equations, Fourier analysis, stochastic processes, pair approximation methods, game theory and adaptive dynamics. When necessary, we turn to numerical analysis.
Lectures, exercise classes, project with numerical analysis / simulations
Exam and exercises + project work, Course will be graded with grades 1-5
Exam, other methods will be described later