This course will introduce the tools from mathematics, physics and computer science that have been used in understanding complex systems. In order to pass the course (grade 3) the student should be able to
implement simulation methods, including state-based, individual-based and cellular automata models;
use mean-field and other approximations in order to increase analytic understanding of simulation results;
explain methods for measuring and quantifying complex systems;
explain the importance of complex systems in modern science;
explain the role of computer simulations in providing understanding of such systems, while also developing an appreciation for the difficulties and limitations involved.
Numerical methods and software for simulations; Individual vs state-based simulations; Random systems and processes; Mean-field approximations; Random walks and diffusion approximations; Chaotic motion of dynamical systems; Measuring Chaos; Self-organised critical phenomena; Cellular Automata; Sandpile and Forest fire models; Models of flocking; Many particle models and self-propelled particles.
Strong emphasis on computer laboratory and project work; also lectures and seminars. The course will consist of a series of four projects and the laboratories will help the students work individually or in small groups on these projects.