This course offers an introduction to the essential concepts and models of complex systems and related mathematical methods and simulation strategies with application to physical, biological and social systems.
Concepts to be discussed include: emergence, complexity, networks, self-organization, pattern formation, evolution, adaptation, fractals, chaos, cooperation, competition, attractors, interdependence, scaling, dynamic response, information, and function. Methods to be discussed include: statistical methods, cellular automata, agent-based modeling, pattern recognition, system representation and data analytics. The course will use of multiscale representations as a unifying approach to complex systems concepts, methods and applications.
The course will cover the basic construction and analysis of models including identifying what is to be modeled, constructing a mathematical representation, analysis tools and implementing and simulating the model in a computer program. Particular attention will be paid to choosing the right level of detail for the model, testing its robustness, and discussing which questions a given model can or cannot answer.
There will be supervised group projects as an integral part of the course.