Introduction to Dynamical Systems and Chaos, the second course to be offered through the Santa Fe Institute's Complexity Explorer project, started on January 6th and enrollment is still open.
This follow on to Melanie Mitchell's Introduction to Complexity is focused on dynamical systems described in the course introduction as:
the interdisciplinary field of applied mathematics that studies systems that change over time.
It is an eight-week course with a workload of 3-6 hours per week with a mix of videos with quizzes to check progress, weekly tests with optional advanced questions and a final exam. Is being taught by Dave Feldman, Professor of Physics and Mathematics at College of the Atlantic. who is a former co-director of the Santa Fe Institute's Complex Systems Summer School in Beijing, China who introduces it in this video:
The only prerequisite for the course is familiarity with basic high school algebra and as the first two weeks of the course are devoted to Iterated Functions and Differential Equations respectively you get a refresher in the math you need.
So why should programmers be interested in this course?
The answer is because dynamical systems provide a way to study, and model, real world problems. The course introduction lists four aspects that will be covered:
- Dynamical systems undergo bifurcations, where a small change in a system parameter such as the temperature or the harvest rate in a fishery leads to a large and qualitative change in the system's behavior.
- Deterministic dynamical systems can behave randomly. This property, known as sensitive dependence or the butterfly effect, places strong limits on our ability to predict some phenomena.
- Disordered behavior can be stable. Non-periodic systems with the butterfly effect can have stable average properties. So the average or statistical properties of a system can be predictable, even if its details are not.
- Complex behavior can arise from simple rules. Simple dynamical systems do not necessarily lead to simple results. In particular, we will see that simple rules can produce patterns and structures of surprising complexity.
The inaugural course from the Complexity Explorer, which is currently finishing its second presentation with a third scheduled for Spring 2013, provides a fascinating insight into complex systems but also gives Dave Feldman a hard act to follow.
However his topics - phase space, bifurcations, chaos, the butterfly effect, strange attractors, and pattern formation - sounds equally fascinating and Introduction to Dynamical Systems and Chaos has already attracted over three and a half thousand students so we can expect interesting forum discussions. To make it even more interesting two of the I Programmer team are also taking the course - see you there.