Welcome to Chaos!
A dynamical system is a system whose state changes according to its past behavior. In this class, we will be studying discrete-time and continuous-time dynamical systems. We, of course, will be primarily interested in the systems exhibiting chaotic behavior. In the last two weeks of the course, we will turn our attention to time series analysis and use our non-linear techniques to measure the complexity (or entropy) of time series, the last part of which will take the form of a short final project.
Homework assignments will be a mixture of problem solving, formal proofs, and computer analysis. You are expected to be working on both weekly problem sets and lab assignments each week.
This course includes a programming component in Mathematica, a computer algebra system that can quickly produce beautiful visualizations and contains a wealth of pre-loaded time series data. The program is well-supported with online help guides and forums, allowing us to quickly perform experiments and analyze our results.