Teaching: New Dynamical Systems Courses in Winter and Spring!

Autumn 2016

  • STAT 22000 Statistical Methods and Applications
    This course introduces statistical techniques and methods of data analysis, including the use of statistical software. Examples are drawn from the biological, physical, and social sciences. Students are required to apply the techniques discussed to data drawn from actual research. Topics include data description, graphical techniques, exploratory data analyses, random variation and sampling, basic probability, random variables and expected values, confidence intervals and significance tests for one- and two-sample problems for means and proportions, chi-square tests, linear regression, and, if time permits, analysis of variance.

Winter 2017

  • STAT 28200 Dynamical Systems with Applications
    This course is concerned with the analysis of nonlinear dynamical systems arising in the context of mathematical modeling. The focus is on qualitative analysis of solutions as trajectories in phase space, including the role of invariant manifolds as organizers of behavior. Local and global bifurcations, which occur as system parameters change, will be highlighted, along with other dimension reduction methods that arise when there is a natural time-scale separation. Concepts of bi-stability, spontaneous oscillations, and chaotic dynamics will be explored through investigation of conceptual mathematical models arising in the physical and biological sciences.

Spring 2017

  • STAT 33580 Topics in Dynamical Systems: Exploring Chaotic Dynamics
    This one-quarter dynamical systems topics course will focus on chaotic dynamical systems and their properties. The aim is for students to get a feel for properties associated with deterministic systems that exhibit chaotic behavior and to explore, through computational projects, how these are quantified. What is meant by “sensitive dependence on initial conditions” and how is this measured? How are correlations rapidly lost as nearby initial states evolve forward in time, and at what rate? How do we estimate an invariant measure on a chaotic attractor? What are typical “return times” in phase space, and how might we estimate their variance? What are generic properties of chaotic systems, and how can we understand these with simple paradigmatic constructions? What are generic mechanisms for creating chaotic dynamics by varying parameters of a dynamical system? This course investigates these questions through examples and takes an applied perspective.