Dynamical systems theory is the branch of mathematics that studies the properties of time-evolving phenomena. It finds a great variety of applications in areas spanning physics, engineering, ecology, finance, among many disciplines. Math 27 is an introductory course, studying aspects of dynamical systems that evolve in discrete time, as well as continuous-time systems described by ordinary differential equations. A primary objective will be to explore and understand the qualitative properties of dynamics, such as the existence of attractors, periodic orbits and chaos. We will do this by means of mathematical analysis, as well as simple numerical experiments.
A tentative weekly plan for the course can be found here.