An understanding of linear algebra, including linear independence, bases, dimension, and linear transformations is a required prerequisite. We will learn some topics from advanced linear algebra along the way, including tensor products, direct sums and quotients. A one semester course in undergraduate abstract algebra would be preferred as background. We will cover topics on ideals and factor rings at the beginning of the program, as needed. This project will involve studying both continuous and discrete dynamical systems, that is, systems modeled by either difference equations or differential equations.
Difference equations are the discrete analog of differential equations.
We will spend several weeks learning the theoretical background by reading through a recently written textbook together. A good background in basic differential equations and linear algebra is needed. A semester course in analysis will aid in understanding and general sophistication.