We've all heard the buzzwords - chaos, fractals, networks, power laws. What do these terms mean in a rigorous, mathematical sense? This 1-2 credit seminar will explore formalisms associated with the study of complex systems. These include non-linear dynamics (and their associated phase space mappings, as well as chaos), graph theory (networks), and fractals (and their associated power laws). Through readings, in-class problem sets, and hands-on computer-based simulations, we will pursue a concrete understanding of these concepts as well as the ability to implement them as mathematical tools. A basic course in calculus and differential equations and some coding experience would be helpful but is not required.