Computational Topology

We will study various algorithmic problems that arise in the study of topological phenomena, such as winding number, turning number, knot polynomials, topology of covering spaces (especially Riemann surfaces), and discrete Morse theory. The mathematical topics will be briefly introduced before we move to computations, but some a priori mathematical sophistication will make the course more valuable to the student. Prerequisite: CSCI 0160 , 0180 , or 0190 .