Euclidean geometry, inverse and projective geometries, topology (Möbius strips, Klein bottle, projective space), and non-Euclidean geometries in two and three dimensions; contributions of Euclid, Gauss, Lobachevsky, Bolyai, Riemann, and Hilbert. Research project and paper required. The graduate student will be expected to describe how this relates to their research. Prerequisite: Mathematics 122, 112L, 122L, or consent of instructor.