MATH 393 - Topics in Geometry and Topology

Credits: 3

Prerequisite: MATH 342 or 343. Topics vary but can include knot theory, topology and geometry of surfaces, differential geometry, Riemann surfaces, 3-manifolds, tilings, geometric probability, geometry of spacetime, finite geometry, computational geometry, differential topology, and projective geometry. May be repeated for degree credit if the topic is different.

Winter 2022, Math 393A-01: Topics in Geometry and Topology: Differential Topology (3).
Prerequisite: Math 342 or 343. This course builds on material from multivariable calculus, linear algebra and geometry. We cover a range of topics: an introduction to manifolds with boundary, derivatives as linear transformations, tangent spaces, inverse and implicit function theorems, transversality, and intersections of manifolds. Then integration on manifolds, differential forms, and the generalized Stokes’s Theorem. Denne.

Winter 2021, MATH 393A-01: Topics in Geometry and Topology: Experimenting with Geometry (3). Prerequisite: MATH 342 or 343. This course will be run in an experimental format modeled on the notion of a “Geometry Lab.” Students will study unsolved problems in geometry, learning whatever background material is relevant for understanding and approaching the selected problems. Topics are likely to include algebraic geometry, hyperbolic geometry, and projective geometry. Abrams.