MTH 415 - Topics in Geometry

This course is an introduction to linear geometry in space and convex 3-polytopes. Topics to be discussed include coordinates in space, linear/affine/convex combinations, linear systems of inequalities, faces and f-vectors of polytopes, regular/archimedian solids, 3-dimensional symmetry groups, and planar graphs. Covers classical results such as Cauchy’s rigidity theorem, Eberhard’s theorem, Euler’s theorem, Hilbert’s third problem, and Steinitz’ theorem. The theoretical discussions will be supplemented with plenty of concrete examples and hands-on projects.

Prerequisites & Notes
MTH 237 or MTH 238.

(Cr: 3)