MTH 415 - Topics in Geometry

This course is an introduction to linear geometry in space and convex 3-polytopes. Topics 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. Also covered are classical results such as Cauchy’s rigidity theorem, Eberhard’s theorem, Euler’s theorem, Hilbert’s third problem, and Steinitz’ theorem. The theoretical discussions are supplemented with concrete examples and hands-on projects.

Prerequisites & Notes
MTH 237 or MTH 238.

(Cr: 3)