MATH 4550 - [Applicable Geometry]

(MQR-AS, SMR-AS)

Spring. Not offered: 2023-2024. Next offered: 2024-2025. 3 credits. Student option grading.

Prerequisite: MATH 2210, MATH 2230, MATH 2940, or equivalent. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course. Offered alternate years.

Staff.

Introduction to the theory of n-dimensional convex polytopes and polyhedra and some of its applications, with an in-depth treatment of the case of three dimensions. Discusses both combinatorial properties (such as face counts) as well as metric properties (such as rigidity). Covers theorems of Euler, Cauchy, and Steinitz, Voronoi diagrams and triangulations, convex hulls, cyclic polytopes, shellability and the upper-bound theorem. Relates these ideas to applications in tiling, linear inequalities and linear programming, structural rigidity, computational geometry, hyperplane arrangements, and zonotopes.