MATH 4550 - Applicable Geometry

(MQR-AS, SMR-AS)

Spring. Offered alternate years. Next offered: 2022-2023. 4 credits. Student option grading.

Prerequisite: good introduction to linear algebra (e.g., MATH 2210, MATH 2230, MATH 2310, or MATH 2940) or permission of instructor. Students will be expected to be comfortable with proofs. Does not assume students know the meaning of all words in the following description.

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.