Geodetic surfaces are studied in geodetic science, the science of Earth measurements. They are determined directly or indirectly by measurements and models of the Earth's gravity, distribution of mass, magnetic properties, topography and other phenomena that cover large areas or even encompass the whole planet. Data for analyzing the surface is obtained using diverse instruments, from Global Positioning Systems (GPS), to radar measurements taken from the space shuttle, all the way down to surveying done on the ground. These point-set measurements are then used by computer algorithms and mesh-building graphics software to reconstruct the surfaces. This is a beautiful subject with a tremendous amount of active research, relating powerful ideas from mathematics, elegant tools from computer science, and concrete data from geodetic science. This course is designed to introduce fundamental ideas of this subject, such as curvature, polyhedral geometry, Voronoi diagrams, Delaunay triangulations, and combinatorial topology, possibly touching on advanced topics such as noise handling, Morse theory, and smoothing. We will work with theoretical tools as well as actual data sets using the Cocone software. This course is intended for students interested in mathematics, physics, engineering, and computer science. Format: lecture. Evaluation will be based primarily on problem sets and exams. Prerequisites: Mathematics 211, or Computer Science 256. No enrollment limit (expected: 15).