2015-2016 Academic Catalog

Dec 12, 2024

2015-2016 Academic Catalog [ARCHIVED CATALOG]

MATH 230 - Differential Geometry

Spaces such as curves and surfaces, along with their higher dimensional generalization, the manifold, are studied in this course. Local properties, defined initially in the vicinity of a point, are examined along with global ones, which concern the space as a whole. A main theme is the interplay between the notion of distance, and that of curvature. The latter comes in many forms, such as the Gauss curvature, mean curvature and principal curvatures, all related instances of a multifaceted concept. The techniques used in this study have their origin in Calculus, especially Multivariable Calculus. Differential Geometry is renowned for its applications in Physics, most notably General Relativity. In its modern form it has been utilized in many other disciplines, ranging from Architecture to Economics. Some of these will be touched upon if time permits.

Prerequisites: MATH 130 - Linear Algebra MATH 131 - Multivariate Calculus

Anticipated Terms Offered: Fall