Math 465: Intro to Differential Geometry
Contents
Catalog Information
Title
Differential Geometry.
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Prerequisite
Math 214; 315 or equivalent. Recommended: Math 316 or equivalent.
Description
Geometry of smooth curves and surfaces. Topics include the first and second fundamental forms, the Gauss map, orientability of surfaces, Gaussian and mean curvature, geodesics, minimal surfaces and the Gauss-Bonnet Theorem.
Desired Learning Outcomes
The main purpose of this course is to provide students with an understanding of the geometry of curves and surfaces, with the focus being on the theoretical and logical foundations of differential geometry.
Prerequisites
The prerequisite of Math 214 is to ensure that students have some understanding of partial derivatives and differentiation for functions of more than one variable. 315 is required so students have a rigorous understanding of the real number system and of real-valued functions. Math 316 is recommended so students have a rigorous understanding of functions with more than one variable.
Minimal learning outcomes
Outlined below are topics that all successful Math 465 students should understand well. As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems.