MATH 3370: Differential Geometry
Description: Differential geometry is the study of geometric objects using techniques from multivariable calculus and differential equations. It has applications to areas such as general relativity and computer graphics. In this course, we will study curves and surfaces in three-dimensional space, considering both their local properties (those that depend on the object only near each point) and their global properties (those that depend on the object as a whole).
An important example of a local property is curvature, which describes how a curve or surface bends near each point. One goal of this class is to understand curvature both geometrically and computationally. To illustrate how a local property (curvature) across a surface tells us a gloabl property (the overall shape), knowing the curvature at each point of a surface can tell us whether the surface has a hole, like a doughnut, without having to look at the object extrinsically (from the outside). Being able to study geometry without working extrinsically is important in applications to physics: we want to understand the large-scale geometry of the universe but we can't look at it from outside!
Prerequisites: A grade of C or better in MATH 2142 or 2710, and either (i) MATH 2110 or 2130Q, and 2410Q, or (ii) MATH 2144Q.
Offered: Fall (even years)
Sections: Fall 2017 on Storrs Campus