### 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 (odd years)

**Credits:** 3

**Sections: **Spring 2018 on Storrs Campus