MATH 381

Differential Geometry

This course is an introduction to the application of calculus and linear algebra to the geometry of curves and surfaces. Topics include the geometry of curves, Frenet formulas, tangent planes, normal vectors and orientation, curvature, geodesics, metrics, and isometries. Additional topics may include the Gauss-Bonnet Theorem, minimal surfaces, calculus of variations, and hyperbolic geometry. After completion, students will have the background to begin studying further mathematical and theoretical physics topics such as Riemannian geometry, differential topology, general relativity, and gauge theory. Students will additionally develop their mathematical intuition and ability to use calculations and proofs to verify theorems and solve problems. Satisfies the proof-based requirement in the major contracts and the standard major.

Prerequisites: MATH 280 and 290 or equivalents. All prerequisite courses must have been completed with a grade of C- or higher.