MAA306 - Topics in Differential Geometry (2022-2023)

This course provides an overview of the classical differential geometry of curves and surfaces.
More precisely, we will study the local theory of (regular, parametrized) curves (curvature, torsion), topological and regular surfaces, and the local theory (first and second fundamental forms) and intrinsic geometry (Theorema Egregium and Gauss-Bonnet theorem) of the latter.

Weekly exercise sessions form an integral part of the course.
The instructor will provide lecture notes covering the material seen in class.

Prerequisites: some basic linear algebra, as seen is any undergraduate class (such as MAA101 and 201), and familiarity with multivariable calculus (differential of functions from ℝ^n to ℝ^2, as seen for example in MAA202). The most important notions will be briefly reviewed during the first lecture.