MAT5343

MAT 5343 Differential Geometry

Sample textbook: Victor V. Prasolov: Differential Geometry, Springer (2022)

Catalog entry:

Prerequisite: A course in Linear Algebra and Calculus sequence

Contents: This course offers an in-depth study of differential geometry, focusing on the geometric properties of differentiable manifolds. Topics include smooth manifolds, vector fields, differential forms, tensors, connections, Riemannian metrics, and curvature. Emphasis will be placed on understanding the interplay between geometry and topology, as well as applications in physics, particularly in general relativity.

Topics List

Week	Topic	Chapter from textbook	SLO
1	Curves in space and on the plane	1	Understand how to compute the curvature of a space/planar curve
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