This class is an introduction to geometry of differential manifolds. Topics covered include inverse function theorem, Morse-Sard theorem, embeddings and immersions, Whitney's 2n+1 embedding theorem, connections, metric, curvature.
Real analysis, and basic topology.
Instructor's notes in addition to excerpts and reference to
An Introduction to Differential Manifolds by Barden and Thomas; Notes on Differetial Geometry by Hicks; and Riemannian Geometry by Do Carmo.
The grade is based largely on class participation (the students are expected to attend all lectures). There may be one or two take home tests as well.