This is an introduction to differential and Riemannian manifolds. Topics covered include the inverse function theorem, differential forms, Poincare Lemma, integration, Stokes theorem, deRham's Theorem.
Real analysis, and basic topology.
An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised, by William M. Boothby, Academic Press, 2002.
The grade is based on class participation, homework assignments, and possibly one or two take home exams.