Introduction to Manifolds

Inverse Function Theorem, manifolds and submanifolds, tangent and cotangent bundles, transversality, flows and vector fields, Frobenius Theorem, vector bundles, tensors and differential forms, Sard’s Theorem, introduction to Lie groups. Pre-reqs: MATH 1060 , MATH 1140 and preferably MATH 1410 and undergraduates require permission from the instructor.