Math 761: Differentiable Manifolds

This course is the first introduction to differentiable manifolds. We will cover the basics: differentiable manifolds, vector bundles, implicit function theorem, submersions and immersions, vector fields and flows, foliations and Frobenius theorem, differential forms and exterior calculus, integration and Stokes' theorem, De Rham theory, etc. If time allows it, we will branch into Riemannian manifolds.