Introduction to differential manifolds and smooth maps between them. Topics covered include tangent bundles, differential map,
regular values, Morse functions, transversality, degree theory,
tensors and forms,
integration on manifolds, Stokes theorem and de Rham cohomology.
A basic course in topology or real analysis.
Instructor's notes, and Differential Topology by Guillemin and Pollack.
The grade is based on class participation (the students are expected to attend all lectures), and homework assignments.