Students should achieve mastery of the topics listed in the minimal learning outcomes section of the Math 565 Wiki page. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove theorems in analogy to proofs given by the instructor.

1. Differential topology
2. Riemannian metrics
3. Geodesics
4. Curvature
5. Integration on manifolds