Theorems which the student is expected to state and apply: the inverse function
theorem, the existence of partitions of unity, the existence and uniqueness of flows of vector fields and
their properties, the general theorem of Stokes. Theorems which the student is expected to be
able to prove: the theorem on rank, the existence of a Riemann metric on a manifold, the theorem on
embedding of a closed manifold into
.
The material on differential topology is generally covered in Math 124, which assumes as undergraduate
preparation a course on analysis on manifolds at the level of Spivak's ``Calculus on manifolds''. Students
who do not have this background should normally enroll during the first year in Math 73, which furnishes the
necessary prerequisites for Math 124.

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2009-10-15