MATH 744 - Differential Topology

(3 units)

Introduction to differential topology, including smooth manifolds and smooth maps, tangent and cotangent bundle, differential forms, and integration on manifolds, Whitney’s Embedding Theorem, Sard’s Theorem, and Stokes’ Theorem.

Prerequisite(s): MATH 311. Corequisite: MATH 731.

Grading Basis: Graded
Units of Lecture: 3
Offered: Every Fall - Odd Years

Student Learning Outcomes
Upon completion of this course, students will be able to:
1. demonstrate an understanding of smooth manifolds and differentiable maps through proofs and examples.
2. appropriately apply foundational theorems in differential topology, including Sard’s Theorem, Whitney’s Embedding Theorem, and Stokes’ Theorem.
3. appropriately apply the concepts of the tangent bundle, the cotangent bundle, and the derived exterior algebra bundles on manifolds, and master integration and manipulation of differential forms.

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