Overview
Description
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.
Requirements
Prerequisites
MATH 311
Corequisites
MATH 731
Original catalog text
Prerequisites
Prerequisite(s): MATH 311.
Corequisites
Corequisite: MATH 731.
Units
Lecture3
Catalog Details
Offering
Offered: Every Fall - Odd Years
Terms
fall
Attributes
Standard
Learning Outcomes
- demonstrate an understanding of smooth manifolds and differentiable maps through proofs and examples.
- appropriately apply foundational theorems in differential topology, including Sard’s Theorem, Whitney’s Embedding Theorem, and Stokes’ Theorem.
- 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.