MATH 72.01 Calculus on Manifolds

Manifolds provide mathematicians and other scientists with a way of grappling with the concept of “space” (from a global viewpoint). The space occupied by an object. The space that we inhabit. The space of solutions to a system of equations. Or, perhaps, the space of configurations of a mechanical system. While manifolds are central to the study of geometry and topology, they also provide an appropriate framework in which to explore aspects of mathematical physics, dynamics, control theory, medical imaging, and robotics, to name just a few. This course will demonstrate how ideas from calculus can be generalized to manifolds, providing a new perspective and toolkit with which to explore problems where “space” plays a fundamental role.

Prerequisite

Math 13, Math 22 or Math 24, and Math 35, or Permission of the Instructor

Degree Requirement Attributes

Dist:QDS

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