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.

Instructor

Erchenko

Prerequisite

MATH 71, or permission of the instructor. Depending on the specific topics covered, MATH 31 may not be an acceptable prerequisite; however, in consultation with the instructor, MATH 31 together with some outside reading should be adequate preparation for the course.

Degree Requirement Attributes

Dist:QDS

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Offered

• Fall