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Organization, Regulations, and Courses 2022-23

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.



Degree Requirement Attributes


The Timetable of Class Meetings contains the most up-to-date information about a course. It includes not only the meeting time and instructor, but also its official distributive and/or world culture designation. This information supersedes any information you may see elsewhere, to include what may appear in this ORC/Catalog or on a department/program website. Note that course attributes may change term to term therefore those in effect are those (only) during the term in which you enroll in the course.


  • Fall