Geometry of Manifolds OpenCourseWare: A Free Graduate Level Course by MIT on the Study of Manifold Geometry

Published Jan 23, 2009

RSS Feed

'Geometry of Manifolds,' a free OpenCourseWare from MIT, examines the geometry of symplectic manifolds and studies long digressions into complex geometry and the theory of 4-dimensional manifolds from a topological perspective. Students earning a master's degree in Engineering or Physics will find this graduate-level course fascinating and beneficial. A background in manifolds, vectors, cohomology and advanced mathematics is recommended for all students interested in this course.

Geometry of Manifolds: Course Specifics

Degree Level Free Audio Video Downloads
Graduate Yes No No Yes

Lectures/Notes Study Materials Tests/Quizzes
Yes Yes No

Geometry of Manifolds: Course Description

'Geometry of Manifolds' is a free course that is presented by Professor Denis Auroux from the MIT Department of Mathematics. The course places an emphasis on symplectic manifolds, which are simply smooth manifolds equipped with a non-degenerable 2-form. The prerequisite for this course is a introductory course on the geometry of manifolds or a solid understanding of manifolds, vector fields, differential forms, vector bundles and cohomology. This OpenCourseWare is predicated on a series of lectures that focus on the mathematics of symplectic manifolds. The primary topics discussed in this course come from many branches of mathematics, including a review of differential forms, Lie derivatives, and de Rham cohomology, smooth 4-manifolds, Seiberg-Witten equations and symplectic sum along codimension 2-symplectic submanifolds.

The materials for this course include lecture notes and assignments that are available in downloadable PDF files. Also included is a list of recommended readings. If you are interested in taking advantage of this free course, visit the geometry of manifolds course page.

Featured School Choices: