Differential Geometry OpenCourseWare: MIT's Free Bachelor Level Geometry Course on Differential Geometry

Published Jan 27, 2009

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Geometry has its ups and downs, but there's nothing to lose by taking the Massachusetts Institute of Technology's free bachelor's-level online course 'Differential Geometry.' This course, which has recommended prerequisites of Analysis I and Linear Algebra, introduces students to the concepts of differential geometry as it relates to the curvature and surfaces found in Euclidean space of three dimensions. The equivalent 'for credit' version of this self-study OpenCourseWare satisfies requirements for a Bachelor of Science in Mathematics.

Differential Geometry: Course Specifics

Degree Level Free Audio Video Downloads
Undergraduate Yes No No Yes

Lectures/Notes Study Materials Tests/Quizzes
Yes Yes No

Differential Geometry: Course Description

Students learning from this course can use readings from the textbook Differential Geometry: Curves--Surfaces--Manifolds by Wolfgang Kuhnel to examine how differential and integral calculus can be applied to problems in geometry. Lecture notes for 'Differential Geometry' utilize the formal mathematical model of defining elements, stating theorems and presenting proofs. With his lecture series, Professor Paul Seidel led Mathematics students through the first and second fundamental forms, mean and Gaussian curvature, geodesic equations, Gauss-Bonet theorem, the Hopf Umlaufsatz theorem and other related topics. OpenCourseWare students may practice their understanding of geometrical curvature by solving downloadable problem sets. A background in mathematical analysis is recommended for this course, and an appropriate OpenCourseWare is available through MIT.

Lecture notes, assignments and a list of readings are available for this course. For downloads and more information, visit the differential geometry course page.

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