This course is an introduction to differential geometry. Students should have a good knowledge of multivariable calculus and linear algebra, as well as tolerance for a definition–theorem–proof style of exposition. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.
- Local and global geometry of plane curves
- Local geometry of hypersurfaces
- Global geometry of hypersurfaces
- Geometry of lengths and distances
Analysis I (18.100) plus Linear Algebra (18.06 or 18.700) or Algebra I (18.701)
Other Useful Sources
Spivak, Michael. A Comprehensive Introduction to Differential Geometry. Vol. 4. Boston, MA: Publish or Perish, 1999.
The course will follow the first half of Kuhnel, but rather loosely. For that reason, attendance, and taking notes in classes, is strongly encouraged.