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Description

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.

Topics

• Local and global geometry of plane curves
• Local geometry of hypersurfaces
• Global geometry of hypersurfaces
• Geometry of lengths and distances

Prerequisites

Analysis I (18.100) plus Linear Algebra (18.06 or 18.700) or Algebra I (18.701)

Textbook

Kuhnel, Wolfgang. Differential Geometry: Curves – Surfaces – Manifolds. Student mathematical library, vol. 16. Providence, RI: American Mathematical Society, 2002. ISBN: 9780821826560.

Other Useful Sources

Spivak, Michael. A Comprehensive Introduction to Differential Geometry. Vol. 2. Boston, MA: Publish or Perish, 1999. ISBN: 9780914098713.

Spivak, Michael. A Comprehensive Introduction to Differential Geometry. Vol. 4. Boston, MA: Publish or Perish, 1999.

do Carmo, Manfredo Perdigañ. Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall, 1976. ISBN: 9780132125895.

Pressley, Andrew. Elementary Differential Geometry. Springer undergraduate mathematics series. London, UK: Springer, 2002. ISBN: 9781852331528.

Gray, Alfred, Simon Salamon, and Elsa Abbena. Modern Differential Geometry of Curves and Surfaces with Mathematica. Boca Raton, FL: Chapman & Hall/CRC, 2006. ISBN: 9781584884484.

The course will follow the first half of Kuhnel, but rather loosely. For that reason, attendance, and taking notes in classes, is strongly encouraged.

Grading