### 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

ACTIVITIES | PERCENTAGES |
---|---|

Midterm exam | 30% |

Homework | 30% |

Final exam | 40% |