- The final is here.

- The midterm will be in class on Thursday March 23.
- My office hours this term are Tuesdays 2:30--3:30pm and Wednesdays 3--4pm in Simons 510. I will also be available in the MLC (S-235) on Thursdays 11am--12pm.

The following is a tentative schedule for the course. As homework is assigned it will be posted here. You are encouraged to work with others, but please make sure to write up solutions in your own words.

For each homework you turn in, please write an estimate of how long it took you for each problem.

Each week 3 problems will be graded. The ones in parenthesis are ones that I think you will benefit from, but won't be graded. You should still do them!

Week | Date | Topic(s) Covered | Reading | Homework |
---|---|---|---|---|

1 | 1/24 | Properties of R^3 | Chapter 1-2 | 3, 5 |

1/26 | Smooth maps, curves | 1-3 | 6, 8, 10 | |

2 | 1/31 | Geometry of the vector product | 1-4 | 1, 6 |

2/2 | Local theory of curves (invariants) | 1-5 | 1, 2, 4, 6, 11 | |

3 | 2/7 | Regular surfaces | 2-2 | 1, 8, 11, 12, 13 |

2/9 | Snow Day! | 2-2 | Read the book! | |

4 | 2/14 | Regular surfaces continued | 2-2 | 16 |

2/16 | Differentiable functions on surfaces | 2-3 | 1,(2),3,13,(16) | |

5 | 2/21 | Tangent planes of a regular surface | 2-4 | 1, (2), (8), 21, (24), (25) |

2/23 | Vectors, the first fundamental form | 2-5 | 1 b & d, 3, (9, see pp 76-77) | |

6 | 2/28 | Area | 2-5 | 5, (12), (14) |

3/2 | Oriented surfaces | 2-6 | (2), 4, 5, 7 | |

7 | 3/7 | The Gauss map | 3-2 | (4), (8) |

3/9 | The Gauss map (continued) | 3-2 | . | |

8 | 3/14 | Spring Break! | . | . |

3/16 | Spring Break! | . | . | |

9 | 3/21 | Review | . | . |

3/23 | Midterm | . | . | |

10 | 3/28 | What is Curvature | 3.2 3.3 | 2, (4), 8, (16) 1 |

3/30 | Isometries | 4.2 | 1, 2, (3) | |

11 | 4/4 | Isometries | 4.2 | (7), (8), 9, 11 |

4/6 | Geodesics | 4.4 | 3, (4), 5a | |

12 | 4/11 | Connections | 4.3 | 3, 8, (9) |

4/13 | Parallel vector fields, geodesics | 4.4 | 4, 15 | |

13 | 4/18 | More Parallel transport | 4.4 | 6, 12, (13) |

4/20 | The Gauss Bonnet theorem | 4.5 | 1, (2), 4 | |

14 | 4/25 | Local Gauss Bonnet | 4.5 | Compute the Euler Characteristic of the projective plane. |

4/27 | Finish proof of Gauss Bonnet | 4.5 | 2, 3 | |

15 | 5/2 | So you want to know what is a category | None | |

5/4 | And some homotopy theory | None |