- MWF 1-2 in room 2-139
- Professor Guillemin
- Email: vwg AT math DOT mit DOT edu
- Office hours: MWF 2-3 in office 2-170

- Ana Rita Pires (grader)
- Email: arita AT math DOT mit DOT edu
- Office Hours: M 4-5 in office 2-251

- November 5: Here is the material for the rest of the semester. Four lectures on manifolds: 1, 2, 3, 4; two lectures on vector fields: 1, 2; and six lectures on integration: 1, 2, 3, 4, 5, 6.
- October 27: The material for the next few weeks is BR: Birkhoff-Rota, chapter 6.
- October 27: Midterm was today.
- October 22: On Friday (Oct 24), there will be a review session for the midterm on Monday (Oct 27). The midterm will cover Munkres sections 1-16.
- September 29: The class website is up and with information up to date. Sorry for the one month delay!

- Homework 1, due September 26
- Homework 2, due October 3
- Homework 3, due October 17
- Homework 4, due October 31 (actually, due the Monday after that, November 3)
- Homework 5, due November 21
- Homework 6, due December 5

Lecture 1 | (September 3): | Munkres, section 3. | Recommended problems: | Munkres, section 3, exercises 4,7,9 | |

Lecture 2 | (September 5): | Munkres, section 4. | Recommended problems: | Munkres, section 4, exercises 1,2,3 | |

Lecture 3 | (September 8): | Munkres, section 5. | Recommended problems: | Munkres, section 5, exercises 2,3,4,6 | |

Lecture 4 | (September 10): | Munkres, section 6. | Recommended problems: | Munkres, section 6, exercises 1,2,5,6,7 | |

Lecture 5 | (September 12): | Munkres, section 7. | Recommended problems: | Munkres, section 7, exercises 1,2,3 | |

Lecture 6 | (September 15): | Munkres, section 8. | Recommended problems: | Munkres, section 8, exercises 1,2,3,4 | |

Lecture 7 | (September 17): | Munkres, section 9. | Recommended problems: | Munkres, section 9, exercises 5 and Spivak, exercise 2-37 | |

Lecture 8 | (September 19): | Munkres, section 10. | Recommended problems: | Munkres, section 10, exercises 1,2,3,4,5 | |

Lecture 9 | (September 24): | Munkres, section 11. | Recommended problems: | Munkres, section 11, exercises 1,2,3,4,6,8 | |

Lecture 10 | (September 26): | Munkres, section 11. | |||

Lecture 11 | (September 29): | Munkres, section 12. | Recommended problems: | Munkres, section 12, exercises 1,2 | |

Lecture 12 | (October 1): | Munkres, section 13. | Recommended problems: | Munkres, section 13, exercises 1,2,4,5 | |

Lecture 13 | (October 3): | Munkres, section 14. | Recommended problems: | Munkres, section 14, exercises 1,2,5,6,7,8 | |

Lecture 14 | (October 6): | Munkres, section 15. | Recommended problems: | Munkres, section 15, exercises 1,2,4,5 | |

Lecture 15 | (October 8): | Munkres, section 16. | Recommended problems: | Munkres, section 15, exercise 8 | |

Lecture 16 | (October 10): | Munkres, section 16. | Recommended problems: | Munkres, section 16, exercises 1,2,3,4 | |

Lecture 17 | (October 15): | Munkres, section 17. | Recommended problems: | Munkres, section 17, exercises 1,3,4,5,6 | |

Lecture 18 | (October 17): | Munkres, section 18. | Recommended problems: | Munkres, section 18, exercise 1 | |

Lecture 19 | (October 20): | Munkres, section 19. | Recommended problems: | Munkres, section 19, exercises 1,2,5ab | |

Lecture 20 | (October 22): | Munkres, section 20. | |||

Review Session | (October 24): | Review Session. | |||

Midterm | (October 26): | Midterm. | |||

Lecture 21 | (October 29): | BR, section 6.3. | Recommended problems: | BR, section 6.3, exercises 1,4,7,12 | |

Lecture 22 | (October 31): | BR, sections 6.4 and 6.5. | Recommended problems: | BR, section 6.5, exercise 4 (see example 2 on p. 158) | |

Lecture 23 | (November 3): | BR, sections 6.6 and 6.7. | Recommended problems: | BR, section 6.7, exercises 1,3,6,7 | |

Lecture 24 | (November 5): | BR, section 6.7. | Recommended problems: | BR, section 6.7, exercises 11,13,14 | |

Lecture 25 | (November 7): | BR, section 6.7. | Recommended problems: | BR, page 180 exercise 8 | |

Lecture 26 | (November 12): | Material posted online | Recommended problems: | Vector fields lecture 2, exercise 3 a),b),c) | |

Lecture 27 | (November 14): | Material posted online | Recommended problems: | Vector fields lecture 1, exercises 1,2,3 | |

Lecture 28 | (November 17): | Material posted online | Recommended problems: | Vector fields lecture 2, exercise 1 and Manifolds lecture 1, exercises 1,2 | |

Lecture 29 | (November 19): | Material posted online | Recommended problems: | Manifolds lecture 1, exercises 3,4,5,6 | |

Lecture 30 | (November 21): | Material posted online | Recommended problems: | Manifolds lecture 3, exercises 2,3,4,5, | |

Lecture 31 | (November 24): | Material posted online | Recommended problems: | Manifolds lecture 4, exercises 2,3,6,8 | |

Lecture 32 | (November 26): | Material posted online | Recommended problems: | Integration lecture 1, exercises 1,2,3,9,10 | |

Lecture 33 | (December 1): | Material posted online | Recommended problems: | Integration lecture 2, exercises 1,2,3,5,7* | |

Lecture 34 | (December 3): | Material posted online | Recommended problems: | Munkres, section 22, exercise 2 (read section 22!), Integration lecture 2, exercise 7* | |

Lecture 35 | (December 5): | Material posted online | Recommended problems: | Integration lecture 1, exercise 3, Integration lecture 2, exercise 8, Integration lecture 4, exercise 2 | |

Lecture 35 | (December 8): | Material posted online | Recommended problems: | Integration lecture 4, exercises 9,10,11 (see also #3 from Friday's homework assignment), Integration lecture 5, exercise 1 |

*Analysis on Manifolds*by James R. Munkres*Calculus on Manifolds*by Michael Spivak