Warning: Reading assignments are tentative until 10 pm the preceding evening.

>Date | Topic | Reading | Homework | |
---|---|---|---|---|

Monday, August 23 | A1: Topological Manifolds Class notes |
Pages 1-8 and 596-602 | ||

Wednesday, August 25 | A2: Smooth manifolds
Class notes |
Pages 10-24 (omit ``fundamental groups") 603-607 | ||

Friday, August 27 | A3: Topology of manifolds and smooth maps Class notes |
Pages 8-9, 25-40, and 607-616. | ||

Monday, August 30 | A4: Partitions of Unity
Class notes |
Pages 40-52 | ||

Wednesday, September 1 | B1: Tangent vectors
Class notes |
Pages 53-60 | HW #1 | |

Friday, September 3 | B2: Tangent bundles
Class notes |
Pages 61-72 | ||

Monday, September 6
Labor Day -- No class |
||||

Wednesday, September 8 | C1: The rank theorem
Class notes |
Pages 73-82 | HW #2 | |

Friday, September 10 | C2: Maps of constant rank
Class notes |
Pages 82-97 [Omit Smooth Covering Maps] |
||

Monday, September 13 | C3: Embedded submanifolds
Class notes |
Pages 98-108 | ||

Wednesday, September 15 | C4: Immersed submanifolds
Class notes |
Pages 104-115 | HW #3 | |

Friday, September 17 | C5: Tangent spaces to submanifolds
Class notes |
Pages 116-124 | ||

Monday, September 20 | D1: Lie groups
Class notes |
Pages 150-160 [Omit Universal Covering groups] |
||

Wednesday, September 22 | D2: Group actions
Class notes |
Pges 161-173 | ||

Friday, September 24 | E1: Intro to Vector Fields
Class notes |
Pages 174-181 | ||

Monday, September 27 | E2: Pushforwards and Lie brackets
Class notes |
Pages 182-189 | ||

Wednesday, September 29 | E3: Lie Algebras
Class notes |
Pages 195-204 | ||

Friday, October 1 | E4: Integral curves
Class notes |
Pages 205-210 | ||

Monday, October 4 | E5: Flows
Class notes |
Read 210-217 | ||

Wednesday, October 6 | E6: Flowouts 217-222
Class notes |
Read 217-222 | ||

Friday, October 8 | E7: Lie derivatives & Vector Bundles
Class notes |
Read 227-231 | ||

Monday, October 11 | F1: Sections of Vector Bundles
Class notes |
Read 249-261 | ||

Wednesday, October 13 | Midterm today! No class | Here are the Solutions | ||

Friday, October 15 | F2: Bundle homomorphisms
Class notes |
Read 261- 264 | ||

Monday, October 18 | F3: Subbundles and fiber bundles
Class notes |
Read 264-268 | ||

Wednesday, October 20 | F4: Dual bundles
Class notes |
Read 272-280 | ||

Friday, October 22 | F5: The differential of a function
Class notes |
Read 280-287 | ||

Monday, October 25 | F6: Line integrals
Class notes |
Read 287-294 | ||

Wednesday, October 27 | F7:The Poincare Lemma
Class notes |
Pages 294-298 | ||

Friday, October 29 | G1: Multilinear algebra
Class notes |
Pages 304-313 | ||

Monday, November 1 | G2: Abstract Tensor product
Class notes |
Page 313-320 | ||

Wednesday, November 3 | G3: Pullback and Lie derivative of Tensor fields
Class notes |
Pages 320-323 | ||

Friday, November 5 | G4: Wedge product
Class notes |
Pages 349-359 | ||

Monday, November 8 | G5: Diffrential forms
Class notes |
Pages 360-368 | ||

Wednesday, November 10 | G6: Exterior differentiation
Class notes |
Pages 369- 373 | ||

Friday, November 12 Drop deadline |
G7: Additional Formulae
Class notes |
Pages 377-383 | ||

Monday, November 15 | G8: Orientations
Class notes |
Pages 383-388 | ||

Wednesday, November 17 | H1 : Integration on Euclidean space
Class notes |
Pages 400-407 | ||

Friday, November 19 | H2: Integration on Manifolds
Class notes |
Pages 407-411 | ||

Happy Thanksgiving! | ||||

Monday, November 29 | H3: Stokes Theorem
Class notes |
Pages 411-415 | ||

Wednesday, December 1 | H4: De Rham Cohomology
Class notes |
Pages415-418 and 440- 443 | ||

Friday, December 3 | H5: Homotopy Invariance
Class notes |
Pages 443-448 | ||

Monday, December 6 | H6: Mayer-Vietoris
Class notes |
Pages 448-452 | ||

Wednesday, December 8 | H7: Proof of Mayer-Vietoris
Class notes |
Pages 460-464 | ||

Monday, December 13 | Final 1:30-4:30 |