Course diary:

Math 518, Fall 2021

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

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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