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Math 8061: Schedule and Homework Assignments

The schedule below will be gradually filled out as the class progresses.
Day Topic Book pages Homework
8/31 Review of metric spacesLee, p. 541-543.
9/2 Topological manifolds Spivak, Chapter 1. Lee, p. 1-8. Homework 1, due 9/9.
9/7 Gluing constructions Spivak, p. 10-19.
9/9 Smooth structures Spivak, p. 27-31. Lee, p. 11-14.
9/14Smooth structures Spivak, Theorems 1.2 and 2.13. Lee, p. 14-16 and 51-53.
9/16 Smooth maps Spivak, p. 31-34. Lee, p. 31-34. (a fixed point!) Homework 2, due 9/23.
9/21 Derivatives in coordinates Spivak, p. 35, 40, 42-44. Lee, p. 163-164.
9/23 Immersions and embeddingsSpivak, p. 45-49. Homework 3, due 9/30.
9/28 Embedding manifolds in Rn Spivak, p. 50-53.
9/30 Sard's theorem Handout
10/5 Tangent vectorsLee, p. 61-65.
10/7 Pushforwards Lee, p. 66-72. Homework 4, due 10/14.
10/12Tangent bundle, vector fields Lee, p. 81-85. Spivak, p. 68-72.
10/14Fiber bundles, review Lee, p. 103-108.
10/19Integral curves and flows Spivak, ch. 5. Lee, ch. 17. Homework 5, due 10/28.
10/21Integral curves and flows Spivak, ch. 5. Lee, ch. 17.
10/26Local and global flows Spivak, p. 147-149. Lee, p. 446-449.
10/28Lie derivatives and brackets Spivak, p. 150-157.
11/2Lie brackets and coordinates Spivak, p. 157-159. Lee, p. 469-473. Homework 6, due 11/11.
11/8Frobenius theorem Spivak, p. 190-193. Lee, p. 500-504.
11/9Tangent covectors Lee, p. 125-134.
11/11Pullbacks and line integrals Lee, p. 136-142.
11/17Multilinear algebra Lee, p. 294-302. Spivak, p. 201-206. Homework 7, due 11/23
11/18Differential forms Lee, p. 302-310. Spivak, p. 207-212.
11/23Closed and exact forms Lee, p. 143-148; 310. Spivak, p. 218-225.
11/30Orientation forms Lee, p. 327-329; 334-340.
12/2 Integration on manifolds Lee, p. 350-356. Homework 8, due 12/13
12/7 Stokes' theorem Lee, p. 359-362.
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Last modified: Fri Aug 21 15:35:22 PDT 2009