
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 spaces  Lee, p. 541543. 
 9/2  Topological manifolds  Spivak, Chapter 1. Lee,
p. 18.  Homework 1, due 9/9. 
9/7  Gluing constructions  Spivak, p. 1019. 
 9/9  Smooth structures  Spivak, p. 2731. Lee, p. 1114. 
 9/14  Smooth structures  Spivak, Theorems 1.2 and 2.13. Lee,
p. 1416 and 5153. 
 9/16  Smooth maps  Spivak, p. 3134. Lee, p. 3134. (a fixed
point!)  Homework 2, due 9/23.
 9/21  Derivatives in coordinates  Spivak, p. 35, 40, 4244. Lee,
p. 163164. 
 9/23  Immersions and embeddings  Spivak, p. 4549.  Homework 3, due 9/30.
 9/28  Embedding manifolds in R^{n}  Spivak,
p. 5053. 
 9/30  Sard's theorem  Handout 
 10/5  Tangent vectors  Lee, p. 6165. 
 10/7  Pushforwards  Lee,
p. 6672.  Homework 4, due 10/14.
 10/12  Tangent bundle, vector fields  Lee, p. 8185. Spivak,
p. 6872. 
 10/14  Fiber bundles, review  Lee, p. 103108. 
 10/19  Integral curves and flows  Spivak, ch. 5. Lee,
ch. 17.  Homework 5, due 10/28.
 10/21  Integral curves and flows  Spivak, ch. 5. Lee,
ch. 17. 
 10/26  Local and global flows  Spivak, p. 147149. Lee,
p. 446449. 
 10/28  Lie derivatives and brackets  Spivak, p. 150157. 
 11/2  Lie brackets and
coordinates  Spivak, p. 157159. Lee, p. 469473.  Homework 6, due 11/11.
 11/8  Frobenius theorem  Spivak, p. 190193. Lee, p. 500504. 
 11/9  Tangent covectors  Lee, p. 125134. 
 11/11  Pullbacks and line integrals  Lee, p. 136142. 
 11/17  Multilinear algebra  Lee,
p. 294302. Spivak, p. 201206.  Homework 7, due 11/23
 11/18  Differential forms  Lee, p. 302310. Spivak, p. 207212. 
 11/23  Closed and exact forms  Lee, p. 143148; 310. Spivak,
p. 218225. 
 11/30  Orientation forms  Lee, p. 327329; 334340. 
 12/2  Integration on manifolds  Lee,
p. 350356.  Homework 8, due 12/13
 12/7  Stokes' theorem  Lee, p. 359362. 

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Last modified: Fri Aug 21 15:35:22 PDT 2009
