Assignment 1, due August 30:
Do problems 2 and 3 on page 50 of the text. (See page 22 for the definition of `diffeomorphism'.)
Let M denote the locus of points in R3 satisfying the equation x3+y3+z3=1. Show that M is a manifold. You may use the implicit function theorem.

Assignment 2, due September 6:
Do problems 5, 7, and 10 from page 50 of the text.

Assignment 3, due September 20:
Do problems 13, 14, and 17 from page 50 of the text, as well as the Lie bracket problem.

Assignment 4, due September 27: Do the exterior algebra problems.

Assignment 5, due October 4: Do problems 10 and 13 from pages 78-79 of the text, and exercise 2 from page 157.

Assignment 6, due October 25: Do problems 11, 12, 15, 16abc, 18, 19 on pages 158-160.

Assignment 7, due November 8: Do problems 3, 4, 6, and 11 on page 216.

Assignment 8, due November 29: Do problems 17 and 21 on page 216.
Compute the Cech cohomology of the constant sheaf R on
S1=R/Z with covering U={(0,2/3),(1/2,1),(3/4,5/4)}, and on
S2={(x,y,z): x2+y2+z2=1} with U={z>0, z<0, x>0, x<0, y>0, y<0}.