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 R

**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

S^{1}=R/Z
with covering U={(0,2/3),(1/2,1),(3/4,5/4)}, and on

S^{2}={(x,y,z): x^{2}+y^{2}+z^{2}=1}
with U={z>0, z<0, x>0, x<0, y>0, y<0}.