The due dates were originally written assuming we were collecting homework on  Fridays.  Starting November 5, however, homework is due on Mondays.

Homework # 1: (due September 7)
    Show that each of the following sets (given a reasonable topology) is a manifold.  What is the dimension of each one?  Which are orientable?

1)    The set of all lines through the origin in R^4.  (This manifold is called RP^3).
2)    The set of all lines through the origin in R^5 (called RP^4)
3)    The set of all planes through the origin in R^4.
4)    The set of all lines (not necessarily through the origin) in R^3.
4)    The set of all complex triples (z1, z2, z3) such that z1^2 + z2^2 +z3^2 = 1.
5)    The set of all invertible 2x2 real matrices.

Exercises 5.1, 7.1, 7.2 and 7.6 (cases 7.1 and 7.2 only) from Chapter 1.

Homework # 2: (due September 14)

Chapter 1: 8.1, 8.3, 8.8, 8.9 (use Euler!)
Chapter 2: 3.1, 3.3,  4.5,  4.6, 4.8, 4.9, 5.1

Homework # 3: (due September 21)
 Chapter 2: 7.1, 7.2,  7.4, 7.5, 8.1
Chapter 3: 3.1, 3.3, 3.4

Homework # 4: (due September 28)
 Chapter 3: 4.1, 4.3, 4.7, 4.8, 5.3, 6.1,

Homework # 5: (due October 5)
  Chapter 4: 3.1, 3.2, 3.3, 4.1, 5.1, 5.2, 5.3

Suggested homework to help study for midterm: (do not turn in)
   Chapter 4: 5.4, 5.5, 5.6, 6.1

Homework # 6: (due October 19)
   Chapter 5: 2.4, 5.1, 6.1, 6.2, 6.4, 6.5

Homework # 7: (due October 26)
   Chapter 5: 7.1, 7.2, 8.1, 8.2, 8.3, 9.3, 10.1

Homework #8: (due November 5)
    Chapter 7: 2.1, 3.3, 5.1, 5.2, 5.4, 5.5 (p 172, not 173)

Homework #9: (due November 12)
    Chapter 7: 6.2
    Chapter 8: 2.1, 2.2, 2.3, 2.5, 2.8, 2.9

Homework #10: (due November 19)
 Chapter 8: 3.1, 3.2, 3.7, 4.1, 4.2, 5.1

Homework #11: (due December 3)
  TBA