There will be weekly homework assignments which will be collected, graded and returned in a timely manner. Late homework will not be accepted.

Only a selected subset of each homework assignment will be collected and graded. The problems to be collected are indicated in each assignment, however the students are expected to do the homework assignment in its entirety. There will be a weekly problem session with the TA to go over the homework after it is handed in. Any of the problems on the homework (not just those handed in) may be discussed at the problem session.

Students are very strongly encouraged to work together on the homework, however each student must write up his/her assignment individually. The emphasis in the homework will be twofold. It will contribute significantly to the understanding and development of the new material which we will encounter each week. Secondly, it will be a forum for students to hone their skills at writing clear precise proofs.

Due to the fundamental importance of the homework, it will account for a significant portion (30%) of the course grade.

Homework assignment #1: due Monday, April 3

• Read sections 3.4, 4.1 and 4.2 in DoCarmo
• Exercises 3.4, pages 185-187: # 1, 3, 4, 7, 8, 10 (hand in # 3, 8, 10).

Homework assignment #2: due Monday, April 10

• Read sections 4.2 and 4.3 in DoCarmo
• Exercises 4.2, pages 227-231: # 1, 2, 3, 4, 9, 10, 14 (hand in # 3, 4, 10, 14).

Homework assignment #3: due Monday, April 17

• Read sections 4.2 and 4.3 in DoCarmo
• Exercises 4.3, pages 237: # 1, 2, 3, 4, 6, 9 (hand in # 2, 3, 6, 9).

Homework assignment #4: due Monday, April 24

• Read sections 5.10 pg. 425-431 and 4.4 in DoCarmo
• (1) Prove that the two descriptions of the real projective plane given in class; as the equivalence class of antipodal points on the 2-sphere and as the set of lines through the origin in 3-space, yield diffeomorphic surfaces
• Exercises 5.10, pages 443: # 1, 2, 3a (hand in # 1, 2).
• Exercises 4.4, pages 260-261: # 1, 2, 4 (hand in # 1, 2).

Homework assignment #5: due Monday, May 1

• Read sections 4.4 and 4.5 in DoCarmo
• Exercises 4.4, pages 260-261: # 3, 11, 12, 13 (hand in all).

Homework assignment #6: due Monday, May 15

• Read section 4.5 in DoCarmo
• Exercises 4.5, pages 282-283: # 3, 5, 6, 7, 8, 9 (hand in # 3, 5, 7, 9) (hand in all).