# Math 637

## Fall 2021

- Syllabus.
- Homework 1 (due 10/1):

Chapter 1: problem 1-7.

Solutions: pdf, tex
(Future homeworks will be longer.)
- Reading 1 (due 10/3):

Chapters 1–3: see how far you can get.

(Future readings will be shorter.)
- Homework 2 (due 10/8):

Chapter 2: problems 2-9 and 2-10, and use the formula from 2-3(c) to prove that **CP**^{1} is diffeomorphic to S^{2}.

Chapter 3: problem 3-1, and choose one “exercise” from the body of the chapter that interests you.
- Reading 2 (due 10/10):

Chapter 4. Tell me if you want me to cover the proof of the classical inverse function theorem (Theorem C.34).

Skim Chapter 5 if you want.

- Homework 3 (due 10/15): Chapter 4: problems 4-2, 4-6, 4-8, 4-13.
- Reading 3 (due 10/17): Chapter 7.
- Homework 4 (due 10/22): Chapter 7: problems 7-2, 7-3, 7-4, 7-20, 7-21.
- Reading 4 (due 10/24): Chapter 8, and start Chapter 9.
- Homework 5 (due 10/29): Chapter 8: problems 8-2, 8-13, 8-16.
- Midterm, solutions, tex.
- Homework 6 (due 11/5): Chapter 8: problem 8-24.
- Reading 5 (due 11/7): Finish Chapter 9 if possible.
- Homework 7 (due 11/12): Chapter 9: problems 9-7 and 9-22.
- Homework 8 (due 11/19): Chapter 9: problem 9-5.
- Reading 6 (due 11/21): Chapter 20.
- Reading 7 (due 11/28): Chapter 19.
- Homework 9 (due 12/3):

Chapter 20: problems 20-5, 20-7, 20-11.

Chapter 19: problem 19-11.
- Final exam, solutions, tex.