# Math 637

## Fall 2021

• Syllabus.
• Homework 1 (due 10/1):
Chapter 1: problem 1-7.
Solutions: pdf, tex (Future homeworks will be longer.)
Chapters 1–3: see how far you can get.
• Homework 2 (due 10/8):
Chapter 2: problems 2-9 and 2-10, and use the formula from 2-3(c) to prove that CP1 is diffeomorphic to S2.
Chapter 3: problem 3-1, and choose one “exercise” from the body of the chapter that interests you.
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.