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 CP¹ is diffeomorphic to S².
  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.