Math 551, Elementary Topology - Fall 2009


Nigel Boston

Contact Information

303 Van Vleck, 3619 Engineering Hall

Telephone: 263-4753, 265-3817.

E-mail: boston@math.wisc.edu

Homepage

Office Hours: 3:30-5 Tues, 303 Van Vleck; 11-12:30 Weds, 3619 Engineering Hall; or by appointment.

Text

James R. Munkres, Topology (2nd Edition).

Lecture Outline

  1. Sept 3: Overview of course. Section 1.
  2. Sept 8: Sections 2 and 3.
  3. Sept 10: Rest of section 3. Sections 4 and 5.
  4. Sept 15: Section 6.
  5. Sept 17: Section 7 plus other results on uncountability.
  6. Sept 22: Chapter 2, section 12 and part of section 13.
  7. Sept 24: The rest of section 13.
  8. Sept 29: Sections 14, 15, and 16.
  9. Oct 1: Go over 1st HW, some more of section 16.
  10. Oct 6: The rest of section 16 and most of section 17.
  11. Oct 8: The rest of section 17.
  12. Oct 13: Most of section 18.
  13. Oct 15: Go over 2nd HW, finish section 18.
  14. Oct 20: Section 19 and start section 20.
  15. Oct 22: Review for 1st Midterm.
  16. Oct 27: 1st Midterm.
  17. Oct 29: Went over 3rd HW plus more of section 20.
  18. Nov 3: Returned 1st Midterm, went over solutions, finished section 20, and started 21.
  19. Nov 5: Section 21.
  20. Nov 10: Section 23.
  21. Nov 12: Go over 4th HW.
  22. Nov 17: Section 24.
  23. Nov 19: Section 26.
  24. Nov 24: Section 27.
  25. Dec 1: Go over 5th HW and review for 2nd Midterm.
  26. Dec 3: 2nd Midterm.

Sections

Course Description

  1. Elementary Set Theory: Sets, Cartesian products, equivalence relations, countability, the real line
  2. Basic Topology: metric spaces, topological spaces, basis, continuity, connectedness, compactness
  3. Selected Topics (time permitting): Product and quotient topologies, manifolds, normality and extension theorems, the fundamental group, covering spaces

Homework Assignments

  1. HW1: Due Thursday, Sept 24. 1: 1,3. 2: 2. 3: 3,4,15. 4: 10. 5: 4(d)(e)(f). 6: 3. 7: 4.
  2. HW2: Due Thursday, Oct 8. 13: 1, 3, 4, 5. 16: 1, 3, 4, 6. 17: 2, 3.
  3. HW3: Due Thursday, Oct 22. 17: 6, 9, 12, 13. 18: 3, 5, 6, 11, 12. 19: 7.
  4. HW4: Due Thursday, Nov 5. 19: 8. 20: 2, 3, 4, 9, 10. 21: 2, 6.
  5. HW5: Due Thursday, Nov 19. 21: 7, 12. 23: 5, 9, 11. 24: 1, 2, 3.
  6. HW6: Due Tuesday, Dec 8. 24: 9, 11. 26: 3, 5, 6, 7. 27: 2, 4.

Midterms

Final Exam

Grading Policy

Midterms 20% each, HWs 20% (lowest dropped), final exam 40%.