Time: Mondays, Wednesdays and Fridays, at 12:00-12:50pm
Location: East Hall B844
Instructor: Linh Truong (tlinh@umich.edu, office: East Hall 4842)
Office hours: 11am-12pm Tuesdays, 1-2pm Thursdays, and 11am-12pm Fridays
Grader: TBA
Course Information: Syllabus
Textbook: Topology, 2nd edition, by James Munkres
Course Overview: This course is an introduction to point-set topology and algebraic topology.
In the first half of this course, topics will include metric spaces, topological spaces, continuous functions and homeomorphisms, separation axioms, quotient and product topology, compactness, and connectedness. We will then cover elements of algebraic topology including fundamental groups and covering spaces.
| Dates | Topics | |
|---|---|---|
| Week 1: Jan 7 - Jan 9 | Introduction, Topological Spaces (Ch 2, Sec. 12) | |
| Week 2: Jan 12 - Jan 16 | Topological Spaces, Bases, Examples (Ch. 2, Sec. 13-16) | |
| Week 3: Jan 21 - Jan 23 | Limit Points and Continuous Functions (Ch. 2, Sec. 17-18) | |
| Week 4: Jan 26 - Jan 30 | Product, Metric, and Quotient Topologies (Ch. 2, Sec. 19-22) | |
| Week 5: Feb 2 - Feb 6 | Connectedness (Ch. 3) | |
| Week 6: Feb 9 - Feb 13 | Connectedness, Compactness (Ch. 3) | |
| Week 7: Feb 16 - Feb 20 | Compactness (Ch 3, Sections 27-29) | |
| Week 8: Feb 23 - Feb 27 |
Review
Midterm: Friday, Feb 27 |
|
| Feb 28 - Mar 8 | Spring break | |
| Week 9: Mar 9 - Mar 13 | Countability and Separation Axioms (Ch. 4, Sec 30-32) | |
| Week 10: Mar 16 - Mar 20 | Fundamental Group (Ch. 9, Sec. 51-52) | |
| Week 11: Mar 23 - Mar 27 | Covering Spaces (Ch. 9, Sec. 53-54) | |
| Week 12: Mar 30 - Apr 3 | Fundamental Group II (Ch. 9, Sec. 55-57) | |
| Week 13: Apr 6 - Apr 10 | Fundamental Group III (Ch. 9, Sec. 58-60) | |
| Week 14: Apr 13 - Apr 17 | Seifert-Van Kampen Theorem (Ch. 11) | |
| Week 15: Apr 20 | Review | |
|
Monday, April 27
1:30pm - 3:30pm |
Final Exam |