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: Tuesdays 1-2:30pm, Wednesdays 4-5:30pm
Grader: James Walrad (walrad@umich.edu)
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 5 - Jan 7 | Introduction, Topological Spaces (Ch 2, Sec. 12) | |
| Week 2: Jan 10 - Jan 14 | Topological Spaces, Bases, Examples (Ch. 2, Sec. 13-16) | |
| Week 3: Jan 19 - Jan 21 | Limit Points and Continuous Functions (Ch. 2, Sec. 17-18) | |
| Week 4: Jan 24 - Jan 28 | Product, Metric, and Quotient Topologies (Ch. 2, Sec. 19-22) | |
| Week 5: Jan 31 - Feb 4 | Connectedness (Ch. 3) | |
| Week 6: Feb 7 - Feb 11 | Connectedness, Compactness (Ch. 3) | |
| Week 7: Feb 14 - Feb 18 | Compactness (Ch 3, Sections 27-29) | |
| Week 8: Feb 21 - Feb 25 |
Review
Midterm: Friday, Feb 25 |
|
| Feb 28 - Mar 4 | Spring break | |
| Week 9: Mar 7 - Mar 11 | Countability and Separation Axioms (Ch. 4, Sec 30-32) | |
| Week 10: Mar 14 - Mar 18 | Fundamental Group (Ch. 9, Sec. 51-52) | |
| Week 11: Mar 21 - Mar 25 | Covering Spaces (Ch. 9, Sec. 53-54) | |
| Week 12: Mar 28 - Apr 1 | Fundamental Group II (Ch. 9, Sec. 55-57) | |
| Week 13: Apr 4 - Apr 8 | Fundamental Group III (Ch. 9, Sec. 58-60) | |
| Week 14: Apr 11 - Apr 15 | Seifert-Van Kampen Theorem (Ch. 11) | |
| Week 15: Apr 18 | Review | |
|
Tuesday, April 26
10:30am - 12:30pm |
Final Exam |