Math 4530, Introduction to Topology
A few key points from the syllabus:
- Prerequisites: linear algebra + at least one 3000-level course. You should be comfortable and have practice writing proofs. Some analysis course is a bonus!
- Instructor office hours: Friday 2:30-4:30. Malott 511.
- TA office hours: Monday 2-4
- Lectures: Tu/Th 11:40am - 12:55pm in 406 Malott. You are required to attend, arrive on time, and participate!
- Textbook: no book is strictly required.
I will follow K. Janich's boook, Topology (Springer, UTM series). Munkres Topology is a good alternative.
- See the syllabus for homework policy, test info, grading scheme, etc.
Homework will be posted on the course canvas site. Students should get access through canvas.
Some LaTeX resources if you wish to type your work. Ask a friend how to install LaTeX on your computer, or google for instructions!
cheat sheet with many symbols
More examples
Homework template as a .tex and as a .pdf file.
Weekly outline and homework sets
- 8/29. Introduction and motivation.
- 9/3 and 9/5 . Basic definitions and examples, metric spaces, product and subspace topology, bases.
Problem set 1
- 9/10 and 9/12. Continuity, connectedness.
The extra resources/reading listed on the HW can be found here.
Problem set 2
- 9/17 and 9/19. Connectedness. Sequences. The Hausdorff property. First definition of compact.
Extra reading for next week on compactness.
Problem set 3
- 9/24 and 9/26. Compactness
Problem set 4
- 10/1 and 10/3. Quiz. Spaces of functions and convergence. Equivalence classes and universal properties.
Problem set 5
- 10/8 and 10/10. Quotient topology.
Problem set 6
- 10/15 and 10/17. More quotients. Connect sum. The classification of surfaces.
Problem set 7
- 10/22 Prelim exam
- 10/29 and 10/31 Homotopy equivalence
Problem set 8
Here are solutions and comments to problems on HW 7: hw7comments.pdfPreview the document Email the TA if you see any typos!
- 11/ 5 and 11/7 Coverings
Problem set 9
- 11/12 and 11/14 Lifting paths and lifting homotopies, the monodromy (endpoint) lemma.
Problem set 10
- 11/19 and 11/21 Paths, Loops and the Fundamental group. Warm up: hanging paintings at a museum.
Problem set 11
- 11/26 The lifting criterion. Every space has a "universal cover"
- 12/3 and 12/5 Applications: the fundamental theorem of algebra and the Borsuk-Ulam theorem.
Problem set 12
- 12/10 Final lecture: Euler characteristic and back to the classification of surfaces.