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.
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.