Topology
Math 631-001 (Spring 2023)
This web page will be updated regularly and always contain the latest information on the course.
| Instructor: | Thomas Wanner |
|---|---|
| Office: | Exploratory Hall 4404 |
| E-mail: | twanner@gmu.edu |
| Web Page: | http://math.cos.gmu.edu/~wanner/ |
| Fax: | (703) 993-1491 |
| Office hours: | T 2-3pm, R 1-2pm, and by appointment |
| Learning Assistant: | Swan Klein |
| Office: | Exploratory Hall 4311 |
| E-mail: | hklein2@gmu.edu |
| Office hours: | M 3-4pm, W 10-11am, W 5-6pm |
| Prelim Session: | F 12pm-2pm |
| Lectures: | TR 5:55-7:10pm, Exploratory Hall 4106 |
|---|---|
| Prerequisites: | Grade of C or better in Math 315. In addition, familiarity with the "Theorem-Proof" style of presentation is important. |
| Textbook: | Topology by James Munkres, 2nd edition, Pearson Modern Classics, 2017. |
Important Links
- Detailed syllabus (including recommended books)
- Youtube links to selected lecture videos (in case you miss class, or you want to relisten to me in double-speed)
- Relevant official GMU policies
Detailed lecture notes, reading assignments, and additional materials can be found on the Blackboard site for this course. Homework assignments can be found on Gradescope, which is linked through Blackboard as well. Please make sure to check there regularly! Note also that the above Youtube lecture videos are not are replacement for class attendance! They are only meant as an additional resource, and will not cover all the material that is covered in the course.
Syllabus
The course introduces basic concepts from topology. Specifically, it covers the definition and basic examples of topological and metric spaces, open and closed sets, subspaces and finite products, sequences and convergence, compactness and separability, continuous functions, uniform continuity, the metric space C(X) and uniform convergence, and homotopy. A more detailed syllabus can be found here, and it will be updated weekly. This course is one of the core courses of the graduate program, and will therefore cover all the topics outline in the Topology Preliminary Exam Syllabus.
Homework Assignments
Homework problems will be assigned once a week and posted on Gradescope, which you can access through the left sidebar in Blackboard. Most of these assignments will be graded and count towards your homework score. While the remaining ones do not have to be handed in, I do advise everyone strongly to study them and write out the solutions properly. I will go through many of the homework problems in the following class and you will not benefit from this if you have not made a serious attempt at solving them.
Grading Policy
Your final grade in the course will be determined from your performance in a midterm exam, the homework assignments, and a final exam. Weights for these items will be distributed approximately according to the following schedule:
| Homework | Midterm Exam | Final Exam | Attendance |
|---|---|---|---|
| 50% | 20% | 20% | 10% |
The assignment of your course grade is based on the total course score. The following grading scale may serve as a guideline, although changes are possible:
| Score above | 90% | 80% | 70% | 60% | otherwise |
|---|---|---|---|---|---|
| Letter grade | A | B | C | D | F |