Math 40740: Topology

Math 40740: Topology (Fall 2018)

Coverage: Time permitting, we will start with chapter 1, followed by a more rigorous treatment of general topology in chapter 10. After briefly discussing graphs (Ch 2), we will move onto surfaces, including the classification of surfaces (Ch 3). We will then discuss knots (Ch 5), including the Jones polynomial. We will then discuss the fundamental group, and study the fundamental group of surfaces (AKA 2-manifolds) and knot complements (ch 9). We will end the class with 3-manifolds.

Grade: Homework 50%, Take home midterm 20%, Final exam 30%.

Homework: Homework will be typically assigned on Wednesdays, due the following Wednesday. Homework may be done individually or in small groups, with the caveat that (1) you list your collaborators, and (2) you write up your own solutions, independently of your collaborators. Some problems assigned have answers in the back of the book - these still should be turned in, and you should attempt them before checking the back of the book. Full explanations/proofs (as appropriate) are expected for all problems. Late assignments, unless there is a legitimate reason (e.g. medical), but I will drop your lowest homework score (i.e. the homework where the most points were deducted).

Exams: There will be a take-home midterm exam and a final exam.No collaboration is allowed on either. Both are open-book, open-note.

Honor code: All students are expected to adhere to the Notre Dame Honor code.

Assignments (you may have to refresh your browser to get this page to update)