Welcome! The purpose of this course is to begin
exploring topology, which is the
qualitative study of shapes. We will also be honing
our skills as clear expositors, both in writing
and speaking, through the homeworks and problem
presentations. I think it's gonna be fun, and I hope
you enjoy it!
Topics and Timeline
We will be learning about point-set topology with an eye
towards connections to geometry and algebraic topology. In
particular, there will be an emphasis on (topological) manifolds
and well-behaved spaces. The textbook we will use is
Lee's Introduction to Topological Manifolds, 2ed.
The second edition is quite a bit different than the first,
so make sure you get the right one.
Here is an expected timeline, subject to change as we go along if needed:
Classes will be standard lecture format; they will be
most fruitful if you skim the reading before class, and
maybe work through some of the in-chapter exercises. Homework is due
on Friday and returned Monday. Earlier in the week
(to be scheduled during first class) you will sign up for slots to
present a problem or two during office hours.
Assignments and Grading
The goal of this grading schema is for you to be able to spend
as little time as possible worrying about grades, and
as much time as possible learning.
If you start to become worried about your grade, just
talk to me about what's going on and we'll figure it out.
50%: Homework
Homework will be assigned at most weekly.
It is graded on a reasonable attempt
basis, not on correctness. Clearly explain your
attempt. You may be asked to hand in a problem again
if it seems like it would be helpful to do so.
10%: Attendance
Simply arrive.
20%: Problem presentations
Show up and walk me through what you've thought about
and you're good!
20%: Final project
A write-up of notes on a topic of interest.
More information will be given later.
Policies
I have attempted to devise policies that minimize the use
of email. So please read carefully and try to see if one
of the below protocols applies before sending emails.
Attendance
If you arrive late please stay for a little
after class to discuss anything missed.
If you know you will be absent in the future,
attend office hours ahead of time and get marked
present. If you have an absence, attend office hours
within a week of the missed class and get marked
present. If you have unresolved absences or if
there is some issue not covered here, sign up
for a meeting through
Calendly.
Collaboration
Fine and encouraged but please give credit where
credit is due. Remember that homework is graded
solely on a reasonable attempt basis, so no need
to reach too hard for outside resources and help.
Try exploring what you can on your own, when possible
and supportive.
Late Work
Show up at next office hours or stay after class
to discuss.