Instructor: Mladen Bestvina
Office: JWB 210
Office hours: By appointment. I'll also hang around after
class for any brief questions.
Text: There are many complex analysis textbooks
out there. They mostly cover the standard material (up to the
Cauchy integral formula and consequences) in more or less the
same way, and might differ in the additional material. I plan to
cover hyperbolic geometry and use it to prove classical theorems
such as Little and Great Picard theorems. I also plan to cover
the Uniformization theorem. Here are some books that I'll be
using:
I'll follow Stein-Shakarchi up to the Cauchy theorem, and then
we'll see.
Meets: MWF 2:00PM-2:50PM at CSC
25
Midterm: Feb 28.
Final: Thursday, April
24, 2025, 1:00 – 3:00 pm
Grading: The final grade is based on homework
(30%), problem session activity (10%), the midterm (20%) and the
final (40%).
Homework: It
will be assigned weekly. You are encouraged to work in groups, but
what you write should be your own work and you should list the
other people in your group. It will be due every week on Mondays
at 9 am Tuesdays at 11:59pm and you should turn it in through
canvas in latex. Late homework is not accepted but
the lowest two scores are dropped from the count. You should
read the assigned reading for the week before the
corresponding lecture. I will also typically give out several
problems each week that you are not required to turn in. We'll
have a problem session every two weeks outside the class time
where you are expected to present solutions to unassigned
problems.
Problem sessions: Fridays 1-2 at CSC 25. There will
be one approximately every two weeks.
| Homework | ||
|---|---|---|
| Problems to turn in: | Due date: | Assigned reading: |
| 1,3,5,11,12b from hw01, latex file | 1/14 |
Stein-Shakarchi Ch 1:2.2,2.3 Holomorphic functions,
Cauchy-Riemann equations, power series. Also glance
through the material before these sections -- I am
assuming you are comfortable with it. Here
is a convenient list of common power series. |
| 2,3,4,5b,9 from hw02,
tex |
1/21 |
Integration along curves, primitives,
Goursat, Cauchy's theorem, Cauchy's integral formula,
Cauchy inequalities, Liouville |
You can contact me by email.
