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. 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 AEB
306
Midterm: Feb 22.
Final: Tuesday, May 2,
2023, 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 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 week or
two outside the class time where you are expected to present
solutions to unassigned problems.
Problem sessions: at JWB 308. The time will
alternate weekly between Tuesdays 9-9:45 and Fridays 12-1. You
should plan to attend one every two weeks.
| Homework | ||
|---|---|---|
| Problems to turn in: | Due date: | Assigned reading: |
| 1,2,3,7,8. Extra credit:9 from hw01 |
Tuesday 1/17 |
Stein-Shakarchi Ch 1:2.2,2.3 Also glance through the
material before these sections -- I am assuming you are
comfortable with it. Also, here is a handy list of some
frequently used power series. |
| 1-5, Extra credit 6 from hw02 |
Monday 1/23 |
Stein-Shakarchi Ch1, section 3 and Ch2
sections 1,2. |
| 1,2,4,6,8. Extra credit: 5 from hw03.pdf |
Monday 1/30 |
S-S the rest of Ch 2 |
| 1,5,6,9,10. EC: 7 hw04 |
Monday 2/6 |
S-S 3.1-3.3 |
| 1,2,4,6,12. EC: 7 hw05 |
Monday 2/13 |
S-S 3.4, Ahlfors 5.3 |
| 1,7,10,18,20. EC: 22 hw06 |
Tuesday 2/21 |
S-S 3.4,3.5,3.6 Prepare for the midterm on 2/22. It's on topics
covered by homework so far. |
| 4,6,7,8,10. EC: 2 hw07 |
Monday 2/27 |
Marshall 6.1 or Ahlfors 3.3 |
| 1,2,3,4,6. EC: 7 hw08 |
Monday 3/13 |
Ahlfors 3.3 and 3.4, Marshall Ch 6. |
| 1,2,4,5,6. EC: 7 hw09 |
Monday 3/20 |
Cannon
et al, Intro to hyperbolic geometry, trig
formulas from Buser:
Geometry_and_Spectra_of_Compact_Riemann_Surfaces.
Check canvas for one more resource. |
| 1,2,6,9,10. EC: 3 hw10 |
Monday 3/27 |
S-S 8.3 |
| 2,3,5,6,7. EC: 1 hw11 |
Monday 4/3 |
For the hyperbolic point of view I like
Noguchi: Introduction to Complex Analysis, Ch 6. |
| 1,2,3,5,6. EC: 10 hw12 |
Monday 4/10 |
Marshall 11.1-11.3 |
| 4,6,12,14,20 EC: 19 hw13 |
Monday 4/17 |
Ahlfors 7.2-7.3. The proof of the
Uniformization Theorem I'll present is from somewhat
obscure book Sansone-Gerretsen: Lectures on the Theory
of Functions, vol 2, published in 1969. |
| No more homework! To prepare for the final
study homework and old prelims http://www.math.utah.edu/graduate/qualifying_exams/ and http://www.math.utah.edu/grad/qualexams.php |
||
You can contact me by email.
Accommodation: The University of Utah
seeks to provide equal access to its programs, services and
activities for people with disabilities. If you will need
accommodations in the class, reasonable prior notice needs to be
given to the Center for Disability Services (CDS), 162 Olpin Union
Building, 581- 5020 (V/TDD). CDS will work with you and me to make
arrangements for accommodations. All information in this course
can be made available in alternative format with prior
notification to CDS.