Math 185: Introduction to complex analysis, Fall 2022

Instructor: Zhiyan Ding (zding.m at berkeley dot edu). In all e-mail correspondence, please include "[Math185]" in the subject line.

GSI: Thomas Browning (email: tb1004913 at berkeley dot edu)

Lecture: MWF 11:00am-11:59am in Etcheverry 3109

GSI Office hours: Location: Evans 1041; Office hours: 

Monday: 2pm - 3pm

Tuesday: 8am - 9:30 am, 11am - 12pm

Wednesday: 10am - 11am, 12pm - 1pm, 2pm - 3:30pm

Thursday: 8am - 9:30am, 11am - 12:30pm

My Office hours: Location: Evans 1053; Office hours: MW 4:00pm-5:00pm. Please e-mail me if you'd like other office hours.

Prerequisites: Math 104 or equivalent. Students should be familiar with basic concepts from (real) analysis like sup, inf, Cauchy sequences, etc. In addition, basic knowledge of multivariable calculus is expected, including partial derivatives and line integrals. 

Students can check "Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross" for these basic concepts. 

Text: 

The primary text for this course is Complex Analysis by Stein and Shakarchi [S-S].

Students should feel free to consult other books for additional exercises and/or alternative presentations of the material (see in particular the book by Gamelin [G] linked below, which is available electronically to all UCB students). 

Students are expected to read the relevant sections of the textbook, as the lectures are meant to complement the textbook, not replace it, and we have a lot of material to cover.

Grading: 

Choice 1: 20% homework, 2 x 20% in-class midterms, 40% final exam. 

Choice 2: 20% homework, 20% in-class midterm (higher one), 60% final exam. 

There will be 12 homework. The lowest two homework scores will be dropped. 

No makeups for the midterms will be given except in cases requiring special accommodation. 

Course policies:

• Homework will be assigned regularly (see the syllabus) and due at the beginning of class. I grant extensions at most twice in reasonable circumstances, but you must talk to me as early as possible. The longer you wait, the less flexible I will be.

• Collaborating on homework: You may work together to figure out homework problems, but you must write up your solutions in your own words in order to receive credit. In particular, please do not copy answers from the internet or solution manuals. Also, please do not let others copy your homework. You might lose points in homework if I find out your homework is the same as others.

The major purpose of the homework is to help you check your understanding of the material and prepare for the exams. I will try to make the difficulty of homework be similar to the exams. I highly encourage you to take some time to think about each problem by yourself (say, at least thirty minutes) before discussing it with others. If you're stuck on a problem, another choice is to come to office hours and ask for a hint. The more you figure out on your own, the better you'll do both on the exams.

• The usual expectations and procedures for academic integrity at UC Berkeley apply. Cheating on an exam will result in a failing grade and will be reported to the University Office of Student Conduction. Please don't put me through this.

Special announcements:

• If you are a disabled student (with or without a document from the Disabled Students' Program) and require special accommodations of any kind, please e-mail the instructor as soon as possible, and no later than the end of the second week of classes. It really helps if you tell me earlier rather than later.

• If you are representing the university on some official duties (say if you are an athlete or in a band), and if there is a conflict with any of the mid-terms, please let the instructor know before the end of the second week of classes.

Additional resources:

• Complex Analysis by Theodore W. Gamelin (accessible from UCB IP addresses)

• Complex Analysis by George Cain 

• Class notes by Ved V. Datar

• For multivariable calculus, Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross

Course Overview: 

The goal of this course is to introduce students to complex analysis. Simply speaking, complex analysis is differentiating and integrating with respect to a complex variable rather than a real variable. However, the two-dimensional nature of complex numbers gives complex analysis many interesting and surprising features unknown to students of real analysis. This course will introduce the basics of complex analysis and cover Chapters 1-3 of [S-S]. If time allows, I might cover some advanced topics like conformal mappings, the gamma function, and the Riemann zeta function.