Math 185: Introduction to complex analysis

UC Berkeley, Spring 2016


Michael Hutchings
Office phone: 510-642-4329.
Office: 923 Evans.
Tentative office hours: Thursday 2:00-3:30.


In addition to my office hours, I have set up a piazza page for the course here. Please feel free to ask questions about the course content there.

Head GSI

The head GSI for Math 185 (all sections) is Anh Nguyen. She will hold office hours from 4-6 pm on MTWThF in 961 Evans. Her annoucements and schedule changes (including some homework hints) are posted here.


The textbook for this course is Theodore Gamelin, Complex analysis. If you connect to the internet through the UCB network or proxy server, then you can (legally!) download the book for free from Please be sure to also download the errata. I will sometimes do things differently from the book, or in a different order. I may also occasionally post supplemental notes here. In any case, the course will cover most of the first part of the book, some of the second part, and possibly a bit of the third part.

There are many other complex analysis books available. The classic text by Ahlfors is more challenging and a bit old-fashioned, but very good. If you like pictures, check out Visual Complex Analysis by Tristan Needham. Some other nice books at an advanced undergraduate to beginning graduate level are Complex function theory by Sarason, Complex analysis by Lang, Functions of one complex variable I by Conway, Complex analysis by Stein-Shakarchi, and Basic Complex Analysis: A Comprehensive Course in Analysis, Part 2A by Barry Simon. All these books cover the same basic topics that are covered our course, but with different styles, and most of them include additional more advanced topics which vary from one book to the next.


Homework is due on most Tuesdays at the beginning of class. You can either bring it to class or slide it under my office door. (If it doesn't fit under the door, please be more concise!) Homework assignments will be posted below at least a week before they are due. No late homeworks will be accepted for any reason, so that we can go over the homework right after it is handed in (which is when people are most eager to see solutions to troublesome problems). However it is OK if you miss the deadline once or twice, because your lowest two homework scores will be dropped.

When preparing your homework, please keep the following in mind:

1) You are encouraged to discuss the homework problems with your classmates. Perhaps the best way to learn is to think hard about a problem on your own until you get really stuck or solve it, then ask someone else how they thought about it. However, when it comes time to write down your solutions to hand in, you must do this by yourself, in your own words, without looking at someone else's paper. In addition, you must acknowledge any collaboration.

2) All answers should be written in complete, grammatically correct English sentences which explain the logic of what you are doing, with mathematical symbols and equations interspersed as appropriate. Results of calculations and answers to true/false questions etc. should always be justified. Proofs should be complete and detailed. Avoid phrases such as "it is easy to see that"; often this means "I don't feel like explaining that", and what follows is actually a tricky point that needs justifiction, or even false. You can of course cite theorems that we have already proved in class or from the book.

Now here are the assignments. Below, "x.y" means exercise y on page x of the book.

Exams and grading

There will be in-class midterms on Thursday 2/25 and Thursday 4/7. The final exam is on Thursday 5/12.

There will be no makeup exams. However you can miss one midterm without penalty, as explained in the grading policy below.

There is no regrading unless there is an egregious error such as adding up the points incorrectly. Every effort is made to grade all exams according to the same standards, so regrading one student's exam would be unfair to everyone else.

The course grade will be determined as follows: homework 25%, midterms 25% each, final 50%, lowest exam score -25%. The homework score will not be dropped. All grades will be curved to a uniform scale before being averaged.


The following is the core syllabus, listed in the order in which it is presented in the book, which is not always the order in which I will cover it. I may discuss some additional topics as time permits. I will also skip the last couple of sections of some chapters of the book (which tend to contain more optional or specialized material).

Math 104 or equivalent is a prerequisite; I may briefly review some of this material as needed, but assume that you are generally comfortable with basic real analysis.

What we actually did in class