Math H185: Honors introduction to complex analysis

UC Berkeley, Spring 2012

Instructor

Michael Hutchings
hutching@math.berkeley.edu
Office phone: 510-642-4329.
Office: 923 Evans.
Tentative office hours: Wednesday 2:00-4:00.

Textbook

The textbook for this course is Ahlfors, Complex analysis, 3rd edition, Addison-Wesley. A custom edition is available in the Cal store at a reduced price (but still rather expensive, sorry). It's a nice book, but you can maybe survive without it if you copy the homework assignments from someone. Lectures will generally correspond to parts of the book (indicated on the syllabus), but I will sometimes do things differently. I may also post some notes here.

Homework

Homework is due every Tuesday (except for the first two Tuesdays and the weeks of the midterms) 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.

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 what follows such a phrase 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 Ahlfors.

Exams and grading

There will be in-class midterms on Thursday 3/1 and Thursday 4/5. The final exam is on Wednesday 5/9.

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%. All grades will be curved to a uniform scale before being averaged.

Syllabus

The following is the core syllabus; I hope to discuss some additional topics as time permits. Math 104 or equivalent is a prerequisite; I will briefly review some of this material as needed, but assume that you are generally comfortable with basic real analysis.

What we did in class

Review sheet for the final exam