MATH 427 Complex Analysis

Spring 2006 

Description

Complex analysis is a 200 year old mathematical discipline that is very rich in its own development and in its applications. The course will feature a rigorous treatment of the subject, together with ample treatment of many applications.

The basic object of study is a class of functions defined on a region in the plane, taking values in the plane. Consequently the major prerequisite for the course is multi-variable calculus. However, unlike that subject which in its generality has little coherence, complex analysis limits its view to the class of holomorphic or analytic functions. Each of these functions individually has important and properties that give it substance, and the class of all such functions has attributes that provide a certain rigidity that is very useful.

Complex analysis is one of the most beautiful parts of mathematics. It is filled with surprises in itself, and its applications to other parts of mathematics and to other areas of science and engineering are many and exciting.

Staff

Instructor

John C. Polking
Office: HB 450. Office hours: 1:30 to 4:00 on days before homework is due, Tuesdays and Thursdays immediately after class, and by appointment.
Email: polking@rice.edu
Telephone: ext 4841
Teaching Assistants

Soomin Kim
Office: HB 48. Office hours: 2:30 to 4:00 Wednesdays and Thursdays, and by appointment.
Email: soomin@rice.edu
Telephone: ext 2786

Text

The text for this course is Complex Analysis, By Elias M. Stein and Rami Shakarchi.

Computer and Owlnet information

Computers will not be widely used in this course, but there is one program which you will find useful. It is called holo and it runs under MATLAB. You can find information about it here. The picture at the beginning of this page exemplifies what holo can do.

 In order to use holo you will need to download the filec holo.m.

Grading

Half of your final grade for the course will be determined by your performance on the homework. Working problems is the best way to learn the material in this course. In addition there will be two projects, each counting for one fourth of the final grade.

Homework

There will be a homework assignment each week. The lowest homework grade will not be counted in determining the grade.

 All homework is due in class on the date announced. This will typically be about a week after the assignment is posted. Each student will be allowed to have at most one late homework assignment during the semester. The one late homework will be accepted up to seven days after the due date, with or without excuse, and without penalty. No other late homeworks will be accepted even with an excuse. There will be absolutely no exceptions to these rules.

Many of the Exercises in the book extend the material in the text. Therefore they are as important as the text itself. Many homework assignments will contain more problems to be done than are to be turned in. It should be emphasized that a person learns mathematics by doing problems. You are encouraged to at least look at all of the exercises in the book.

A homework assignment is meant to convince the grader that you understand the material. The best way to do that is to use complete sentences and to organize your work in paragraphs. In your writing, attempt to achieve the same clarity you find in textbooks. The grader has instructions that if he cannot understand your writing, he is not to grade your paper.

The homework is not pledged. You are encouraged to discuss the homework, and to work together on the problems. However each student is responsible for the final preparation of his or her own homework papers.

Homework Assignments and Projects:

John C. Polking <polking@rice.edu>

Last modified: Tuesday, January 23, 2006