Instructor           John E. M^cCarthy
Class                  MWF 10.00-11.00 in 216 Cupples I
Office                 105 Cupples I
Office Hours      MF 11:00-12:00, and by appointment
Phone                 935-6753

Exams    There will be two exams in the course:

                        1) Exam 1       February 28 (take home)
                        2) Exam 2       Final exam, on TBA

Homework

There will be weekly homework sets during the semester, handed out on Wednesday in class and due the following Wednesday. Some problems are fairly routine, but many are quite challenging. There will be no homework due after the end of classes!

Homework Problems

Content

This is a continuation of Math 421. The main topics are: Normal Families; the Riemann mapping theorem; Infinite products; the prime number theorem; Picard's theorem.

Basis for Grading

The midterm will be 20% of your grade, the final and the homework 40% each.
 

Homework

Homework is the most important part of the course. Whilst talking to other people about it is not dis-allowed, too often this degenerates into one person solving the problem, and other people copying them (often justified to themselves by saying "I provide the ideas, X does the details" - but the details are the key. If you can't translate the idea into a real proof, you don't understand the material well enough). So I shall introduce the following rules:
(a) You can only talk to some-one else about a problem if you have made a genuine effort to solve it yourself.
(b) You must write up the solutions on your own. Suspiciously similar write-ups will receive 0 points.
Note, too, that a significant part of this course is learning how to write mathematics. Thus serious attention will be paid to how the solutions are written up. They should be written in full English sentences, and it should be clear what is going on (so, for example, if the argument is lengthy, dividing the proof into well-marked stages is a good idea). Faulty logic will be penalised with negative points. So, if you cannot prove something is true in general, but can do so if you assume an extra hypothesis, you should say so, and state the extra hypothesis you need. This will earn partial credit. But if you claim to prove the result in general, whilst implicitly assuming this hypothesis, you will lose many points, and may end up getting less than zero on a problem. If you really have no idea how to prove something, don't waffle. If you have an idea that you cannot make into a rigourous proof, say "This is an idea, but I cannot make it into a rigourous proof".

I do expect you to come to class every day, and to participate in class discussions. I also expect you to stay abreast of the material we are covering, and may call on you at any time to answer a question.

Please feel free to talk to me about the course at any time. My office hours are just times when I will definitely be in my office. I welcome you to stop by whenever you wish. I shall not tell you how to do current homework problems, but if you've made some progress, I may give hints.
 

Web Pages

The following web pages may be give some interesting sidelights on the material.

The MacTutor History of Mathematics Archive

Augustin-Louis Cauchy
G. F. Bernhard Riemann
Karl Weiersrass

History of Analysis

Bibliography

The following is a brief bibliography you may find useful. Most books on complex analysis cover the same material, so choose one whose style suits you.
 

L.V. Ahlfors                  Complex Analysis: an introduction to the theory of                                                       analytic functions of one complex variable
J.B. Conway                 Functions of one complex variable
T.W. Gamelin                Complex Analysis
R.E. Greene and S.G. Krantz       Function Theory of one complex variable