January 22, 1999

This is a message to a mailing list I've established for students in section 1 of Math 403 given during the Spring 1999 semester. Please let me know if you should not be on this mailing list. More interestingly, please let me know if you should have gotten this message! I will give out hard copy of student names, majors, and e-mail addresses at the next class meeting.

HOMEWORK & QUIZ POLICY: UNLESS SPECIFICALLY STATED OTHERWISE I encourage students to work together on any homework problems and quizzes. I will be happy to answer questions and give hints either in person, on the telephone, or via e-mail (which may be the best way!). I generally would like each student to hand in a separate writeup of the problems that are requested. There may be, however, cases where students feel that it would be very difficult or impossible to hand in distinct writeups. This should occur rarely. In such cases, please write on the material handed in the names of all students whose efforts are included.

I will rarely accept late homework, and will try diligently to return graded homework as soon as possible. Homework will be graded not only for mathematical content, but ALSO for exposition. If I find the homework difficult to read, or the line of reasoning inadequately explained, then the grade will be lower. By now you should be able to write brief, comprehensible English language explanations of technical work USING COMPLETE ENGLISH SENTENCES.

I expect you to try all the homework problems listed on the syllabus. At each class meeting I may request one or more of these problems to be handed in at the next class meeting. I may also (an example is below!) request one or more additional problems to be written up and handed in.

EXAMS: No outside texts, notes or machines (!) may be used on exams. Each exam is to represent only the work of the student whose name is on the paper. Let me know as soon as possible if you cannot take any exam at the time that it is scheduled.

ATTENDANCE: I assume you'll be in class. I may cover (rarely!) material not in the book, or not in the order or manner discussed in the book. I may assign work to be handed in at the next class meeting.

FURTHER COMMENTS: Please let me know if you have any comments or questions on the policies above at any time during the semester. I'd really like the course to be a straightforward environment for learning mathematics, avoiding as much as possible any misunderstandings or stress about academic integrity.


Textbook: section 4: problems 10,12; section 6: problem 4

Additional problem: suppose Q(z)=2z^4+(1+i)z^2+7. Use the technique demonstrated in class to create three positive constants C_1 and C_2 and C_3 so that the following implication is true:

If |z|>C_1, then C_2 |z|^4 <= |Q(z)| <= C_3 |z|^4.

Note: there are MANY possible equally valid answers to this question. I am NOT interested in any specific answer. I AM interested in how you find your answer, and how you demonstrate to me the validity of your answer. Write something that I can read easily: I don't want to have to guess about your reasoning! Thank you.

Notation: |A| means the modulus of the complex number A. <= means "less than or equal to". ^ means exponentiation, so 2^4 is 16. _ means subscript, so C_2 could be read "the constant C-sub-2".

January 27, 1999

Good evening. I've created a web page for our section of Math 403. It is at

OR you may find it more convenient to look at my homepage in the Math Department and follow the Math 403 link indicated.


I'd like to also mention that a POSSIBLY interesting and relevant colloquium is being given in the Math Department this Friday (January 29) at 4:30-5:30 in Hill 705. The Colloquia are SUPPOSED to be comprehensible talks and not overly technical. I would say (unfortunately!) that you should attend at your own risk since academic lectures may sometimes be incomprehensible! The topic is

"The Mandelbrot Set, the Farey Tree, and the Fibonacci Sequence"

and the speaker is Professor Robert Devaney of Boston University.

Here is a published description:

ABSTRACT: In this talk we describe some "folk theorems" regarding the geometry of the Mandelbrot set. We show how to use the geometry of the bulbs in the Mandelbrot set to predict the behavior of the associated quadratic dynamics. We also show how the dynamics determines the geometry of the bulbs.


The topic of Mandelbrot sets and fractals is quite fascinating and has actually had applications in physics and engineering (!). If you want to look at some lovely pictures, try the following site at Clark University:

March 19, 1999

I hope you've had a nice vacation. I'd like to repeat the remarks I made when returning the exam during the last class before vacation.

I found the grades and the exam performance disappointing. I thought when I first met and talked with the students in the class that I had an intelligent and knowledgeable group of students. I still do, but now I realize that although I am in love with complex variables, the attraction of the subject may not yet be apparent to you, and also the need to do work in the subject must compete with other demands on your time.

I'd like to increase the chances that each of you can get a good grade in the course and learn the material. Therefore, I will assign 5 problems in each lecture to be turned in at the next lecture. I will randomly choose 2 of these 5 to grade. Each problem will be graded on a 5 point scale. I will continue to do this until I've accumulated 100 points (10 meetings). I'll use the accumulated points as another 100 point test score.

I will try to assign more computable and simpler problems on Tuesday, recognizing the fact that there's not much time until the next class. I will try to return graded homework in a more timely manner than I have done. The rules for homework continue as previously expressed. You may see the archived messages on the Math 403 web page, which also has e-mail addresses for the students in the course.

I look forward to discovering power series with you next week.


38 #2, 40 #3, 42 $2, 42 #8, 43 #2.

Maintained by and last modified 3/19/99.