Last updated Jan. 22
Instructor: Paul Kainen, 252 Reiss, tel. 72703; kainen@georgetown.edu; Class location: Reiss 284 (MWF 2:15-3:05) Text is Number Theory by G. E. Andrews, Dover Publications, New York, NY, 1994 (originally publ in 1971).
Number theory is elementary in the sense that the entities it studies are intuitively fundamental. However, it sometimes uses arguments from a wide variety of mathematical areas, including calculus, complex variables, combinatorics, algebra and geometry. We'll focus on geometric and combinatorial number theory, using as a text, G. E. Andrews' Number Theory, Dover Publications, NY 1994 (originally published by Saunders in 1971). This book has a list price of $9.95 in the latest Dover Catalog and can be ordered from their web site (or I guess from Amazon, etc.) Dover Publications . I have not ordered it through the book store. If anyone has trouble getting a copy, please let me know and I can at least give you a xerox copy of the first chapters till you get your copy of the book.
The following is a brief description of course mechanics. Each student will do a project instead of a final exam. Your project will involve covering some material outside the common core which we will cover in class. I will be giving some examples in the extra sessions on weekend afternoons - beginning Sat. Jan. 25 at 2:30 pm - in or near Reiss 284. Each student (or small group of students) will take a topic (which I must approve) and present it to the class. For example, one suitable topic might be to give an overview of what it means for a Gaussian integer to be "prime"; another might be to discuss "p-adic" numbers; another could be to talk about rings and ideals, etc. Your project will include both a brief written summary of your main points and definitions (possibly including some xeroxed material from books) so that others in the class can read and study it, as well as the actual class presentation.
To make things more interesting, on the last take-home midterm, at the end of the course, each student will be given a set of problems from which you can pick five. One must be on the topic you or your group presented in class (where I'll expect a bit more proficiency of course), while the other four must be on topics presented by other groups.
Be sure to do homework, whether collected or not, since I count homework, including your ability to do it at the board, toward the grade. In addition, homework is one of the ways you actually learn the math, i.e., by doing problems. Homework is due on the day specified and won't be accepted late; if you can't be in class, please have a classmate hand it in for you.
There will be four midterm exams - all of equal weight. The last one will be take home. They are scheduled 7:30 - 9:30 pm but one hour should be sufficient for many of you.
Please note: The first three midterm exams will be given on the evenings of Feb. 5, Mar. 5, (both Wed.), and April 8 (Tues.) in WGR 211 at 7:30 pm. The fourth midterm will be given as a take-home, and it will include problems related to the class projects. Please let me know if you have a conflict with any of the evening exams.
There will be unannounced quizzes designed to encourage you to keep up with the reading and to focus on class discussions. In general, no make ups are permitted; however, I may make exceptions in some circumstances.
Grades will be based on the following:
Information on other topics is at my home(ly) page or classroom page and current assignments are on the number theory page. To contact me, you can use voice mail (7-2703) or e-mail kainen@georgetown.edu