640:492-H1 Junior-Senior Honors Seminar (Spring 2005)

The main purpose of the seminar is to help students learn how to read, understand, and present advanced mathematics. We will follow the book "A Classical Introduction to Modern Number Theory" by K. Ireland and M. Rosen (see the syllabus). No prior knowledge of number theory will be assumed. We will begin with congruences and progress through counting the number of solutions to certain congruences, reciprocity laws, zeta functions and further applications. The course will meet once a week. Additionally, students will be required to meet with each other in small discussion groups at least once more per week.

The time for the seminar will be Tuesdays 1:10 - 2:30 in Hill 323 (the undergraduate mathematics lounge).

Every fortnight, a pair of students (presenters) will be chosen to prepare and present the material for the next 2 weeks. The remaining students will be divided into discussion groups of 3 or 4.

It is expected that the presenters will help each other prepare the material, and take turns presenting it to the seminar. Professors Tunnell and Woodward will be available to discuss the topics with the presenters and to rehearse their presentations. Graduate Students John Bryk and Eric Rowland will also assist with the seminar.

In order to encourage participation of the students who are not presenting material in a particular two-week period, the study groups will meet at mutually agreable times once a week to discuss the material of the upcoming lecture. Each student is expected to keep notes of any observations/questions arising out of the discussions. These notes are to be turned in (or better yet, sent by e-mail) no later than the day before the seminar.

Sometimes the "notes" might be mostly questions, such as "How can a function be a vector?", "Please explain figure 4.2", or "We don't see how this graph gives a matrix!" This is ok; the important part is that every student maintain involvement with the topics discussed in the seminar and that the speakers respond to the questions.

Grades will be based on the presentations and the weekly notes.

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