MATH 499: VIGRE
Introduction to p-adic numbers (Spring 2012)

Instructor:Evan
Bullock Office: Herman Brown 408 Office Hours: Wed 4:00-6:00pm, Thu 1:15-2:15pm Email: Time: 10:50am-12:05pm Location: Herman Brown 453

Homework

For 3/27: Problem 116
For 3/20: Problem 117
For 3/15: Problem 112
For 3/13: Problem 104
For 3/8: Problem 103
For 3/6: Problem 96i
For 2/21: Problem 83, 84
For 2/16: Problem 79
For 2/9: Problems 60, 69
For 2/7: Problems 68, 59
For 2/2: Problems 51, 56
For 1/31: Problems 49, 50
For 1/26: Problems 38, 37
For 1/24: Problem 23
For 1/19: Problems 13, 18
For 1/17: Problems 11, 12
For 1/12: Problem 6

Description

This course will be an introduction to the p-adic numbers. We
will cover congruences modulo prime powers, notions of absolute value
on the rational numbers, open and closed sets, construction of the
field Q_{p} of p-adic numbers, Hensel's Lemma, Newton's Method, p-adic power series, and p-adic elementary functions.

This course will be based in large part on student participation.
A portion of each class will be spent on student presentation of the
exercises. Please sign up for 3 credit hours or come see me.

Prerequisites

The only prerequisite for this course will be some knowledge of
congruences (e.g. Math 365 or Math 373 or Math 356). It is also
recommend that students have seen (or are seeing at the same time) some
real analysis (e.g. Math 221 or Math 302).

The grade for the course will be based on the following:

Attendance/Participation (70%): This course will follow a seminar
format, so attendance is critical. There will be homework
problems to be presented in class by the students, and students will be
expected to be
involved with the class discussion.

Final Exam (30%): Take-home final
exam. It is the
policy of the mathematics
department that no final exam may be
given early to accommodate student travel plans.

Disability Support

If you have a documented disability that will impact your work in
this class, please contact me to discuss your needs. Additionally, you
will
need to register with the Disability
Support Services office in the
Allen
Center.