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).

Textbook

The textbook for the class will be p-adic Numbers: An Introduction, by Fernando Q. Gouvêa.

Grading

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.

Return to Evan Bullock's web site or to Rice's VIGRE PFUG: Computational algebraic geometry.

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