This course is a continuation of MCS313.  I will assume that at one time you knew the basics of group and ring theory and that you remember the basic facts about fields.  While I do not expect you to remember everything you learned in MCS313, I do expect that you will be willing and able to look things up in your notes and in the text and relearn certain topics if necessary.

We will cover Galois Theory and the Sylow Theorems.  In addition you will each be researching a special topic.

Galois theory brings together the study of polynomials, group theory and field theory and from their interplay creates a very rich and powerful theory that can answer questions that baffled mathematicians before the 19th century. These include the question of when you can find a general formula for the roots of a polynomial and which polygons can be constructed using only a straightedge and a compass.

Prerequisites

MCS-313.

Text

The primary text for the course will be Contemporary Abstract Algebra, 4th edtion, by Joseph A. Gallian, Houghton Mifflin, 1998.  There will be some supplementary material on Galois Theory.

Evaluation

Your final grade will be assigned using the following percentages as a guide:
 

Homework	25%
Class Work & Participation	25%
Exams	25%
Project	25%

Academic Integrity

The academic honesty policy can be found on page 31 of the 2000-2001 college catalogue.  I call your attention to the following excerpt:  "In all academic exercises, examinations, papers, and reports, students shall submit their own work. Footnotes or some other acceptable form of citation must accompany any use of another's words or ideas."

Quizzes and Exams

We will have one or two exams during the semester.

Class Format

I would like this class to be more like a seminar than MCS313 was.  This means that we will all be responsible for presenting material at various times during the semester.  Also, it is imperative that you read the assigned material carefully and with the writing implement of your choice in hand before class.  Keep a notebook.  Write down your questions.

Homework

I hear, and I forget;
I see, and I remember;
I do, and I understand.
                               - Proverb

If you do work with other students on the homework, I would like you to follow these guidelines:

1. Each person should write up the answers independently.
2. Each person should be able to work each one of the problems independently.
3. Each person gives credit to the others who helped.

The course can be loosely  divided into three segments:

• Fields and Galois Theory
• Sylow Theorems
• Special Topics

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