Overview
This course is a continuation of MCS-313. I will assume that at one time you knew the basics of group theory and that you remember the basic facts about rings and fields. We will cover field theory and Galois theory in detail. While I do not expect you to remember everything you learned in MCS-313, 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.

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

Course web site: The best source of information about this course is available at www.gac.edu/~mmcdermo/mcs314/s03. There you will find a complete syllabus, course description, current homework assignments, and so on.

Text

Contemporary Abstract Algebra, 5th edition, by Joseph A. Gallian, Houghton Mifflin, 2002.

There will be supplemental material for Galois Theory.

Quizzes and Exams
We will have 2 or 3 exams. The first exam will cover rings etc. (13-18) and the second will cover field theory (19-23). We may have a third exam on Galois theory, but we may have presentations instead of an exam.

Academic Integrity
You are expected to work together in an honorable way in this course. This means that while you can discuss problems and their solutions, each of you should make a real effort to solve each problem by yourself, and you should give credit to any people or texts that helped you find solutions. Needless to say, you are expected to work completely by yourself on tests.

Cheating is not allowed in this course. I have zero tolerance for cheating. If I discover that someone has cheated, then I will take action ranging from giving a zero for the assignment in question to assigning a grade of F for the entire course. I will also notify the Dean of Students.

The academic honesty policy can be found in the 2002-2003 college catalog.

Classes
During the first half of the course, while we are still using Gallian, classess will be fairly similar to last semester. We cannot afford to go over every detail in class or we will never make it to Galois theory. Therefore, 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.
Once we get to Galois theory, classes will be run more like a seminar. You will each be responsible for presenting proofs and examples in class.

Homework
We will have a mixture of regular homework assignments and portfolio type problems. In addition, you will be expected to prepare material for class when we are learning Galois theory.

Course Material
The course can be loosely divided into three segments:

• Rings, domains and fields
• Field theory
• Galois theory

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

Accessibility:  Please contact me during the first week of class if you have specific physical, psychiatric, or learning disabilities and require accommodations. I will do my best to facilitate the  necessary arrangements.  All discussions will remain confidential.

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