Offered: Fall 1999
Instructor: Kevin J. Mitchell
Room: ET 105
Time: MWF 10:40 to 11:50 AM
Text: Contemporary Abstract Algebra, Fourth Edition
by Joseph A. Gallian
Abstract Algebra is a core course in the mathematics curriculum because of its focus on the basic underlying structures that occur in many mathematical systems. You have already been introduced to these notions (in fact, much more complicated notions) in Math 204 and Math 331 or CS 221 and CS 325. The basic object of our study this term will be groups. These are systems which are closed under some operation * (often addition or multiplication). Further, there must be an identity element, every element must have an inverse, and * must be asociative. Some familiar examples of groups include the ingtegers under addition, the field of real numbers under addition, the real numbers (without 0) under multiplication, and any vector space under its operation of addition.
In some sense, groups are simpler than vector spaces and fields since the latter have two operations, but there is only one operation in a group. Since there are "fewer restrictions'' on groups than on vector spaces or fields, there are "more of them.'' In fact, groups are almost everywhere you look. For example, the set of motions that slide the tiles on a floor into the same pattern or that take a wallpaper pattern into itself form a group.
The goal of this course is to make you a confident worker with some of the basic concepts mathematicians use in working with groups. This will require you to work out lots of specific examples and also force you to think quite generally about the properties that all groups satisfy. Being able to write clear and concise proofs of such general results is important in this course, and the labs (described below) are one way in which you will get help and practice doing this.
The course rewards careful, attentive reading and regular review of previously covered material. Be sure to read with a pencil in your hand, especially to draw figures that relate to the material being discussed.
The text we will be using is Contemporary Abstract Algebra by Joseph A. Gallian. We will try to cover material in chapters 0 through 11 of the text, omitting some parts of certain chapters. I have chosen this text for three reasons: I think it is quite readable, it has lots of examples, and it has lots of exercises. When reading any math text, you should always have a pencil in hand. Take notes, but more importantly, work out examples of the things being discussed.
Homework reading and exercises will be assigned at the beginning of each class. I will collect selected problems about once a week to grade. These problems will count for 15% of your grade. The three tests will count for 20% each and the final exam for 25%. I reserve the right to take lab and class participation into account in your grade.
There will be three in-class tests plus a final exam. The tests will be on Monday, September 27, Monday, October 18, and Monday, November 8. The final exam is scheduled for Sunday, November 21, at 7:00 PM. Tests will be cumulative but will concentrate on the most recent material.
Attendance is required. If you have to miss a class for some good reason beyond your control, talk to me about it beforehand. The same rules apply to tests. In this course, each class is important. I can't imagine anyone wanting to miss class. Missing more than three classes will automatically reduce your grade by one full letter.
Assignments are due at the beginning of class. Late assignments will incur a substantial penalty and will be rejected entirely if more than two days late. Since the course builds on each assignment, it is extremely important for you to get them done on time.
I encourage you to discuss material with each other. However, each person should write up her or his work individually.
Special Class on Thursday, September 16. Note that on Friday, September 17, all regular classes at the Colleges are cancelled for the day. I would like to make up the class on Thursday, September 16 at a mutually agreed upon time. Be prepared to make your preferences known.
The following texts have been placed On Reserve in the Library for your reference. Most could have been used as texts in the course.