### MATH 420, Fall 2006

Section 1, 10:00-10:50, M W F, DU 302

INSTRUCTOR:
**Professor John Beachy**,
Watson 355, 753-6753; email: beachy@math.niu.edu

OFFICE HOURS: W Th 12:00-1:50, or by appointment.
COURSE DESCRIPTION:
**Algebra I** (3).
Introduction to group theory.
Properties of the integers, functions, and equivalence relations.
A concrete approach to cyclic groups and permutation groups;
isomorphisms and the theorems of Lagrange and Cayley.

TEXT:
**Abstract Algebra**, *3rd Ed*,
by John Beachy and William Blair

SYLLABUS: Chapter One, Integers;
Chapter Two, Functions;
Chapter Three, Groups

COURSE OBJECTIVES:
The student is expected to acquire an understanding
of the elementary theory of groups, together with the
necessary number theoretic prerequisites. There will
be some discussion of the computational aspects of
these topics, but the main thrust of the course will
be theoretical. The student will be expected not
only to follow the proofs presented in class and in
the text, but also to learn to construct new proofs.
Proofs must be logically correct and care must be
taken to write them precisely and in grammatically
correct English.

COURSE PREREQUISITE:
MATH 240, Linear Algebra.
We will use matrices in some important examples, but
the main reason for the requirement is to attempt to
guarantee a certain level of "mathematical maturity."

GRADING:
Final grades will be based on 600 points:
3 hour tests (300), homework (100),
and a comprehensive final exam (200).
The homework problems are extremely important.
In many ways the course is like an English composition
course, since it requires you to write out very carefully
the reasons for each step in your solutions of problems.
The last day to withdraw from the course without penalty is
Friday, October 20.

FINAL: The final exam is scheduled for
Monday, December 11, 10:00-11:50 a.m.

SCHEDULE OF LECTURES AND EXAMS (TENTATIVE):

MONDAY WEDNESDAY FRIDAY M Tu W Th F
Week of 2006
08/28 1.1 1.1 1.1 AUG 28 29 30 31 1
09/04 HOLIDAY 1.2 1.2 SEP 4 5 6 7 8
09/11 1.2 1.3 1.3 11 12 13 14 15
09/18 1.3 1.4 1.4 18 19 20 21 22
09/25 1.4 2.1 TEST I 25 26 27 28 29
10/02 2.1 2.1 2.2 OCT 2 3 4 5 6
10/09 2.2 2.2 2.3 9 10 11 12 13
10/16 2.3 2.3 3.1 16 17 18 19 20
10/23 3.1 3.1 TEST II 23 24 25 26 27
10/30 3.2 3.2 3.2 30 31 1 2 3
11/06 3.3 3.3 3.3 NOV 6 7 8 9 10
11/13 3.4 3.4 3.4 13 14 15 16 17
11/20 3.5 THANKSGIVING HOLIDAY 20 21 22 23 24
11/27 3.5 3.5 TEST III 27 28 29 20 1
12/04 3.6 3.6 3.6 DEC 4 5 6 7 8
12/11 FINAL 11 12 13 14 15
FINAL EXAM Monday 12/11/2006 10:00-11:50 a.m.