Department of Mathematical Sciences, Northern Illinois University

## MATH 420, Summer 2005

#### 12:30-1:45, M T W TH, RH 302

INSTRUCTOR: Professor John Beachy, Watson 355, 753-6753

OFFICE HOURS: to be announced

email: beachy@math.niu.edu | My faculty homepage | My personal homepage

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, 2nd Ed, by John Beachy and William Blair

OnLine Study Guide for the text

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

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 500 points: 4 hour tests (400) and homework (100).
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.

ASSIGNMENTS:

```Assignment 1:  Due Wednesday, 6/15   Section 1.1 #8-12

Assignment 2:  Due Tuesday, 6/21
#6  Give the lattice diagram of all divisors of 90.
#7  Let a,b,c be integers. If b|a and c|a and (b,c) = d,
#8  Section 1.2 #12
#9  Section 1.2 #22

Due Monday, 7/18
3.1 #8,9,20,21
3.2 \$4,6,14,15,19,20

Due Thursday, 7/21
3.3 #2,5,6,9,11

```

SCHEDULE OF LECTURES:

```       MONDAY   TUESDAY  WEDNESDAY  THURSDAY         M Tu  W Th
Week of                                         JUN     2005
6/13   1.1       1.1        1.2      1.2           13 14 15 16
6/20   1.3       1.3        1.4      1.4           20 21 22 23
6/27  EXAM 1     2.1        2.1      2.2           27 28 29 30
7/04  HOLIDAY    2.2        2.3      2.3       JUL  4  5  6  7
7/11  EXAM 2     3.1        3.1      3.2           11 12 13 14
7/18   3.2       3.2        3.3      3.3           18 19 20 21
7/25  EXAM 3     3.4        3.4      3.5           25 26 27 28
8/01   3.5       3.6        3.6     EXAM 4     AUG  1  2  3  4
```