Department of Mathematical Sciences, Northern Illinois University

## MATH 420, Spring 2003

#### Section 1, 9:00-9:50, M W F, DU 348

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

OFFICE HOURS: MWF 11:00-12:00, or by appointment.

My faculty homepage   |   My personal homepage

Review for the Final

The Final Exam is scheduled for Wednesday, May 7, 8:00-9:50 a.m., in DU 348

There will be a review session at noon on Tuesday, May 6, in DU 252.

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 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.
Note that the last day to withdraw from the course without penalty is Friday, March 7.

FINAL: The final exam is scheduled for Wednesday, May 7, 8:00-9:50 a.m.

HANDOUTS:       Review of groups for Exam 3     |     Homework 10

ASSIGNMENTS:

```
Wednesday, 4/30     Assessment 3.5, p 125: #2, 3, 7, 11

Friday, 4/25/03:    EXAM III   Sections 3.1 - 3.4

Wednesday, 4/23:    Hmwk #12   3.4, p 118: #2, 8, 9, 14

Friday, 4/18/03:    Hmwk #11   3.3, p 110: #1, 4, 8, 12 - 14

Friday, 4/4/03:     Hmwk #10   3.1, p 90:  #13, 19, 20
3.2, p 101: #6, 9, 14

Friday, 3/28/03:    EXAM II    Sections 2.1 - 2.3, 3.1

Hmwk #9    3.1, p 90: #4, 6, 8, 9. 11

Hmwk #8    2.3, p 75: #1bdf, 4, 5bd, 10 - 12

Friday, 3/7/03:     Hmwk #7    2.2, p 62: #2, 4, 7, 10

Friday, 2/29/03:    Hmwk #6    1.4, p 40: #7 - 10;
2.1, p 55: #10, 14, 15, 17

Monday, 2/24/03:    Hmwk #5    2.1, p 54: #1bc, 3bc;
2abc, 4abc;
8ce

Friday, 2/14/03:    EXAM I     Sections 1.1 - 1.4

Friday, 2/07/03:    Hmwk #4    1.3, p 30: #4, 7, 13, 18, 22, 25

Monday, 2/03/03:    Corrections on Hmwk #1 and 2

Friday, 1/31/02:    Hmwk #3    1.2, p 22: #6, 12, 17, 22

Monday, 1/27/03:    Hmwk #2    1.1, p 14: #4ce, 11, 17, 18

Friday, 1/17/03:    Hmwk #1    1.1, p 14: #2, 9, 10

```

SCHEDULE OF LECTURES:

```       MONDAY  WEDNESDAY   FRIDAY          M Tu  W Th  F
Week of                               JAN     2003
1/13   1.1       1.1        1.1          13 14 15 16 17
1/20  HOLIDAY    1.2        1.2          20 21 22 23 24
1/27   1.2       1.3        1.3          27 28 29 30 31
2/03   1.3       1.4        1.4      FEB  3  4  5  6  7
2/10   1.4       2.1       TEST I        10 11 12 13 14
2/17   2.1       2.1        2.2          17 18 19 20 21
2/24   2.2       2.2        2.3          24 25 26 27 28
3/03   2.3       2.3        3.1      MAR  3  4  5  6  7
SPRING BREAK              10 11 12 13 14
3/17   3.1       3.1        3.2          17 18 19 20 21
3/24   3.2       3.2       TEST II       24 25 26 27 28
3/31   3.3       3.3        3.3      APR 31  1  2  3  4
4/07   3.4       3.4        3.4           7  8  9 10 11
4/14   3.5       3.5        3.5          14 15 16 17 18
4/21   3.5      TEST III    3.6          21 22 23 24 25
4/28   3.6       3.6   READING DAY   MAY 28 29 30  1  2
5/05            FINAL                     5  6  7  8  9
FINAL EXAM   Wednesday 5/7/2003 8:00-9:50 a.m.
```