Department of Mathematical Sciences, Northern Illinois University

## 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.

My faculty homepage   |   My personal homepage

Thursday morning (12/14/2006) Exam scores and semester grades have been posted on Blackboard. Final exam solutions

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

Study Guide for the 3rd edition (in pdf format)     |     OnLine Study Guide for the 2nd edition

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

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 for an undergraduate to withdraw from the course without penalty is Friday, October 20.

FINAL: The final exam for Section 1 is scheduled for Monday, December 11, 10:00-11:50 a.m.

EXAMS:       Exam 1   Solutions   |   Exam 2   Solutions   |   Exam 3   Solutions   |   Final Exam   Solutions

HANDOUTS:       Hmwk 1   |   Hmwk 2

ASSIGNMENTS:

```Friday, 12/8          Optional Homework:  3.5 #4,10,11,18
If you decide to turn in these problems, I will
use your score to replace the lowest homework or
quiz score that you have.  Since I do not plan to
drop any of these scores, if you missed a quiz
or homework assignment, replacing a 0 is high priority.

Monday, 12/4          Exam 3     3.1-3.4

Monday, 11/20         Hmwk 10: Hand in 3.3 #2,5,8,11

Friday, 11/17         Quiz 7  Definitions and statements of results only!
But covering 3.1, 3.2, and 3.3.1-3.3.4

Friday, 11/10         Quiz 6 on Sections 3.1, 3.2
Know the definitions and statements of results!!
Suggested problems for the quiz:
3.1 #1-3,6-8,15,23  3.2 #1,4,5,7,11,12,14,15

Hmwk 8,9: Hand in 3.1 #10-13;  3.2 #6,8,19,24

Friday, 10/27         Exam 2 on sections 2.1-2.3

Wednesday, 10/25      Hmwk 7 Section 2.3 #3,6,13,14

Friday, 10/20/06      Quiz 5 over section 2.2
Suggested problems: 2.2 #1-6,10 Study guide: #13-16,21

Friday, 10/13/06      Quiz 4 over section 2.1
Quiz problems: 2.1 #1-10

Wednesday, 10/11/06   Hmwk 6 Section 2.1 #11,12,15,16

Friday, 10/6/06       NO QUIZ

Monday, 10/2          Exam 1 on sections 1.1-1.4

Friday, 9/27/06       Exam 1 postponed to Monday
Hmwk 5 Section 1.4 #3d,9,12,27

Friday, 9/22/06       Quiz 3
Hmwk 3,4 Section 1.2 #23,25
Section 1.3 #13,17,24,27
Section 1.4 #2,4

Monday, 9/11/06       Quiz 2
Hmwk 2 Section 1.1 # 13,20  1.2 #12,14

Friday, 9/1/06        Hmwk 1 Section 1.1 #7, 10, 16, 21
Quiz 1 (on Section 1.1 #2, 7-10, 15-18, 21)
```

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.

```