### 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.
```