Department of Mathematical Sciences, Northern Illinois University

## MATH 421/521, Fall 2008

#### 6:00-7:15 M W, DU 302

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

OFFICE HOURS: M W 5:00-6:00 pm. (You can always make an appointment at another time.)

My faculty homepage   |   My personal homepage

COURSE DESCRIPTION: Algebra II (3). Homomorphisms and factor groups; commutative rings, with emphasis on polynomial rings; fields and algebraic extensions. Applications to classical geometric problems.

TEXT: Abstract Algebra, 3nd Ed, by John Beachy and William Blair. The text is required, and is essential as a reference.
Study Guide for this edition of the text (in pdf format)     OnLine Study Guide for the previous edition
Revised: Chapter 4 Problems with Solutions
Chapter 5 Problems with Solutions

SYLLABUS: Chapter Four, Polynomials (4.1-4.4); Chapter Three, Groups (3.6-3.8); Chapter Five, Commutative Rings (5.1-5.4); Chapter Six, Fields (6.1-6.3)
Handout

COURSE OBJECTIVES: The student is expected to continue learning the basic results on groups, rings, and fields. The concepts of homomorphism and quotient structure (using an appropriate equivalence relation) are of particular importance. The course will end with a proof of the impossibility of certain geometric constructions.

COURSE PREREQUISITE: MATH 420 (you should have a solid C)

GRADING: Grades will be assigned on the basis of 600 points, with 3 hour exams worth 100 points each, homework and quizzes worth a total of 100 points, and the final exam worth 200 points.
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.

EXAMS:
The first exam has been rescheduled for Wednesday, September 24.
The second exam has been rescheduled for Wednesday, October 22.
Here are two previous exams that can serve as sample for Exam 2:   2004   1996
The third exam has been rescheduled for Wednesday, November 19, and will cover 5.1-5.3.

FINAL: The final exam is scheduled for Monday, December 8, 6:00-7:50 PM.
Review material:   groups   |   rings

ASSIGNMENTS:

```Due date  Assignment  Section  Problems

Mon, 9/8     HMWK 1     4.1    #13,14,19,24
4.2    #2(a,c),3(b,c),4(b,d),8,9,12

Mon, 9/15    HMWK 2     4.3    #12,15,18,21(b,d,f),22,23
4.4    #3(a,c),5(b,c),9,16

Mon, 9/29    HMWK 3     3.6    #7,8,10,19,21,23

Mon, 10/8    HMWK 4     3.7    #2,4,7,14,15,18

Mon, 10/13   HMWK 5     3.8    #2,5,6,7,13,14,18,20,21,24

Mon, 11/4    HMWK 6     5.1    #3(b,d,f),4,7,8,9,10,11,16,18,20

Wed, 11/12   HMWK 7     5.2    #6,7,8,13,17
5.3    #4,9,11,12,13,14,25

Mon, 12/1    HMWK 8     6.1    #1(d,f),2-6

Wed, 12/3    HMWK 9     6.2    #2(b),4,5,9

```

SCHEDULE OF LECTURES: (TENTATIVE)

```Monday      Wednesday    Friday           M Tu  W Th  F
4.1           4.2                   AUG 25 26 27 28 29
Holiday        4.3                   SEP  1  2  3  4  5
4.3           4.4                        8  9 10 11 12
3.6          EXAM 1                     15 16 17 18 19
3.6           3.7                       22 23 24 25 26
3.7           3.7                       29 30  1  2  3
3.8           3.8                   OCT  6  7  8  9 10
3.8          EXAM 2                     13 14 15 16 17
5.1           5.1                       20 21 22 23 24
5.2           5.2                       27 28 29 30 31
5.3           5.3                   NOV  3  4  5  6  7
5.4          EXAM 3                     10 11 12 13 14
6.1           6.1                       17 18 19 20 21
6.2         Holiday                     24 25 26 27 28
6.2           6.3                   DEC  1  2  3  4  5
FINAL                                     8  9 10 11 12
```