Department of Mathematical Sciences, Northern Illinois University

## MATH 421, Spring 2004

#### 9:00-9:50, M W F, DU 328

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

OFFICE HOURS: MWF 10:00-11:00, or by appointment.

My faculty homepage   |   My personal homepage

Review for the Final

The Final Exam is scheduled for Wednesday, May 5, 8:00-9:50 a.m., in DU 328

There will be a review session at 3:00 p.m. on Monday, May 3, in DU 328.

Some new handouts: Quiz 6 solutions   |   Hmwk 8 solutions   |   Spring 1991 final exam

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, 2nd Ed, by John Beachy and William Blair

OnLine Study Guide for the text

SYLLABUS: Chapter Three, Groups; Chapter Four, Polynomials; Chapter Five, Commutative Rings; Chapter Six, Fields (6.1-6.2)
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 2 hour exams worth 100 points each, homework and quizzes worth a total of 200 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.
Please note that the last day for undergraduates to withdraw is Friday, March 5.

FINAL: The final exam is scheduled for Wednesday, May 5, 8:00-9:50 a.m.

HANDOUTS:

For Exam I:   The retest questions (takehome questions)
For Exam II:   Overview of commutative rings   |   Review problems for Exam 2   |   Solutions

ASSIGNMENTS:

``` Due date       Section    Problems

Friday, 1/16   HMWK 1      (Hand in)
3.1       8, 9
3.2       6, 14, 15, 16, 17, 22

Friday, 1/23   QUIZ 1   covering the following problems:
3.3       2, 4, 5, 8, 9
3.4       2, 4, 8, 13, 14

Friday, 1/30   HMWK 2      (Hand in)
3.5       7, 11, 15, 16

Friday, 2/6    QUIZ 2   covering section 3.6
HMWK 3      (Hand in)
3.6       6, 16

Friday, 2/13   HMWK 4      (Hand in)
3.7       4, 5, 7a,e,f, 12, 13

Friday, 2/20   HMWK 5     (Hand in)
3.8       4, 11, 14, 15, 23

Wednesday 2/25 EXAM I   covering Chapter 3

QUIZ 3   covering sections 4.1, 4.2

Friday, 3/19   HMWK 6     (Hand in)
4.1       18, 19, 22
4.2       2b,d, 5b,c, 10, 17b,d
4.3       5b,d, 9, 12

Friday, 3/26   QUIZ 4   covering sections 4.3, 4.4, 5.1
HMWK 7     (Hand in)
4.4       11, 12, 15d,f, 17
5.1       4, 9

Monday, 4/3    HMWK 8     (Hand in)
5.2       1, 4, 16, 17

Monday, 4/12   QUIZ 5   covering problems in 5.3
6 - 14 (Not handed in)

Friday, 4/16   EXAM 2   covering 4.1-4.4, 5.1-5.3
(NOTE THE CHANGE OF DATE)

Monday, 4/27   HMWK 8      (Hand in)
6.1        1d,f, 3, 4
6.2        1d, 3, 6
QUIZ 6   covering 6.1 and 6.2
```

SCHEDULE OF LECTURES: (REVISED)

```Monday      Wednesday    Friday           M Tu  W Th  F
3.1,3.2       3.3         3.3       JAN 12 13 14 15 16
Holiday        3.4         3.4           19 20 21 22 23
3.5           3.5         3.6           26 27 28 29 30
3.6           3.6         3.7       FEB  2  3  4  5  6
3.7           3.7         3.8            9 10 11 12 13
3.8           3.8         3.8           16 17 18 19 20
3.8          EXAM 1       4.1           23 24 25 26 27
4.1           4.2         4.3       MAR  1  2  3  4  5
SPRING BREAK                        8  9 10 11 12
4.3           4.4         4.4           15 16 17 18 19
5.1           5.1         5.1           22 23 24 25 26
5.2           5.2         5.2           29 30 31  1  2
5.3           5.3         5.3       APR  5  6  7  8  9
5.3          Review      EXAM 2         12 13 14 15 16
6.1           6.1         6.2           19 20 21 22 23
6.2           6.3      Reading Day      26 27 28 29 30
FINAL EXAM  Wednesday, 8-9:50 AM    MAY  3  4  5  6  7
```