Department of Mathematical Sciences, Northern Illinois University

MATH 421/521, Fall 2009

10:00-10:50 M W F, DU 428

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

OFFICE HOURS: M W F 11:00-12:00 (You can always make an appointment at another time.)

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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

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

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 500 points, with 2 hour exams worth 100 points each, homework 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 scheduled for Friday, October 2.   Solutions
The second exam has been scheduled for Friday, November 13.

PLEASE NOTE: Exam 2 has been rescheduled for Monday, November 16.
Here are some sample questions.   |   Review of rings. (I just made some revisions.)

FINAL: The final exam is scheduled for Monday, December 7, 10:00-11:50 AM.
Review material:   groups

ASSIGNMENTS:

Due date  Assignment  Section  Problems

Fri,  8/28    HMWK 1     3.2    #22, 27 
                         3.3    #15, 16, 17

Mon,  9/14    HMWK 2     3.4    #11, 19
                         3.5    #19
                         3.6    #7, 14, 19, 21, 22

Wed,  9/23    HMWK 3     3.7    #1, 2, 7, 15, 16, 18, 28, 31
                                Note: the last two are from the Study Guide

Mon,  9/28    HMWK 4     3.8    #2, 5, 7, 13, 14, 23, 40, 41

Mon, 10/12    HMWK 5     4.1    #18 - 20
                         4.2    #2b, 3b, 4b, 5b, 6b, 7b, 8, 11, 12

Wed, 10/21    HMWK 6     4.3    #12,15,19,21b,21d,21f,22,23
                         4.4    #4(b,d),5(b,c),9,14

Wed, 10/28    HMWK 7     5.1    #3(b,d,f),7,8,11,16,18,19,20

Mon, 11/09    HMWK 8     5.2    #15,18
                         5.3    #7,9,11,12,13,14,24,25

Mon, 11/16    EXAM 2     This will cover 4.1-4.4 and 5.1-5.3.

Mon, 11/23    EXAM 2     RETEST, as announced in class

Wed, 12/02    HMWK 9     6.1    #1(d,f),2-4
                         6.2    #2(b),4,5,9

SCHEDULE OF LECTURES: (TENTATIVE)

Monday      Wednesday    Friday           M Tu  W Th  F
 3.1,3.2       3.3         3.3       AUG 24 25 26 27 28
 3.4           3.5         3.6       SEP 31  1  2  3  4
Holiday        3.6         3.6            7  8  9 10 11
 3.7           3.7         3.7           14 15 16 17 18
 3.8           3.8         3.8           21 22 23 24 25
 3.8           REV        EXAM 1         28 29 30  1  2
 4.1           4.2         4.3       OCT  5  6  7  8  9
 4.3           4.4         4.4           12 13 14 15 16
 5.1           5.1         5.1           19 20 21 22 23
 5.2           5.2         5.2           26 27 28 29 30
 5.3           5.3         5.3       NOV  2  3  4  5  6
 5.4           5.4        EXAM 2          9 20 11 12 13
 6.1           6.1         6.1           16 17 18 19 20
 6.2          Holiday     Holiday        23 24 25 26 27
 6.2           6.2         6.3       DEC 30  1  2  3  4
 FINAL EXAM   Monday, 10-11:50 AM         7  8  9 10 11

ACADEMIC CONDUCT: Academic honesty and mutual respect (student with student and instructor with student) are expected in this course. Mutual respect means being on time for class and not leaving early, being prepared to give full attention to class work, not reading newspapers or other material in class, not using cell phones or pagers during class time, and not looking at another student's work during exams. Academic misconduct, as defined by the Student Judicial Code, will not be treated lightly.

CAAR STATEMENT: If you have specific physical, psychiatric, or learning disabilities and require accomodations, please let me know early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to the Center for Access Ability Resources located in the Health Services Building, 4th floor.