Modern Algebra I - Fall 2002

MATH 431

MODERN ALGEBRA I

FALL 2004

Time & Place: 8:35 – 9:50 TR, Science 106

Instructor: Roger G. Olson, Ph.D.

Office: Science 018 (basement) Phone: 866-6295 E-mail: rogero

Office Hours: 11 - 12:30, 2 - 4 T, 1 - 4 W, 2-4 R, or by appointment

TEXT

C.C. Pinter, A Book of Abstract Algebra, Second Edition, McGraw-Hill 1990

A POSSIBLY USEFUL WEB SITE: Abstract Algebra Online

COURSE CATALOG DESCRIPTION

This course is that portion of Abstract Algebra that studies elementary group theory. It considers the properties of groups, subgroups, and functions; this leads to groups of permutations and groups isomorphic to them. Homomorphisms of groups along with the induced quotient groups culminate in the Fundamental Homomorphism Theorem; this rounds out the course. Either Math 432 or this course fulfills the requirement for Modern Algebra by the Indiana State Department of Education for Secondary Teacher Education students of mathematics.

REQUIREMENTS AND GRADING

The course will cover sequentially the first sixteen chapters of the text. Understanding rigorous mathematical proofs is an essential part of this course.

Your course grade will be based on four criteria: Examinations (two in addition to the final), written homework assignments, class presentations, and attendance. Attendance will be taken each class period and will affect your grade by a maximum of two percentage points in either direction. The criteria will be weighted in the following manner:

Examinations:	45%
Homework:	10%
Presentation:	45%
Attendance:	+/-2%

NOTES ON GRADING CRITERIA

There will be an assignment from each chapter covered in the text. I will always announce when an assignment is due, however, in case for any reason you don't hear me give the due date, the game plan will always be as follows: Assignments should be attempted by the next class period (so that questions may be asked in class) and are due at the end of the second class period after the appropriate chapter is finished. E.g., if I complete Chapter 4 on Thursday September 23, the assignment for Chapter 4 is due at the end of the Thursday September 30 class. Late assignments will not be accepted except under extreme circumstances.

I cannot stress enough the importance that doing your homework has to your success in an advanced math course such as this. Math is not a "spectator sport". Even though class attendance and participation will help you a great deal in keeping up with the material, you cannot adequately learn math without practicing it on your own.

Your assignments must be NEATLY DONE, and all work must be shown. Multiple pages must be STAPLED, and each page must have a smooth edge - pages torn out of spiral binders are NOT ACCEPTABLE.

The first two exams will be given during the regular class period (approximately September 23 and November 4), and the third will be given in finals week at 10am on December 14. They will consist mostly of short proofs and definitions, with an occasional computational problem. If you keep up with class notes and do all homework assignments in a timely manner you will be adequately prepared for the exams.

Your class presentations will be given by your team and consist of explanation of proofs and problems from the text. Each team member should put forth the appropriate proportional amount of the effort over the course of the semester. I'll assign problem numbers at the end of the class period before your team's presentation.

Presentation Team Problems and HW Assignments (Problem numbers in parentheses are grouped together as one.)
Chapter	Turn In	Team Presentations
2 - Binary Operations	A1, B1	A2, 5, 6; B2, 3, 5, 6; D1, 2, 3
3 - Definition of Groups	A3, E	B1, 5; C1, 2, 3; D; F(2, 4), 5, 6, 7
4 - Elementary Properties of Groups	A4, D1, 2, 3	A5, 6; B4, 5, 6; C3, 6; F1, 2; H8
5 - Subgroups	A1	A2, 3, 4; B2, 4; C2; D1, 3; F2; E1
6 - Functions	A2, E5	A1, 3; B3, 5; C4; D1, 3, 5; F(1-4); E3
7 - Permutation Groups	A1, 2	A4; B1, 2; C2; E1, 2; F1, 2; H1, 3
8 - Permutations of a Finite Set	A4a-d	A1a,f, 2a,d, 3a,d, 5, 6; B1, 3; C1a,c, 2; E1
9 - Isomorphism	A2, I3	A3; B1, 2, 3; C1, 2, 3; D2, 3; E2
10 - Order of Group Elements	B4	B1, 2, 3, 5; C2, 3; D1, 3; F1
11 - Cyclic Groups	A1	A1, 2, 3, 4, 5; B2, 4; C1; D1
12 - Partitions and Equivalence Relations	A1	A1; B1, 2; C2, 3, 5; D1, 2; E3
13 - Counting Cosets	A3, 4, 5	A1, 2; B1, 2, 3, 4; C1, 2, 3
14 - Homomorphisms	A1	A2, 3, 5; B1, 2; C1, 2, 4; D2
15 - Quotient Groups	A1	A2, 3, 4, 5, 6; B1, 2, 3; C1
16 - The Fundamental Homomorphism Theorem	A1	A2, 3, 4; B1, 2, 3; C1, 2, 3

Presentation Teams

GRADING SCALE

Letter Grade	Overall Percent
A	93 - 100
A-	90 - 92
B+	87 - 89
B	83 - 86
B-	80 - 82
C+	77 - 79
C	73 - 76
C-	70 - 72
D+	67 - 69
D	60 - 66