Department of Computer Science
College of Computer Studies
Course
Code: ICSM219
Course
Title: Abstract Algebra
Credit:
3 units
Prerequisite(s):
Discrete Mathematics (ICSM218)
Term:
Second Semester
School
Year: 2004 – 2005
Schedule: 9:00 A.M. – 10:30 AM (MW)
Instructor: Bernardo R. Marquez, Ph.D.
E-mail: bernard@adnu.edu.ph
Consultation
Hours: 2:00 P.M. – 3:00 P.M. (TTh)
6:00 P.M. – 9:00 P.M. (Th)
2:00 P.M. – 4:30 P.M. (F)
Mathematics is populated by an enormous variety of
sets and operations on the elements of these sets. These sets include the sets
of integers, rational numbers, real numbers, and complex numbers and also the
sets of matrices, polynomials, and continuous functions. However, many of these
sets together with some operations on their elements turn out to be
manifestations of certain algebraic structures. This discovery led to the
axiomatic approach to the study of algebra.
This course covers the basic concepts of abstract
algebra. The students will be provided with the opportunity to encounter the
different algebraic structures such as groups, rings, fields, and integral domains.
Illustrations of the structures will be taken from other branches of
mathematics such as number theory, linear algebra, and calculus. The course
heavily rests on the axiomatic or deductive method.
At the end of the semester, the
students are expected to:
|
1. |
Explain
and illustrate the different algebraic structures. |
|
2. |
Prove
theorems on the properties of these algebraic structures. |
|
3. |
Manifest appreciation of and interest in the various mathematical concepts, and demonstrate positive values and attitudes acquired from mathematics as a discipline. |
|
Topics/Content Area |
Time Frame (in hrs.) |
|
I. Groups and subgroups A. Binary operations B. Isomorphic binary structures C. Groups D. Subgroups E. Cyclic groups and generators |
18 |
|
II. More groups and cosets A. Groups of permutations B. Cosets and the theorem of Lagrange C. Direct products |
12 |
|
III. Homomorphisms and factor groups A. Homomorphisms B. Factor groups |
9 |
|
IV. Introduction to rings and fields A.
Rings and fields B.
Integral domains |
9 |
Note: (1) Four meetings are
allotted to the four major examinations.
(2) Some topics may be deleted or added depending on the
available time.
Boardwork,
Seatwork, Quizzes, Preliminary Examination, Mid-term Examination, Pre-final Examination,
and Final Examination
CFRS = 40%CS + 10%PE + 20%ME + 10%PF + 20%FE
CS = 60%Q +
40%BS
|
where: |
CFRS |
= |
Total Converted Final Raw
Score |
|
|
CS |
= |
Class Standing |
|
|
PE |
= |
Preliminary Examination Raw
Score over the Perfect Score |
|
|
ME |
= |
Mid-term Examination Raw
Score over the Perfect Score |
|
|
PF |
= |
Pre-final Examination Raw
Score over the Perfect Score |
|
|
FE |
= |
Final Examination Raw Score
over the Perfect Score |
|
|
Q |
= |
Total Raw Score in the Quizzes
over the Total Perfect Score |
|
|
BS |
= |
Boardwork\Seatwork Grade |
Textbook
Fraleigh, John B. A First Course in
Abstract Algebra. 6th ed. Singapore: Pearson Education Asia Pte. Ltd.,
2000.
Books
Birkhoff, Garrett, and MacLane, Saunders.
A Survey of Modern Algebra. New York: The MacMillan Pub. Co., 1953.
Gilbert, Jimmie and Gilbert, Linda. Elements
of Modern Algebra. 4th ed. Boston: PWS Pub. Co., 1996.
Goldstein, Larry Joel. Abstract Algebra:
A First Course. New Jersey: Prentice-Hall, Inc., 1973.
Herstein, I. N. Abstract Algebra. New York: The
MacMillan Pub. Co., 1986.
McCoy, Neal Henry. Introduction to Modern Algebra. Boston: Allyn and Bacon, Inc., 1968.
web.usna.navy.mil/~wdj/book/
www.math.miami.edu/~ec/book/
www.math.niu.edu/~beachy/aaol/
www.math.niu.edu/~rusin/known-math/index/20-XX.html
www.wikipedia.org/wiki/Abstract_algebra
Abridged
Version
11-10-03
(First Printing)
11-05-04
(Second Printing)