STATE UNIVERSITY COLLEGE AT BUFFALO

Department of Mathematics

Request for Course

I. Number and title of course

Mathematics 302 - Abstract Algebra II
II. Reasons for addition to the present curricula
A. The course is a continuation of Math 301, providing a completion of the fundamentals of abstract algebra and its applications.

B. Topics such as ring properties and field theory can be introduced. These topics are ordinarily left out in the first semester course.

III. Major objectives of the course
A. To introduce fundamental theorems concerning rings, ideals and fields.
B. To enable the student to be exposed gradually to abstract ideas and proofs, by means of illustrations and familiar examples, so that he /she may develop further facility in understanding abstract systems, their properties and applications.
IV. Topical Outline

A. Rings

1. Integers and divisibility

2. Euclidean domains and factorization

3. Ideals and congruences

4. Applications and examples

B. Fields
1. Finite dimensional extensions

2. Applications to polynomials

3. Applications to geometric constructions

4. Finite fields

5. Splitting fields and solvability

6. Applications from areas such as coding theory, cyclic codes, block designs, latin squares, etc.

V. Bibliography, texts, and readings
Birkhoff, G. and Maclane, S. A Survey of Modern Algebra. New York: Macmillan Co., 1953.

Fisher, J.L. Application Oriented Algebra, Harper & Row, 1977.

Gilbert, William J. Modern Algebra with Applications, New York: John Wiley & Sons, 1976.

Hillman & Alexanderson, A Trial Undergraduate Course in Abstract Algebra, Wadsworth, 1983.

Jacobson, N. Lectures in Abstract Algebra Vol. III. D. Van Nostrand Co. Inc., 1951.

McCoy, N.H. Rings and Ideals Buffalo, Mathematical Assoc. of America, La Salle, Illinois: The Open Court Pub. Co., 1948.

McCarthy, P. Algebraic Extensions of Fields. Waltham, Mass ., Blaisdell, 1966.

Sandler & Foster, Modern Algebra, Harper & Row, 1978

Van Der Waerden, B.L. Modern Algebra. Volume II, Ungar Publishing Co., New York, 1950.

VI. Presentation and Evaluation
Lectures, class discussions assigned problems, examinations.
VII. Prerequisite:
Math 301
VIII. Credit:
Three semester hours
IX. Statement of Approval
This revised course proposal was examined in accordance with recommended procedures and was approved by the faculty of the Mathematics Department

__________________________________Department Chair

X. Catalog Description
Mathematics 302: Abstract Algebra II.  A continuation of Math 301. Quotient fields of integral domains, polynomials rings, Euclidean domains, ideals, and factorization. Finite fields, extension fields, splitting fields, applications to geometric constructions and solvability, applications chosen from contemporary areas of coding theory, block designs, etc.
XI. Qualifications of faculty who will teach the course

All members of the Department of Mathematics

XII. Support Services required

Present classroom facilities are adequate.