Master's Theses

Date of Award

Spring 1981

Degree Name

Master of Arts (MA)

Department

Math

Advisor

Charles Votaw

Abstract

The purpose of this paper is to study the concept of a greatest common divisor in such a way that it may be used as an enrichment topic at the senior high school level. In order to do this, the concept has been approached from both a theoretic and an applied point of view. In the theoretical areas, the algebraic structures involved are explored, along with the Euclidean algorithm, which provides a means for computing the greatest common divisor of two elements in a Euclidean ring and expressing it as a linear combination of these elements. In the more applied sections, such an algorithm is programmed for a computer. It is used in a BASIC program which will compute (a, b) in the ring of polynomial forms over a field and express it as a linear combination of a and b. Some other Euclidean rings, which the teacher might find instructive to explore with a class, are also discussed.

Rights

Copyright 1981 Wanda Sue Reves.

Comments

Notice: This material may be protected by copyright law (Title 17 U.S. Code).

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