Date of Award

6-1940

Level of Access Assigned by Author

Open-Access Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Abstract

This thesis considers a reorganization in the order of arrangement of certain topics in elementary and undergraduate mathematics; i.e. , arithmetic, algebra, plane geometry, solid geometry, trigonometry, analytic geometry, and calculus. Two terms important in the discussion are reorganization, the process of changing the relative position of topics or proofs in mathematics to an earlier or later place in the development of subject matter, and continuity, the logical order of topics arranged according to the need of one to explain the other.

The purpose of the thesis is two-fold; First, to show what arrangement of topics may be desirable; and, Second, to justify the proposed changes by showing that such a reorganization will make it possible to give a simpler and more complete presentation of mathematics without affecting the logical sequence of topics.

The discussion reviews the recent changes in elementary mathematics during the past forty years. These changes, in general, may be thought of as either of a general character indicating a trend or of a special character indicating a rearrangement in the order of particular topics.

The general arrangement of the thesis is somewhat as follows. It is observed that propositions in elementary mathematics have been proved by methods of analytic geometry and calculus. Proofs of certain propositions in plane geometry are possible by coordinate methods. When they are presented in algebra, these proofs are not only simple but provide further understanding of topics in algebra, such as graphs, ratio and proportion, and the operations of algebra. Proofs of certain propositions, or formulas, from elementary mathematics are possible by means of integration. Such proofs by calculus are too difficult to be presented in algebra. These proofs should be postponed to calculus where the simple method of integration justifies the omission of any earlier type of proof of these propositions in elementary mathematics.

In the conclusion of this discussion a rearrangement of topics in elementary mathematics (seventh year mathematics, eighth year mathematics, first year algebra, second course in algebra, and plane geometry) with special attention to the continuity of subject matter is given. Such a rearrangement, of necessity, implies changes in the order of some of the topics in later mathematics.

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