Publication Date

6-3-1966

Abstract

In asserting that people in other fields often tend to be afraid to use mathematics, F.K. Mechta, an economist, expressed an uncertainty which contributes to the hesitancy to use mathematics. “Mathematics is tricky, it maintains silence, does its work quietly; and when we do not understand its ways and misinterpret its message, it just smiles. It never loses its temper, never laughs; we can observe a suppressed smile on its lips. Such is mathematics.” It is the purpose of this paper to conduct a brief survey of the applications of difference equations. The use of these equations is often rather elementary, frequently involving little material more technical than college algebra. An individual does not necessarily need a calculus background to be able to apply them. In the research for this work, applications of difference equations were looked for in the social and physical sciences. This paper covers the types of applications found, and the way they were developed. There is particular emphasis on what is left for the mathematician to do; what he can do to help these other fields benefit from mathematics. It will be sometimes noted throughout the paper whither or not the uniqueness of the solution has been checked for by each author. The first section in this paper is an introduction to difference equations. This section includes a brief summary of some of the theory of difference equations with emphasis on methods of solution, as well as a study of difference equations in probability. In the remaining section, the types of applications found in different fields are reviewed.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Judah Isser Rosenblatt

Second Committee Member

Julius Rubin Blum

Third Committee Member

Abraham P. Hillman

Language

English

Document Type

Thesis

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