Date of Award

4-17-2008

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Mihaly Bakonyi - Chair

Second Advisor

Lifeng Ding

Third Advisor

Irme Patyi

Abstract

In this paper we examine continuous functions which on the surface seem to defy well-known mathematical principles. Before describing these functions, we introduce the Baire Category theorem and the Cantor set, which are critical in describing some of the functions and counterexamples. We then describe generic continuous functions, which are nowhere differentiable and monotone on no interval, and we include an example of such a function. We then construct a more conceptually challenging function, one which is everywhere differentiable but monotone on no interval. We also examine the Cantor function, a nonconstant continuous function with a zero derivative almost everywhere. The final section deals with products of derivatives.

Included in

Mathematics Commons

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