Date of Award
7-1971
Degree Type
Master's Essay - Restricted
Degree Name
Master of Science (MS)
Department
Mathematics, Statistics and Computer Science
First Advisor
Thomas A. Bronikowski
Abstract
Although at one time 'the study of continued fractions may have been more commonplace in advanced courses in mathematics, in recent years its importance has diminished due to the vast amount of new material available. What is attempted in this paper is to give an adequate introduction to the topic. The paper shows that real numbers may be expressed as continued fractions and also that power series and rational expressions may take continued fraction form. Included is an investigation of some of the criteria for convergence of continued fractions, one of which is an interesting application of Moebius transformations. The paper concludes with a method for determining square roots using second order matrices which is based on the theory of continued fractions.
Recommended Citation
Thompson, John D., "Continued Fractions" (1971). Master's Essays (1922 - ). 2886.
https://epublications.marquette.edu/essays/2886
Comments
An Essay Presented to the Mathematics Department of Marquette University as a Partial Requirement for a Master of Science Degree, Milwaukee, Wisconsin.