Date of Award

12-2021

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Wallace, Laura

Abstract

This is an expository study of continued fractions collecting ideas from several different sources including textbooks and journal articles. This study focuses on several applications of continued fractions from a variety of levels and fields of mathematics. Studies begin with looking at a number of properties that pertain to continued fractions and then move on to show how applications of continued fractions is relevant to high school level mathematics including approximating irrational numbers and developing new ideas for understanding and solving quadratics equations. Focus then continues to more advanced applications such as those used in the studies of number theory and abstract algebra. One such application explores patterns found in the convergents of the infinite continued fraction for √d to find solutions to Pell's equation. We can use those patterns to look at the connections between finding solutions to Pell's equation and the convergents of the infinite continued fraction of √d. Another application involves using continued fractions to find the group of units of the ring of integers of the field Q(√d).

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