"Ritt’s Theorem and the Chebyshev Polynomials" by Eric Neuhaus

Date of Award

5-2025

Document Type

Thesis

Degree Name

Bachelor of Science

Department

Math & Statistics

First Advisor

Dr. William Ross

Second Advisor

Dr. Ovidiu Lipan

Abstract

We explore polynomial composition through Ritt’s Theorem and mondromy groups. J.F. Ritt asked the question of when a polynomial can be written as the composition of two other polynomials of smaller, nontrivial degree. Ritt’s Theorem provides a method for determining whether or not a polynomial is composite by observing the actions of its associated monodromy group, a group of permutations acting upon the roots of a given polynomial. In this work, we study the monodromy groups of the Chebyshev polynomials of the first and second kinds to uncover their compositional properties.

Available for download on Saturday, May 16, 2026

Included in

Mathematics Commons

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