Date of Award

4-2022

Degree Type

Thesis

Degree Name

Master of Science

Department

Math and Computer Science

Program

Other

Program

Mathematics

First Advisor/Chairperson

Joshua Thompson

Abstract

There are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles and the set of quandles created by non-oriented knots.

Access Type

Open Access

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