Date of Award

3-26-2021

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Department of Mathematics

First Advisor

Sunil Chebolu

Abstract

Knots are used everyday by all people, mathematicians and non-mathematicians alike. There are certain subsets of people that use knots more frequently than others such as sailors or members of the Scouting Movement.

A mathematical knot is a subset of 3-space that is homeomorphic to the unit circle. A knot used in non-mathematical circles is generally considered when two strings, etc. are wrapped around each other, with the ends potentially hanging. We introduce and explain through examples 1) how mathematical knots differ from general knots; 2) how mathematical knots differ from other mathematical knots via methods of deformation, colorability, and polynomials; 3) apply mathematical methods of knot determinations to practical knots to see how practical knots might behave as mathematical knots.

Comments

Imported from Sanchez_ilstu_0092N_11913.pdf

DOI

https://doi.org/10.30707/ETD2021.20220215070318683439.999977

Page Count

63

Download

Share

COinS