Mathematics is an interconnected subject with many concepts intersecting in various ways that allow for new understanding and research topics to arise. This paper gives an overview of mathematical knots, links, and tangles, and discusses the fundamental question in knot theory: how can we tell two knots apart? We present some ideas used to address this question such as knot colorability and knot determinants. We also combine these ideas in a survey of mathematical knots and tangles which culminates in an overview of DNA Topology. Finally, applications of knot theory to bio-medical research on various diseases such as cancer and leukemia is mentioned.
Knots, Tangles, and Their Applications to DNA
Faculty Mentor Name
Dr. Susan Abernathy
Funded by the Undergraduate Faculty Mentored Research Grant
The Knot Book by Colin Adams