Knots, Tangles, and Their Applications To DNA

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 biomedical research on various diseases such as cancer and leukemia are mentioned.