Introduction to Knot Theory

Introduction to Knot Theory

In this course, Professor Colin Adams (Williams College) explores knot theory. In the first mini-lecture, we introduce knot theory and take a look at some important historical knots as well as basic mathematical knots. In the second mini-lecture, we look at composition of knots and discuss why scientists became invested in knots in the late 19th century. In the third mini-lecture, we explore different types of knots based on the number of crossings, where we see that mathematicians have already determined 1,701,936 knots. In the fourth mini-lecture, we discuss applications of knot theory, such as in DNA, chemotherapy, and synthetic chemistry, which show why we care about knot theory today. In the fifth mini-lecture, we introduce the petal number of knots and look at petal permutations.

Introduction to Knot Theory

In this mini-lecture, we provide an introduction to knot theory. In particular, we consider: (i) famous knots in history such as the Gordian knot, which was cut by Alexander the Great; (ii) how to describe a mathematical knot; (iii) deforming a knot, which does not change it; (iv) the trivial knot (or unknot) and the trefoil knot; (v) a table of knots; (vi) links, which are a set of knots that are tangled up with each other; (vii) Odin’s knot depicted in a stone carving by Vikings; (viii) the Borromeo family crest, which includes an image of Borromean rings – these rings named after the family; (ix) Brunnian links; (x) Brunnian clothes; (xi) Celtic knots; (xii) knots in seafaring, including the Ashley Book of Knots; and (xiii) The Knot Book<\em> by Colin Adams.