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Introduction to Knot Theory

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About the Course

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.

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