Text: The Knot Book, by Colin Adams
Why study knots? For one thing, just because it's fun to learn significant mathematics about objects you can carry in your pocket. For another, without extensive prerequisites, you can learn enough about the subject to work nontrivial problems and to understand the statement of current research problems in knot theory and applications to research in other fields such as genetics and chemistry.
Knot theory is part of an area of mathematics called topology, an area only about 100 years old. Partly for that reason, topology seldom appears in the K-14 curriculum, though it easily could be introduced at these levels. Also knot theory gives an excellent illustration of the interplay of theoretical and applied mathematics. Founded by a physicist and initially focussed on a particular application, knot theory became pure mathematics, dwindled to something of a backwater due to lack of progress, flowered dramatically after a single discovery in 1985, and now serves as both a means and an object of study in both pure and applied mathematics.
Using Adams' book, we will learn techniques for identifying and classifying knots, including the knot invariants discovered in the 1980's. As time permits, we will learn about applications in other sciences and in pure mathematics.
Grades will be based on weekly classwork, weekly homework, and a project.
For more information send e-mail to < arms@math.washington.edu>.