Knot Theory, Knot PracticeFreshman Advising Seminar 18.A39
Advisor: Kyle Ormsby (email@example.com, office 2-275)
Associate Advisor: Danny Shi (firstname.lastname@example.org)
Textbook: The Knot Book by Colin C. Adams, available through the AMS, online booksellers, and the Coop. (The cheapest I've found so far was on a South American river....)
The earbuds in your bookbag know all about them -- do you? Knots pervade culture, science, and technology. They also inhabit a beautiful niche in mathematics that we'll examine in this seminar.
Tie a figure-eight in a rope and fuse the ends. Can you untie the twisted loop into a circle? If you think it's impossible but your friend thinks there's hope, how could you convince her? One persuasive proof (in all of math, but especially in knot theory) might involve assigning a number (or generlization of a number!) to your knot that doesn't change as you attempt to untie it. Such a quantity is called an invariant. If the invariant of the figure-eight differs from the unknot (circle), then you can convince your friend!We will construct and compute knot invariants in this seminar. There are no prerequisites beyond an interest in knots.
The regular class meetings will occur on Wednesdays from 3:00 to 5:00pm in 2-136. Students will lead discussions of relevant mathematical topics taken from Colin Adams's The Knot Book and other sources.
Sep 5 - First meeting: Perspectives on knots, Reidemeister moves
Kyle M. Ormsby
Department of Mathematics 2-275
Massachusetts Institute of Technology
Cambridge, MA 02139