## Knot Theory, Knot PracticeFreshman Advising Seminar 18.A39Wednesdays 3-5pm Room 2-136 Advisor: Kyle Ormsby (ormsby@math.mit.edu, office 2-275)Associate Advisor: Danny Shi (dannyshi@mit.edu)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....)Syllabus [pdf] 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.## Participants- Shi An
- Ravi Bajaj
- Yongquan Lu
- Scott McDonald
- Marissa Stephens
- Anderson Wang
- Patrick Yang
- Angel Yu
## Schedule 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
Kyle M. Ormsby Department of Mathematics 2-275 Massachusetts Institute of Technology Cambridge, MA 02139 Email: ormsby@math.mit.edu Web: http://math.mit.edu/~ormsby |