4
$\begingroup$

I am going to teach a 400-level topics class on knot theory at an American, mid-sized, public university. Prerequisites include multivariable calculus, linear algebra, and a proof course, but no exposure to topology or abstract algebra.

Do you know of resources for such a course? Notes, exercises, etc?

What I have so far:

$\endgroup$
  • 2
    $\begingroup$ Check out Topology Now!, Messer and Straffin $\endgroup$ – Ben Crowell Apr 12 '17 at 17:52
3
$\begingroup$

I don't know much about knot theory but I know that Meike Akveld taught knot theory at both high school and university level. Here's a bibliography of one of her courses at ETH Zürich:

https://www2.math.ethz.ch/education/bachelor/lectures/fs2015/math/knot/bibliography_FS2015.pdf

It includes Englisch and German books both for high school and university level. I only list English books for university level:

General books about knots - accessible to (under-)graduate students:

  • M.A. Armstrong, Basic Topology, Undergraduate Texts in Mathematics, Springer-Verlag, 1983 - Chapter 10 is devoted to knots.
  • G. Burde, H. Zieschang, Knots, Walter de Gruyter & Co., Berlin, 1985.
  • A.Kawauchi, A Survey of Knot Theory, Birkhäuser Verlag, Basel, 1996.
  • W.B.R. Lickorish, An Introduction to Knot Theory, Springer-Verlag. New York, 1997.
  • C. Livingston, Knotentheorie für Einsteiger, Vieweg, 1995 (also available in English).
  • K. Murasugi, Knot Theory & Its Applications, Chapters 5 and 6, Birkhäuser Boston, 2008.
  • J. Roberts, Knots Knotes, unpublished lecture notes, 2010, http://math.ucsd.edu/~justin/Roberts-Knotes-Jan2015.pdf.
  • D. Rolfsen, Knots and Links, AMS Chelsea Publishing, 2003.

There are still old exercises and solutions from the class available online here. They usually get deleted a year or two after the class, so I'd download them just in case. Plus, you can find some hand-drawn examples on the lecture website itself.

$\endgroup$
4
$\begingroup$

You may find the SageMath knot and links capabilities useful for computation and visualization.

The Knot Atlas might be a bit more comprehensive than you are looking for but is certainly a reference to be quite aware of.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.