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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:

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    $\begingroup$ Check out Topology Now!, Messer and Straffin $\endgroup$
    – user507
    Commented Apr 12, 2017 at 17:52

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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  • J. Roberts, Knots Knotes, unpublished lecture notes, 2010, http://math.ucsd.edu/~justin/Roberts-Knotes-Jan2015.pdf.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.

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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.

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