- Colin Adams,
*The Knot Book* - Dale Rolfsen,
*Knots and Links*

- Week 1. Lecture 1, Lecture 2. The first three homework exercises are in these notes. One was not mentioned in class, namely...

Exercise I.3. Prove that there are only a countably infinite number of equivalence classes of knots in**R**^{3}. - Week 2. Lecture 3, Lecture 4. We discussed the first 5 exercises
at the beginning of class Thursday. There are more exercises in the
notes.

**Note:**A typo was pointed out in exercise I.8 in the notes: "sum to 1" should have said "sum to 0".

- Week 3. Lecture 5, Lecture 6. We discussed the exercises from last
week at the beginning of class Tuesday. If you missed because of the
weather, and would like a recap, feel free to drop by before class on
Thursday.

**Note:**Another typo spotted (missing negatives): Exercise II.3, you should prove lk(J,K) = lk(K,J) = -lk(-J,K) = -lk(J,-K).

- Week 4. Lecture 7. Thursday of this week (2/10) will be devoted to presenting homework problems.
- Week 5. Lecture 8 (there is an exercise 15 here which is scratched out.. it's obvious, so skip it if you like). Lecture 9.
- Week 6. We mostly worked exercises Tuesday. After that, we started a new section on the link group and topology. Lecture 10. Thursday we began a section on topology. Exercises III.1--III.6 are to be
**turned in**next Thursday. Lecture 11. Here are some notes on the problems: 29 topologies on a 3 point set, ε-δ implies continuity. - Fixes: In Lecture 11, I forgot to fix the expresssion for the ``Manhattan metric'': as mentioned in class, the expression is different when x = x': you should then get |y-y'|. Another point to make is that this is not what is usually called the ``Manhattan metric''... oh well, we'll call it that.
- Week 7. Lecture 12. There is a minor
discrepancy with the theorem numbering here because I changed the order in
class (10, 11 and 12 were cyclically permuted). The exercises in Lecture
12 are due next Tuesday (March 8). For exercise 7, you only need to hand
in the proofs of parts 3 and 4 (though you should prove each part for
yourself). Here is the proof for part 3. Lecture 13. In the exercise on
stereographic projection, it's probably easier to write down the inverse
π
^{-1}:**R**^{n}→ S^{n}, and write it down as a map π^{-1}:**R**^{n}→**R**^{n+1}(so you should have n+1 functions of n variables). - Week 8. Lecture 14. Lecture 15. The problem(s) here are not to be turned in. We will discuss them in class later.
- Week 9. Lecture 16 and Lecture 17.
- Week 10 (3/29,3/31). Circumstances beyond my control have forced me to be away this week. Professor Dunfield will be filling in for me on Tuesday: please make sure you show up on time for class. There will be no class on Thursday. Here are Profesor Dunfield's lecture (much better pictures than mine!). Make sure you've read through these, including the parts he didn't get to. We will pick up from here next week.
- Week 11. Lecture 18 and Lecture 19.
- Week 12. Lecture 20 and Lecture 21.
- Week 13. Lecture 22 and Lecture 23.
- Week 14. Tuesday we went over exercises. Lecture 24.
- Week 15. Lecture 25, the last lecture. Hope everyone enjoyed the semester and learned something interesting. If you want to talk about anything we did, or learn more about anything this semester, let me know and I'd be happy talk about it, or to point you in the right direction.
- The final exam is here. It's just for fun, but give it a try...

- Knot tables from Rolfsen's book (on Dror Bar-Natan's page) with lots of invariants computed.
- KnotPlot. This is the site for knot visualization software package, knotplot.
- knot programs: Here is an email from a colleague with some knot theory programs. I can't say it any better, so I just copied the email:

"For small knots with known names, the easiest way is just to look this stuff up at either

http://katlas.math.toronto.edu/wiki/Main_Page

or at

http://www.indiana.edu/~knotinfo/

The later site has a Knot Finder:

http://www.indiana.edu/~knotinfo/knotfinder.php

from which can usually tell you the name if you don't know it. You have to write out the DT code for the knot, though, but there's a online KnotSketcher link there... Another simple tool to find DT codes is

http://www.math.uic.edu/t3m/plink/doc/

For more general knots, if the students have Mathematica then Dror has a pretty powerful package for computing many types of knot invariants:

http://katlas.math.toronto.edu/wiki/The_Mathematica_Package_KnotTheory

which has been expanded on here:

http://math.ict.edu.rs/"

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