Week 
Date of Monday 
Topics 
Example sheet 
Lecture notes 
Comments 
1 
Jan. 5 
Basic definitions. Isotopy. Isotopy invariants. 
One 

Make knots out of old shoelaces, sticks,
DNA,
Tangles,
or Klixx
(as seen in class!) 
2 
Jan. 12 
Coloring. Checkerboards. Martix of coloring equations
and the determinant. 
Two 

KnotInfo and
Knot
Atlas. 
3 
Jan. 19 
Determinants. The coloring group. Examples. 
Three 

The coloring group is the first homology of the branched
double cover [Introduction to Knot Theory, Crowell and Fox]. 
4 
Jan. 26 
Mirrors. Inversions. Codes. Alexander polynomials. 
Four 

Hoste, Thistlethwaite, and Weeks use DT codes to find the
first 1,701,936
knots. 
5 
Feb. 2 
Alexander polynomials and connect sums. Bridge position. Plats. 
Five 

Bridge presentation can be exponentially more complicated than
plat presentation. 
6 
Feb. 9 
Flypes. Braids (generators and relations) and their closures. Seifert circles. 
Six 

A braid applet by
Stephen Bigelow. 
7 
Feb. 16 
Every knot is isotopic to a braid closure.
Kauffman states. Kauffman polynomial. 
Seven 

Kauffman's webpage. Alexander's
paper on
the Alexander polynomial. 
8 
Feb. 23 
Jones polynomial. Span and crossing number. 
Eight 

An online calculator
for the Jones polynomial. 
9 
Mar. 2 
Tangles. Surfaces. 
Nine 

Slides
from a lecture by John Conway. (He uses a different sign
convention from Sanderson's.) Conway's ZIP proof, by
Francis and Weeks. 
10 
Mar. 9 
Knot genus and the Alexander polynomial. Conway, HOMFLY
polynomials. Relative strength of invariants. Video. 
Ten 

Stills from the Not
Knot video. Lots of knots,
collected by BarNatan. 