Week 
Date of Monday 
Topics 
Example sheet 
Lecture notes 
Comments 
1 
Jan. 7 
Basic definitions. Isotopy. Isotopy invariants. 
One 
One 
An online knot table. 
2 
Jan. 14 
Coloring. Checkerboards. Martix of coloring equations
and the determinant. 
Two 
Two 

3 
Jan. 21 
Determinants. The coloring group. Examples. 
Three 
Three 

4 
Jan. 28 
Mirrors. Inversions. Codes. Alexander polynomials. 
Four 
Four 
Fixed the statement of Exercise 4.3. Hoste, Thistlethwaite,
and Weeks use DT codes to find the first 1,701,936
knots. (Takes half a minute to download.) 
5 
Feb. 4 
Connect sums. Bridge position. Plats. 
None. 
None. 

6 
Feb. 11 
Flypes. Braids (generators and relations). Every knot is isotopic
to a braid closure. 


A braid applet
by Stephen Bigelow. 
7 
Feb. 18 
Kauffman states. Kauffman polynomial. 



8 
Feb. 25 
Jones polynomial. 


An online calculator
for the Jones polynomial. 
9 
Mar. 3 
Span of the Jones polynomial. Tangles. Surfaces. 



10 
Mar. 10 
Knot genus. Conway, HOMFLY polynomials. Video. 


