Summary of Results

1. Symmetries of the alphabet.
2. The group of symmetries of the square
3. A linear representation of the group of symmetries of the square
4. Group actions of D₈ on the vertices, diagonals and axes of the square.
5. Rigid motions and symmetries of the cube; the octahedral group O.
6. Action of O on the vertices, faces, edges, and long diagonals of the cube.
7. Isomorphism of O and Sym₄.
8. Conjugacy classes of O.
9. Kernel and orbits of a group action, transitive actions.
10. A linear representation of O in R³
11. Rigid motions of the tetrahedron, octahedron and dodecahedron.
12. Conjugacy classes in S_n and A_n
13. Let H be a normal subgroup of a group G. If c is in H, then the conjugacy class of c in G is a disjoint union of conjugacy classes in H.
14. The icosahedral group: its elements, conjugacy classes and generating sets.
15. A₅ is simple.
16. GL(2,R), O(2,R) and SO(2,R).
17. GL(3,R), O(3,R) and SO(3,R).
18. Classification of finite subgroups of O(2,R).
19. Classification of finite subgroups of O(3,R)
20. Groups acting on groups: Cayley's Theorem and Cauchy's Theorem
21. The Sylow Theorems
22. Not Burnside's Lemma and applications to pattern counting
23. Isometries of the Euclidean plane
24. Strip or frieze patterns
25. Plane crystallographic groups and wallpaper patterns
26. The crystallographic restriction and space groups

The rest were not covered in 2000.
 
28. The plane affine group
29. The affine group in n dimensions
30. Linear groups over arbitrary fields: GL(n,F), SL(n,F), Aff(n,F)
31. Projective spaces, projective groups and the Moebius group.

Last update: May 24, 2000