Mon 2/29/00

 * homework

 * more matrix multiplication:
     * permutations as "1's in multiplication table" matrices
        - determinants + or - for even, odd permutations
     * 3x3 rotations about x,y,z :  3 parameter orthogonal group O(3)
     * 6 parameter lorentz group; boosts in special relativity

 * NEW STUFF: 
   Direct product of 2 groups:
     * ordered pairs (g,h) (g',h') = (g g', h h')
     * examples:  C2 X C3

 assign:

     (1) (If you know determinants).  Show that the determinant of a matrix 
         with an odd number of columns swapped in the identify matrix is -1.

     (2) If X and Y are boosts in the X and Y directions, find the matrix
         for X Y X' Y' and show that it's a rotation.  (Lorentz Group)

     (3) 10.11 in Armstrong: Show that D_2n is isomorpnic to D_n X Z_2
         when n is odd.  (What happens when n is even?)