Discovering Group Theory, Day 3

On Day 3, we did two different sets of activities:

  1.  We revisited the definition of a group and its properties in the context of cyclic groups, namely C1, C2, C3, C4, and C6,  encoding the rotational symmetry of polygons we played with on Day 2. Particular features of the cyclic groups prompted a natural introduction to a few new concepts and new terminology:
    • Order of a group
    • Order of an element of a group
    • Group generators
    • Group multiplication (Cayley) table, which students worked out for C3, C4, and C6 .
  2. We began exploring the symmetries of a rectangle, but this time including the reflections. This allowed us study the above-listed concepts in a different context and practice carrying out group multiplication and finding inverses.

The plan was to use 2 to segue into dihedral groups, but it seems more pedagogical to spend another class or two on exploring the cyclic groups in more depth.