In this unit we use the geometric concept of symmetry to introduce some of the basic ideas of group theory, including group tables, and the four properties, or axioms, that define a group.
We discuss intuitive ideas of symmetry for a two-dimensional figure, and define the set of symmetries of such a figure. We then view these symmetries as functions that combine under composition, and show that the resulting structure has properties known as closure, identity, inverses and associativity.
