"Algebraists usually define groups as sets with operations satisfying a long list of difficult-to-remember axioms. To my mind, such a definition is impossible to understand. I think that algebraists put such obstacles on the way of those wishing to study their subject to make it more difficult for the uninitiated to get into, and thereby to raise their authority."
(V. I. Arnold, "Mathematics with a human face", "Priroda", 1988)
The notion of a group serves for a mathematical description of
symmetry (see http://en.wikipedia.org/wiki/Group_theory). For this reason, groups surround us everywhere. The goal of this course is to become familiar with the notion of a group and numerous examples of groups, and to learn to see and use groups in the world around us. It should be accessible to high school students interested in mathematics.