The Math Explorer’s Club is an NSF supported project aiming at
developing materials and activites to give middle school and high
school students an experience of more advanced topics in mathematics.
Group theory is a branch of mathematics that originated in the need
to study a broad range of "symmetries" in a unified framework. These
symmetries include the symmetries found in crystals, or more complex
physical systems, as well as those found in art, music and "puzzles".
It
is a beautiful example of how mathematical abstraction can lead to very
fruitful theories, by extracting the core relevant notion out of a
variety of concrete examples, then studying it abstractly using the
powerful language of algebra.
This Math Explorer's Club activity
targets high school students and aims at providing them with a sequence
of short texts and activities through which they can learn not only
about group theory but also about set theory and mathematical
abstraction in general.

