The binary operation * for combining sets is defined as the union
of two sets minus their intersection. Prove the set of all subsets
of a set S together with the binary operation * forms a group.
An introduction to the sort of algebra studied at university, focussing on groups.
This article only skims the surface of Galois theory and should
probably be accessible to a 17 or 18 year old school student with a
strong interest in mathematics.
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
An environment for exploring the properties of small groups.
An article for students and teachers on symmetry and square dancing. What do the symmetries of the square have to do with a dos-e-dos or a swing? Find out more?
Explore the properties of some groups such as: The set of all real
numbers excluding -1 together with the operation x*y = xy + x + y.
Find the identity and the inverse of the element x.
Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
What groups of transformations map a regular pentagon to itself?
Discover a handy way to describe reorderings and solve our anagram
in the process.
Can you work out what simple structures have been dressed up in these advanced mathematical representations?