Groups

problem
Sheep in wolf's clothing

Age

16 to 18

Challenge level

Can you work out what simple structures have been dressed up in these advanced mathematical representations?
problem
Rose

Age

16 to 18

Challenge level

What groups of transformations map a regular pentagon to itself?
problem
Simplifying transformations

Age

11 to 14

Challenge level

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?
problem
Groups of sets

Age

16 to 18

Challenge level

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.
problem
What's a group?

Age

16 to 18

Challenge level

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.
article
Paint rollers for frieze patterns

Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
article
Dancing with maths

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?
article
Grouping transformations

An introduction to groups using transformations, following on from the October 2006 Stage 3 problems.
article
An introduction to mathematical structure

An introduction to the sort of algebra studied at university, focussing on groups.
article
An introduction to Galois theory

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.