article
Small groups
Learn about the rules for a group and the different groups of 4
elements by doing some simple puzzles.
Groups
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articleAn 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.
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articleAn introduction to mathematical structure
An introduction to the sort of algebra studied at university, focussing on groups. -
articleGrouping transformations
An introduction to groups using transformations, following on from the October 2006 Stage 3 problems. -
articleDancing 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? -
articlePaint 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.
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problemRose
Age16 to 18Challenge level
What groups of transformations map a regular pentagon to itself? -
problemWhat's a group?
Age16 to 18Challenge 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. -
problemGroups of sets
Age16 to 18Challenge 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. -
problemSimplifying transformations
Age11 to 14Challenge 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?