Resources tagged with: Groups

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There are 11 NRICH Mathematical resources connected to Groups, you may find related items under Patterns, Sequences and Structure.

Broad Topics > Patterns, Sequences and Structure > Groups

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?

Paint Rollers for Frieze Patterns.

Age 11 to 16

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

Rose

Age 16 to 18 Challenge Level:

What groups of transformations map a regular pentagon to itself?

Dancing with Maths

Age 7 to 16

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?

Grouping Transformations

Age 11 to 18

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

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?

An Introduction to Mathematical Structure

Age 16 to 18

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

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.

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.

An Introduction to Galois Theory

Age 16 to 18

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.

Small Groups

Age 16 to 18

Learn about the rules for a group and the different groups of 4 elements by doing some simple puzzles.