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Resources tagged with Groups similar to What's a Group?:

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Broad Topics > Advanced Algebra > Groups

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What's a Group?

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Grouping Transformations

Stage: 3, 4 and 5

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

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An Introduction to Mathematical Structure

Stage: 5

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

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Groups of Sets

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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An Introduction to Galois Theory

Stage: 5

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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Sheffuls

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Discover a handy way to describe reorderings and solve our anagram in the process.

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Dancing with Maths

Stage: 2, 3 and 4

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?

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Paint Rollers for Frieze Patterns.

Stage: 3 and 4

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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Rose

Stage: 5 Challenge Level: Challenge Level:1

What groups of transformations map a regular pentagon to itself?

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Shuffles

Stage: 5 Challenge Level: Challenge Level:1

An environment for exploring the properties of small groups.

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Zodiac

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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Sheep in Wolf's Clothing

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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