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Time: 20 hours
Level: Intermediate
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 Introduction Resource- In this unit we use the geometric concept of symmetry to introduce some of the basic ideas of group theory, including group tables, and the four properties, or axioms, that define a group.
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| | 1 Symmetry in two dimensions
- 1 Symmetry in two dimensions Resource
- In Section 1 we discuss intuitive ideas of symmetry for a two-dimensional figure, and define the set of symmetries of such a figure. We then view these symmetries as functions that combine under composition,...
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| | 2 Representing symmetries
- 2 Representing symmetries Resource
- In Section 2 we develop an algebraic notation for recording symmetries, and demonstrate how to use the notation to calculate composites of symmetries and the inverse of a symmetry.
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- 3 Group axioms Resource
- Section 3 is an audio section. We begin by defining the terms group, Abelian group and order of a group. We then demonstrate how to check the group axioms, and we extend the examples of groups that we...
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- 4 Proofs in group theory Resource
- In Section 4 we prove that some of the properties of the groups appearing earlier in the unit are, in fact, general properties shared by all groups. In particular, we prove that in any group the identity...
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| | 5 Symmetry in three dimensions
- 5 Symmetry in three dimensions Resource
- In Section 5, the video section, we extend our ideas of symmetry to three dimensions and consider, in particular, the regular (Platonic) solids.
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| | 6 Solutions to the exercises
- 6 Solutions to the exercises Resource
- Section 6 contains solutions to the exercises that appear throughout sections 1-5.
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| | References and Acknowledgements | |
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