Free course

Introduction to group theory

Introduction to group theory Copyright free Icon

This free course is an introduction to group theory, one of the three main branches of pure mathematics. Section 1 looks at the set of symmetries of a two-dimensional figure which are then viewed as functions. Section 2 introduces an algebraic notation for recording symmetries and calculating composites and inverses of symmetries. Section 3 introduces definitions and looks at how to check axioms for a group. Section 4 looks at how to prove that some properties of groups already looked at are general properties shared by all groups. Section 5 extends the ideas of symmetry to three-dimensions.

Course learning outcomes

After studying this course, you should be able to:

  • explain what is meant by a symmetry of a plane figure
  • find the composite of two symmetries
  • find the inverse of a symmetry
  • determine whether a given set and binary operation form a group by checking group axioms
  • describe the symmetries of some bounded three-dimensional figures.

First Published: 08/12/2017

Updated: 18/04/2018

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