Introduction to group theory
Learn the fundamentals of group theory in this free course. Discover symmetries of two-dimensional figures, algebraic notation for symmetries, and how to check group axioms. Expand your knowledge to three-dimensional figures and enhance your understanding of symmetry. Start your journey today!
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.