Group Theory
Symmetry, structures and the abstract algebra behind modern mathematics
In the beginning...
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Lessons
What is a group?
The four rules
Testing the rules
Practice: Check the four rules
Cayley tables
Practice: Complete the table
Clock arithmetic
The integers mod n
Practice: Sums and inverses
The order of an element
Practice: Find the order
Cyclic groups and generators
Practice: Pick the generators
Dihedral groups
Order matters
Practice: Combine symmetries
Subgroups
Practice: Spot the subgroups
Lagrange's theorem
Practice: Use Lagrange's theorem
Permutations
Practice: Match the shuffles
Groups everywhere
Course Complete
Up nextRecommended first Launch Lesson
What is a symmetry?
Learn the four group axioms, explore cyclic and dihedral groups, Cayley tables, subgroups, and Lagrange's theorem through interactive visualisations.
