In this course, you will learn :
- What transforms a set into a group?
- Explore group axioms using cube symmetries.
- Explore some real-world applications to learn more about groups.
- Discover the structure of groups within groups.
- Use groups to help you understand this perplexing toy.
- By categorising a group's elements, you can learn a lot about it.
- Investigate the interaction between a group and the set on which it acts.
- Discover a useful method for constructing larger groups from smaller ones.
- Investigate the structure of finite groups to discover fascinating new relationships.
- Combining Symmetries
- Group Axioms
- Cube Symmetries
- Axioms and Basic Examples
- More Group Examples
- Abelian Groups
- Number Theory
- Puzzle Games
- Rubik's Cubes
4. Advanced Topics
- Normal Subgroups
- Isomorphism Theorems
- Conjugacy Classes
- The Symmetric Group
5. Group Actions
- Group Actions
- Burnside's Lemma
- Semidirect Products
- Sylow Theorems