Topic 8 – Option: Sets, relations and groups
Sets
Cartesian Product
Relations
Functions
Functions
Binary Operations
Binary Operations
Groups
Groups
- What defines a group
- Different types of groups
- Commutative groups
- Order of a group
- Subgroups
- Lagrange’s theorem
- Generators
- Proof that all cyclic groups are Abelian
- Permutations under composition of permutations
- Cycle notation for permutations
- Result that every permutation can be written as a composition of disjoint cycles
- The order of a combination of cycles