| || |
To give a gentle introduction to groups.
Definitions and examples: the integers, the integers mod n, permutation groups, finite groups of symmetries (for example dihedral groups). Mappings: group homomorphisms and isomorphisms, kernel and image definitions, examples. Subgroups: examples, orders of elements and groups, Lagrange's Theorem. Conjugacy, normal subgroups, quotient groups. Groups of matrices: examples (to include GL(n), O(n), and SO(n)), geometry of corresponding linear transformations, Euclidean isometries.