A broad overview of the elementary theory of groups, rings and fields. Group theory: cyclic, symmetric, alternating, dihedral and classical matrix groups, cosets and Lagrange's theorem, group homomorphisms, normal subgroups, quotient groups and the isomorphism theorem. Rings and fields: the integers modulo n, polynomial rings, ring homomorphisms, ideals, quotient rings the isomorphism theorem, unique factorization domains, principal ideal domains, Euclidean domains and the construction of finite fields.
A broad overview of the elementary theory of groups, rings and fields. Group theory: cyclic, symmetric, alternating, dihedral and classical matrix groups, cosets and Lagrange's theorem, group homomorphisms, normal subgroups, quotient groups and the isomorphism theorem. Rings and fields: the integers modulo n, polynomial rings, ring homomorphisms, ideals, quotient rings the isomorphism theorem, unique factorization domains, principal ideal domains, Euclidean domains and the construction of finite fields.
