Introduction to Groups. Symmetries of a Square.The Dihedral Groups.Definition and Examples of Groups.Elementary Properties of Groups Finite Groups; Subgroups, Terminology and Notation. Subgroup Tests, Examples of Subgroups.
Chapters 2 and 3.
Cyclic Groups, Properties of Cyclic Groups. Classification of Subgroups of Cyclic Groups, Permutation Groups, Properties of Permutations, Isomorphisms, Definition and Examples. Cayley's Theorem, Properties of Isomorphisms.
Automorphisms, Cosets and Lagrange''s Theorem, Application of Cosets to Permutation Groups.Normal Subgroups, Factor Groups, Applications of Factor Groups. Group Homomorphisms, Definition and Examples,Properties of Homomorphisms, The First Isomorphism Theorem.
Rings-Motivation and Definition, Examples of Rings.Properties of Rings.Subrings.Integral Domains.
Quotient Rings and Ideals. Homomorphism of rings and rings of polynomials.