Relations and functions -- The integers and modular arithmetic -- Groups --introduction to groups -- Factor groups and homomorphisms -- Direct products and the classification of finite abelian groups -- Symmetric and alternating groups -- The sylow theorems -- Rings -- Introduction to rings -- ideals, factor rings and homomorphisms -- Special types of domains -- Fields and polynomials -- Irreducible polynomials -- Vector spaces and field Eextensions -- Applications -- Public Key cryptography -- Straightedge and compass constructions -- A tThe complex numbers -- B Matrix algebra -- Solutions