Group : definition, examples, subgroups, counting Principle, Langrange’s theorem, Normal subgroups, Quotient groups, Homomorphisms, Fundamental theorem of homomorphism and related theorems. Cyclic Groups.
Rings : Definition and examples of Rings, Elementary properties of Rings. Sub-rings, Homomorphism, ideals and Quotient Rings, Field of Quotient of Integral domain, division rings. Euclidean Rings, Principal ideals, examples.