Groups. Cyclic groups and permutation groups. Cosets and Lagrange theorem. Homomorphisms. Normal subgroups and factor groups. Group action and counting. Rings. Integral domains. Ring homomorphisms. Ideals and quotient rings. Field of quotients. Rings of polynomials. Introduction to Fields.

CILO-1: Explain and apply fundamental Group Theory. CILO-2: Apply the concept of Lagrange Theorem to solve problem. CILO-3: Explain and apply homomorphism and isomorphism. CILO-4: Use the first isomorphism theorem to demonstrate the results related to rings and modules. CILO-5: Explain and apply fundamental Ring Theory.