Fourth Semester

Course Objective:

 1. To develop and understanding of the basic concepts of group theory and rings.

 2. To encourage precision in the use of mathematical language, and to develop further the ability          to       understand and produce proofs in an algebraic context.

Course Learning Outcomes:

 CO  1: An exposure of well-defined operations and recognise the algebraic structures. 

CO 2: Use the subgroup criterion to prove that various subsets are subgroups of some given group

CO 3 Decide whether a given group is cyclic, and given a finite cyclic group, find a generator for a subgroup of a given order

CO 4: Understand the notions of homomorphism and isomorphism in groups 

CO 5: Understand the notion of normal subgroup and determine whether a given subgroup is normal 

CO 6: Identifying the set of axioms that define the algebraic structure of a ring

 CO 7: Understand the notion of ideal and determine whether a given subset of a ring is an ideal 

CO 8: Identifying the properties that determine that a mapping between rings is a homomorphism.