MODERN ALGEBRA (4 Credits)

Learning Outcomes:

On successful completion of this Course, students will be able to: recognize several ways to prove mathematical expression in set theory, mapping and binary operation; demonstrate knowledge and understanding of groups, subgroups, and order of groups and elements in finite groups; demonstrate knowledge and understanding of the concept of cosets of a subgroup of a group and normal subgroups; demonstrate  knowledge and understanding of the concept of group and ring homomorphism and isomorphism; explain the structure of rings, fields and its properties.

Topics:

1. Fundamental Concept: Sets, Mapping, Binary operation, Groups and Its properties;
2. Subgroups and Lagrange Theorem;
3. Groups Isomorphism and  Homomorphisms;
4. Group of Permutations;
5. Rings, Ideals and Quotient Rings;
6. Rings of Polynomials;
7. Introduction to Finite Fields.