Modern Algebra

Learning Outcomes:

On successful completion of this Course, students will be able to: Recognize several ways to prove mathematical expressions and will be able to determine divisibility, prime factor, GCD, and their applications.; Identify the structure of sets with binary operations.; Explain the concept of algebraic structures, mainly about group and ring theory.; Apply the concept of algebraic structure in coding theory and cryptography.; Demonstrate to determine divisibility of polynomials, to find the GCD of polynomials, to factorize polynomials, and to find zeroes of polynomials.

Topics:

1. The Set of Integers and Its Properties;
2. Group Theory;
3. Homomorphism and Factor Groups;
4. Group of Permutations;
5. Rings and Fields;
6. Ideals and Quotient Rings;
7. Rings of Polynomials;
8. Introduction to Coding Theory and Crypthography