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.
- The Set of Integers and Its Properties;
- Group Theory;
- Homomorphism and Factor Groups;
- Group of Permutations;
- Rings and Fields;
- Ideals and Quotient Rings;
- Rings of Polynomials;
- Introduction to Coding Theory and Crypthography.
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