MA3560 Applied Modern Algebra and Number Theory

This course is devoted to aspects of modern algebra and number theory that directly support applications, principally in communication. The algebraic emphasis is on ring and field theory, with special emphasis on the theory of finite fields, as well as those aspects of group theory that are important in the development of coding theory. Elements of number theory include congruences and factorization. Applications are drawn from topics of interest to DoN/DoD. These include error correcting codes and cryptography.

Prerequisite

MA3025

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

• Define basic algebraic structures, like groups, rings, fields.
• Define sub-structures (like subgroup, subring, ideal, subfield, as well as the order of an element, or of a group.
• Know the most used examples of such structures, like integers Z, rational numbers Q, Reals R, complex, integers modulo primes Z_p, rings of polynomials over a field, field of fractions.
• Know the abstract concepts such as permutation groups, factor groups and Abelian groups.
• Know and be able to check irreducibility, primitivity of polynomials over a field.
• Know various constructions of fields, finite or infinite.
• Know how these structures relate to each other via isomorphisms, homomorphisms, etc.