Abstract Algebra

Catalog description

Abstract Algebra is the axiomatic and rigorous study of the underlying structure of algebra and arithmetic. It covers the knowledge and skills necessary to understand, apply, and prove theorems about numbers, groups, rings, and fields. Topics include the well-ordering principle, equivalence classes, the division algorithm, Euclid's algorithm, prime factorization, greatest common divisor, least common multiple, congruence, the Chinese remainder theorem, modular arithmetic, rings, integral domains, fields, groups, roots of unity, and homomorphisms. Linear Algebra is a prerequisite for this course.