MATH 348: Introduction to Ring Theory

Course Description

A ring is an algebraic system described by a set equipped with addition and multiplication operations. Rings arise naturally as generalized number systems. The integers, for example, form a ring with the usual addition and multiplication operations. Ring theory has applications in diverse areas such as biology, combinatorics, computer science, physics, and topology. Topics include rings of matrices, integers modulo n, polynomials, and integral domains. Some of the important theorems covered are the Fundamental Theorem of Algebra, the Division and Euclidean Algorithms, and Eisenstein’s Criterion. Prerequisite: MATH 222 with a grade of C or better. 348/548