Algebra

Algebra may be viewed as an abstraction of the fundamental properties of arithmetic. It is a broad area of mathematical research, ranging from purely theoretical to highly applicable, and is central to many other areas including representation theory, algebraic geometry, algebraic topology, quantum physics, and cryptology. Research interests in this department include the classification and properties of various classes of infinite abelian groups, the interplay between properties of a ring and modules over that ring, representations of finite partially ordered sets over fields and rings, and set theoretic techniques applicable to algebraic structures of large cardinality. A variety of courses in algebra are offered at the graduate level. Courses in applications of algebra taught at the undergraduate level include Numerical Linear Algebra, Cryptology, Matrix Algebra, and Error Correcting Codes (as a special topics course).