MATH 3293 Students explore and expand the properties of basic algebra into abstract structures. Students determine which subsets of the complex numbers are groups, rings, integral domains, and fields using the operations of arithmetic. Students utilize the theory of complex differentiation and integration as well as manipulative skills developed in this course to study functions of a complex variable. Topics covered include analytic functions, complex integration, Cauchy theory of integration, power series, residues and poles. Students investigate algebraic structures such as groups, rings, and fields.
Students write proofs involving algebraic concepts.
Topics include group theory, elementary ring theory, and an introduction to field theory. MATH 2253 Students develop an understanding of vector spaces, linear operators and linear systems. Emphasis is placed on finite-dimensional vector spaces, linear transformations and matrix algebra. MATH 2174 Students study first order partial differential equations and canonical second order linear partial differential equations. They apply the concepts and procedures learned in this class to solve partial differential equations that arise in mathematical physics and engineering fields.