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. Students make systematic use of the fundamental concept of convergence to study continuity, differentiation and integration of functions. Students devise algorithms and develop programs to solve mathematical problems using Taylor approximation, polynomial evaluation, computer representation of numbers, numerical solution of equations, interpolations and numerical solutions of differential equations. Each student develops an individual plan for reviewing objectives of the exit examination in mathematics or mathematics education.