40000

Develops rigorous understanding of algebraic structures.  Students construct and critique proof of properties concerning finite groups, finite simple groups, rings, integral domains, fields, polynomial rings, ring factorization, extension fields, finite fields, Sylow Theorems, and Lagrange's Theorem.  Prerequisite:  A "C" or better in MAT 30243 Transitions to Higher Mathematics.

This course introduces the theory of functions of a complex variable.  Topics include the study of analytic functions, The Cauchy-Riemann equations, logarithmic and other elementary functions of a complex variable, integration of complex functions, the Cauchy integral theorem and its consequences, conformal mappings, power series expansions, residue theorem and applications of definite integrals as they related to mathematical, physics and/or engineering problems.

Introduces numerical techniques and algorithms fundamental to scientific computer work including discussion of error, roots of equations, interpolation, systems of equations, numerical integration and methods of solution of ordinary differential equations.  Prerequisite: MAT 21144 Calculus II.

This course introduces the theory of partial differential equations, including diffusion, elliptic and hyperbolic, using mathematical tools, real-world examples and applications.  Topics include a derivation of the wave equation, Laplace equation, heat equation, Fourier series and integrals, boundary value problems, Bessel functions and Legendre polynomials, and numerical methods for approximating solutions.

Introduces the student of mathematics to university instruction of an advanced undergraduate mathematics course. The course offered will be chosen from the following and determined by mutual consent of instructor and students with interest at point of offering. Students in the online program take Complex Analysis.  Prerequisite: A "C" or better in MAT 30243 Transition to Higher Mathematics.

• Complex Analysis

• Partial Differential Equations

• Topology

• Algebraic Number Theory

• Differential Geometry

Develops the theory of calculus carefully and rigorously from basic principles, giving the student of mathematics the ability to construct, analyze and critique mathematical proofs in analysis. Prerequisite: A "C" or better in MAT 30243 Transitions to Higher Mathematics.

Capstone course that evaluates comprehensive knowledge of undergraduate mathematics.  Assessment includes narrative from student describing his/her understanding of the program's learning objectives, comprehensive assessment of intuitive undergraduate mathematics, and a research component whereby the student submits some original mathematics. Prerequisite:  Completion of all required major courses or consent of instructor.