Mathematics (MTH)
Emphasis on the language of Modern Elementary Algebra. Recommended for preservice elementary teachers and for elementary and secondary in-service teachers. May not be used for a degree offered by the Department of Mathematics of in the twelve hour content block of the Secondary Education MA Degree program for students with mathematics certification in grades 7-12.
Informal development of geometry. Recommended for preservice elementary teachers and for elementary and secondary in-service teachers. May not be used for a degree offered by the Department of Mathematics or in the twelve hour content block of the Secondary Education MA Degree program for students with mathematics certification in grades 7-12.
The number system, limits, sequences, partial differentiation with applications, maxima and minima of functions of several variables. Theory of definite integrals, multiple integrals, line and surface integrals, improper integrals, infinite series.
The number system, limits, sequences, parital differentiation with applications, maxima and minima of functions of several variables. Theory of definite integrals, multiple integrals, line and surface integrals, infinite series.
Pre-req: MTH 527 with a minimum grade of C.
Finite geometrics, basic background material for the modern development of Euclidean Geometry, other geometries.
Projective geometry using both synthetic and algebraic methods.
Structure of the abstract mathematical systems; groups, rings, fields, with illustrations and applications from Number Theory.
Structure of the abstract mathematical systems; groups, rings, fields, with illustrations and application from Number Theory.
Pre-req: MTH 550 with a minimum grade of C.
Courses on special topics not listed among the current course offerings.
A seminar on topics relevant to graduate students in mathematics, including college-level teaching, conducting research, professional ethics, and mathematics careers. This course does not satisfy any degree requirements.
Elementary partial differential equations. Heat equation, Laplace’s equation, separation of variables, Fourier series, vibrating strings, eigenvalue problems, finite differences, Bessel functions, Legendre polynomials.
Differential equations are studied qualitatively. Topics include the existence and uniqueness of solutions and the behavior of solutions including the stability of nonlinear systems, periodic solutions, and approximation using perturbation methods.
General topology including separation axioms, connectedness, compactness, convergence, continuity, metric spaces, product and quotient spaces.
The course is designed to introduce students in mathematical sciences to the theorems, techniques and applications of graph theory and combinatorics.
A study of algebra, topology, and geometry of the complex plane; holomorphic functions; conformal mapping; analytic functions and analytic continuation; complex integration; representation theorems; convergence theorems and related topics.
Direct and iterative methods for numerical solution of linear systems of equations. Eigenvalues and eigenvectors. Error analysis and norms. Related Topics.
The theory and technique of numerical computation involving the difference calculus, the summation calculus, interpolation methods, solutions of equations, and methods of solution of ordinary differential equations.
A study of measure and integration and related topics.
Pre-req: MTH 528 with a minimum grade of C.
A survey of some basic properties of the integers: divisibility (prime numbers,factorization,perfect numbers), congruences (modular arithmetic, linear and quadratic congruences, the Chinese Remainder Theorem), and Diophantine equations.
Finite difference methods for elliptic, parabolic, and hyperbolic PDEs. Study of properties such as consistency, convergence, and stability. Computer implementation.
Pre-req: MTH 527 with a minimum grade of C.
An independent program of study of advanced topics not normally covered in other courses. The topics are chosen upon mutual agreement between the student and the instructor
Courses on special topics not listed among the current course offerings. (PR: Permission of Instructor)