MATH 5011 - Foundations of Arithmetic for Teachers I***.............................................3.00 credits Sets, whole numbers, fractions, elementary number theory, algorithms, elementary geometry and a study of the metric system. Designed for teachers of grades K-4. MATH 5012 - Foundations of Arithmetic for Teachers II***............................................3.00 credits Numeration systems, elementary number theory, rational numbers, real numbers, basic algorithms, graphs and measurements. For teachers of grades 4-8. MATH 5110 - Algebraic Structures for Teachers***...............................................3.00 credits Elementary study of the properties of groups, integral domains and fields. Prerequisite: 5011 or consent of instructor MATH 5111 - Theory of Numbers............3.00 credits Properties of integers, divisibility, congruence of numbers. LaGrange's theorem, residues and Diophantine equations. Prerequisite: Graduate standing MATH 5112 - Linear Algebra.................3.00 credits Vector spaces and linear transformations. Other topics include equations, matrices, determinants, characteristic values, the special theorem, linear functions and dual space. Prerequisite: Graduate standing. MATH 5113-5114 - Modern Algebra I & II*................................................................6.00 credits Groups, permutation groups, finite groups, group mappings, rings, ideals, quotient rings, fields, finite fields, polynomial rings, field extensions, vector spaces, algebra of linear transformations. Prerequisite: Graduate standing. MATH 5202 - Technology-Oriented Mathematics............................................. 3.00 credits Applications of mathematical software and graphic calculators in doing and teaching mathematics. Problem-solving and simulations using software such as Mathematics, Maple, Math Lab and statistical packages. MATH 5211-5212 - Fundamental Concepts of Analysis I & II*.........................................6.00 credits Sets and functions, real number system, topological concepts in real Cartesian spaces, sequences, limits, continuity, uniform continuity, differentiation and integration, convergence, uniform convergence. Prerequisite: Graduate standing MATH 5213 - Complex Analysis............ 3.00 credits Complex numbers, analytic functions, complex series, Cauchy's theory, residue calculus and conformal mappings. Prerequisite: MATH 5211 MATH 5214 - Differential Equations......3.00 credits Ordinary differential equations of first and higher order, solutions in series, Laplace transforms numerical solutions. Prerequisite: MATH 5211 or consent of instructor MATH 5215 - Numerical Analysis............3.00 credits Nature of error, Gaussian elimination for linear systems, iteration, Newton's method, steepest descent for nonlinear systems, zeros of polynomials and interpolation. Prerequisite: MATH 5211or consent of instructor |
MATH 5311 - Geometry for Teachers**.3.00 credits Points, lines, planes, parallel and perpendicular lines, congruence, similarity, measurement, constructions, space figures, analytical geometry and non-Euclidean Geometry. Prerequisite: Graduate standing . MATH 5312 - Foundations of Geometry.3.00 credits Euclidean and non-Euclidean geometry, including incidence, order and the parallel postulate. Prerequisite: Graduate standing MATH 5313 - Modern Geometry.............3.00 credits An algebraic approach to geometry using vectors and transformations. For secondary teachers. Prerequisite: MATH 5112 or consent of the instructor MATH 5314 - Introduction to Point Set Topology......................................................3.00 credits Set theory, general topological spaces, product spaces, sequences, compactness, connectedness, metric spaces and Tcychonoff theorem. Prerequisite: Graduate standing MATH 5410 - Probability and Statistics for Teachers`**.................................................3.00 credits Probability, gathering and recording data, construction and use of tables, tabulating and graphing percentiles, mean and standard deviation, frequency distributions, normal distribution and statistical interference correlation. Prerequisite: Consent of instructor MATH 5412 - Methods of Statistical Analysis....................................................... 3.00 credits Estimation and inference using basic probability distributions, analysis of variance, analysis of covariance, regression, correlation and basic experimental design. Prerequisite: A previous course in statistics. MATH 5414 - Introduction to Operations Research.................................................... 3.00 credits Linear programming, the simplex method, network theory, games theory, Markov analysis, other topics including inventory analysis and queuing theory. Prerequisite: Graduate standing. MATH 5511 - History of Mathematics.... 3.00 credits Growth and development of the discipline of Mathematics from antiquity to modern times. Special emphasis given to the evolutionary character of the principal ideas of modern Mathematics. MATH 5670 - Special Topics In Mathematical Sciences................................................... 3.00 credits An exploration of special topics of current interest in the Mathematical sciences. Prerequisite: Consent of instructor. * Required course. ** Required if not previously fulfilled at the undergraduate or graduate level. *** No credit is given toward the graduate program in Mathematics Education. |