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# Description of Mathematics

 MAT 431 -Mathematical Statistic 1 Introduction to theory and application of probability models. Topics include random variables, mathematical expectation, Chebyshev's inequality, marginal and conditional distribution, independence, probability distributions and their properties, transformation of variables, moment-generating functions, limiting distribution, and central limit theorem. MATHEMATICS 245 -Linear Algebra (5hours) Geometric vectors and vector spaces, matrices and linear transformations, inner product spaces, the determinant function, and eigenvalues and eigenvectors. Prerequisite: Mathematics 233 with a grade of C or better. MATHEMATICS 270 -Differential Equations (5 hours) Equations of first order with applications; homogeneous linear equations of higher order with constant coefficients; non-homogeneous linear equations of higher order with constant coefficients, method of undetermined coefficients (use of differential operators), method of variation of parameters; linear equations with given initial conditions solved by the LaPlace transform method; applications of second and higher order differential equations; linear equations; linear equations with variable coefficients, the power series method; systems of linear equations and numerical solutions of first order equations. Prerequisite: Mathematics 234 with C or better. MATHEMATICS 234 (IAI M1 900) -Calculus and Analytic Geometry IV (5 hours) Geometry of space, cylindrical and spherical coordinate systems, vector functions with physics applications, arc length, curvature, multivariate functions, partial derivatives, multiple integrals and their applications, vector fields, and line integrals and their applications. Prerequisite: Mathematics 233 with a grade of C or better. MATHEMATICS 233 (IAI M1 900) -Calculus and Analytic Geometry III (5 hours) Indeterminate forms, improper integrals, sequences and series, Taylor and Maclaurin expansions, power series, conics, parametric equations, polar coordinates, introduction to vectors, and operations on vectors. Prerequisite: Mathematics 232 with a grade of C or better. MATHEMATICS 232 (IAI M1 900) -Calculus and Analytic Geometry II (5 hours) Integration, the fundamental theorem of calculus, applications of the definite integral, transcendental functions and techniques of integration. Prerequisite: Mathematics 231 with C or better.