MAP-MATHEMATICS: APPLIED
 

MAP 2302         Differential Equations               3

Prerequisite: MAC 2313.

Introduction to ordinary differential equations; emphasis on linear equations, operator methods, systems of equations. Applications. (Gordon Rule Course: Theoretical Math)

MAP 4103         Mathematical Modeling              3

Prerequisite: MAP 2302.

Mathematical models of physical problems leading to differential equations. Problems selected from biology, electrical circuitry, mechanics, etc. Methods of solution include Laplace transform, Fourier series, separation of variables and calculus of variations. (Gordon Rule Course: Theoretical Math)

MAP 4341         Partial Differential Equations          3

Prerequisite: MAP 2302.

First-order equations, derivation and classification of second-order equations. Solution techniques of boundary value and initial value problems; applications. (Gordon Rule Course: Theoretical Math)

MAP 4403         Mathematical Methods for Engineers        3

Prerequisite: MAP 2302.

Complex variables, including derivatives and integrals, singularities, Taylor/Laurent series and residues; Linear Algebra, including Gaussian elimination, determinants, inversion, linear independence, norms, inner product, orthogonality, Gram-Schmidt procedure, eigenvalues and eigenvectors, systems of differential equations.

MAP 4470         Probability and Distribution Theory          3

Prerequisite: MAC 2313.

Mathematical methods of probability, conditional probability, stochastic independence; mathematical derivation of expectations, moment generating functions of discrete and continuous random variables, expectations, joint densities, marginal and conditional densities, conditional expectations; theory of probability inequalities, transformation of random variable’s order statistics.

MAP 5471         Advanced Probability and Inferences             3

Prerequisite: MAC 2313.

Advanced topics in probability, limit theorems, limiting distributions, order statistics, weak law of large numbers, strong law of large numbers, central limit theorem. Advanced topics in point and interval estimation, measures of quality of estimates, Exponential families, Completeness, Unbiasedness, Cramer-Rao inequality, Rao-Blackwell theorem, minimum variance unbiased estimators, maximum likelihood estimators principles, Bayes’ and minimax estimation, Robust estimation; Advanced hypothesis testing.

MAP 6106         Mathematical Methods of Operations Research I                 3

Prerequisite: MAS 3105 or MAS 5107 and STA 4321.

Mathematical linear programming models, theory of simplex method, revised simplex methods, dual simplex methods; duality theory and sensitivity analysis, transportation problems, theory of integer programming. Credit may not be received for both MAP 6106 and STA 6607.

MAP 6107         Mathematical Methods of Operations Research II              3

Prerequisite: MAP 6106 or STA 6607

Interior-point algorithm, linear goal programming, game theory, nonlinear programming, network analysis, PERT/CPM, queuing theory. Credit may not be received in both MAP 6107 and STA 6608.

MAP 6108         Mathematical Modeling and Initial and Boundary Value Problems        3

Prerequisite: MAA 4212, MAP 2302, and MAS 3105.

Methodology and framework for mathematical modeling. Current topics in applied mathematics will be presented emphasizing the interdependency of mathematics and its applications to physical, societal and other “real world” phenomena.

MAP 6406         Multivariate Analysis               3

Prerequisite: STA 4321, STA 5206, STA 5207.

Eigenvalue decomposition; interpreting eigenvalues and eigenvectors; multivariate extensions of chi-square and t-tests; discrimination and classification procedures; multivariate analysis of variance; factor analysis; principal components analysis; applications to diagnostic problems in biological, medical, anthropological and social research.