Approved Math Courses

The following courses are approved for ME-PhD students to satisfy their Math credit requirements. In addition to the courses listed below, 600-level Math courses are permitted by approval from your academic advisor. 800-level, 900-level MATH courses and MATH-534 SAS Programming, MATH-560 Matlab Programming, can not be used to satisfy Math credit requirements.

ME-MS students may take Math courses listed below to satisfy Math credit requirements. Additionally, with advisor approval, certain courses outside of Mathematics department, with significant Math content, may count as Math courses for MS students.

List of Approved Math Courses

15MATH701. Analytical Methods. 3 gr.cr. Linear and nonlinear ordinary differential equations; solutions by series and transforms; Bessel’s equation; numerical methods; boundary value problems; applications to vibrations, heat transfer, etc. Prereq.: Calculus and Diff. Equations.

15MATH702. Analytical Methods. 3 gr.cr. Calculus in higher dimensions: gradient, curl, divergence, Jacobian, curvilinear coordinates, etc.; separation of variables for solving partial differential equations; calculus of variations. Prereq.: 15MATH701.

15MATH703. Analytical Methods. 3 gr.cr. Complex variables: conformal mappings, Cauthy theorems, residue calculus, etc.: partial differential equations: quasi-linear, characteristics, singular curves, applications to heat flow, wave motions, etc.; numerical methods. Prereq.: 15MATH702.

15MATH514. Numerical Analysis. 3 ug. or gr.cr. Floating point arithmetic, roundoff error, error propagation, solving nonlinear equations by bisection, secant, regula-falsi, and Newton methods, error analysis, polynomial interpolation, Runge phenomenon, cubic spline interpolation, orthogonal polynomials, and least squares approximation. Prereq.: programming knowledge.

15MATH515. Numerical Analysis. 3 ug. or gr.cr. Gauss elimination, pivoting strategies, iterative methods for linear systems (Jacobi, Gauss-Seidel), eigenvalue-eigenvector computations by power, inverse power, and Rayleigh Quotient methods, Householder transformations, Hessenberg matrices and the Q-R method, singular value decomposition. Prereq.: 15MATH514.

15MATH516. Numerical Analysis. 3 ug. or gr.cr. Numerical differentiation, Newton-Cotes and Gaussian quadrature, Romberg integration, FFT, adaptive quadrature, numerical methods for initial value problems including Runge-Kutta and predictor-corrector methods, finite difference methods for two-point boundary value problems, decent methods for optimization problems. Prereq.:15MATH515.

15MATH521. Mathematical Statistics. 3 ug. or gr.cr. Random variables, probability distribution functions, mathematical expectation, Chebyshev’s inequality, marginal and conditional distributions, independence, binomial, Poisson, Gamma, and normal distribution. Prereq.:

15MATH522. Mathematical Statistics. 3 ug. or gr.cr. Sampling distributions: transformation of variables, order statistics, moment generating functions, distribution of sample mean and sample variance, stochastic convergence, central limit theorem, maximum likelihood estimation, Bayesian-estimation, confidence intervals. Prereq.: 15MATH521.

15MATH523. Mathematical Statistics. 3 ug. or gr.cr. Hypothesis testing, uniformly most powerful and likelihood ratio tests, sufficient statistics, Rao -Blackwell Theorem, exponential densities, Rao-Cramer inequality, sequential and chi-square tests. Prereq.: 15MATH522.

15MATH524. Linear Programming. 3 ug. or gr.cr. The simplex method (initialization, iteration, termination, sensitivity), the revised simplex method, duality, complementary slackness, the transportation problem, and applications.

15MATH525. Linear Programming. 3 ug. or gr.cr. The transshipment problem, caterer problem, networks, max flow/min cut, matching problems, primal dual algorithm, Ford-Fulkerson algorithm, integer programming (cutting planes and branch and bound), interior point methods (ellipsoid method, Karmarkar’s method), applications. Prereq.: 15MATH524.

15MATH526. Nonlinear Optimization. 3 ug. or gr.cr. Methods of unconstrained optimization, the steepest descent method, Newton’s Method, conjugate direction methods, quasi-Newton and variable metric methods, theory and methods of constrained penalty methods.

15MATH531. Applied Statistical Inference. 3 ug. or gr.cr. Quick review of probability distributions. Inferences about population means and variance.

15MATH532. Applied Regression Analysis. 3 ug. or gr.cr. Correlation, multiple regression, oneway ANOVA, and multiple comparisons. Projects using SAS packages. Prereq.: 15MATH531 or 15MATH361 and 362.

15MATH533. Analysis of Variance. 3 ug. or gr.cr. ANOVA for standard experimental designs and unbalanced designs, repeated measures, and analysis of covariance. Prereq.: 15MATH532.

15MATH553. Partial Differential Equations and Fourier Analysis. 3 ug. or gr.cr. Heat equation, separation of variables, LaPlace equation, Fourier series, vibrating strings, and membranes. Prereq.: 15MATH264; 355 or 273.

15MATH554. Partial Differential Equations and Fourier Analysis. 3 ug. or gr.cr. Sturm-Liouville problems. PDE with at least three independent variables. Green’s functions, non-homogenous problem, Fourier transform, and characterization. Prereq.: 15MATH553.

15MATH555. Applied Linear Algebra. 3 ug. or gr.cr. Gaussian elimination, triangular factorization, band matrices, linear independence, computation of column space and nullspace of a matrix, orthogonality and geometry of Rn projections onto subspaces, least squares approximation, and the pseudo-inverse. Prereq.: 15MATH276 or 351.

15MATH556. Applied Linear Algebra. 3 ug. or gr.cr. Stability of linear differential and difference equations, the Spectral Theorem for symmetric matrices, positive definite matrices, the generalized eigenvalue problem, the Rayleigh quotient, and minimax principles. Prereq.: 15MATH555.

15MATH561. Numerical Methods in Applied Mathematics. 3 ug. or gr.cr. Methodology and ideas behind numerical schemes, focusing on finite difference and finite element methods applied to problems in elasticity, fluid dynamics, heat conduction, groundwater flow, and wave propagation. Prereq.: 15MATH254, 273, and 276.

For a full Math Course list go to: math.uc.edu/course/courseDecs.html