| Course | Title | Credits | Term(s) Offered | ||
| MA4208 | Optimization/Graph Algorithms | 3 | S | ||
|---|---|---|---|---|---|
| Description: | An introduction to linear and integer programming and related Graph problems. Topics include simplex algorithm, duality, Branch-and-Bound and Branch-and-Cut, shortest paths, spanning trees, matchings, network flow, graph coloring and perfect graphs. | ||||
| Prerequisites: | MA3210 | ||||
| Restrictions: | None | ||||
| MA4209 | Combinatorics and Graph Theory | 3 | F | ||
| Description: | An introductory course in combinatorics and graph theory. Topics include designs, enumeration, extremal set theory, finite geometry, graph coloring, inclusion-exclusion, network algorithms, permutations and trees. | ||||
| Prerequisites: | MA3210 | ||||
| Restrictions: | None | ||||
| MA4211 | Inform Theory/Data Compression | 3 | S | ||
| Description: | An introduction to information theory and data compression. Topics include information and entropy, channel and channel capacity, Kraft-McMillan inequality, maximum likelihood decoding, reliability, Shannon's Theorem, lossless data compression, arithmetic coding, higher order modeling, adaptive methods, dictionary methods, transform methods and image compression. | ||||
| Prerequisites: | MA3210 | ||||
| Restrictions: | None | ||||
| MA4308 | Theory of Numbers | 3 | |||
| Description: | Mathematical induction, Euclid's algorithm, prime and composite integers, algebra of congruences, Chinese Remainder Theorem, the Law of Quadratic Reciprocity, number theoretic functions, first degree Diophantine equations, Pythagorean triples, Fermat and Mersenne numbers, factoring algorithms, tests for primality, various applications. | ||||
| Prerequisites: | MA3150 or MA3160 | ||||
| Restrictions: | None | ||||
| MA4310 | Abstract Algebra | 3 | S | ||
| Description: | Topics on groups, rings and fields such as : group actions, the Sylow theorems, integral domains, factorization theory, Euclidean domains, principal ideal domains, splitting fields, zeros of irreducible polynomials, field extensions, and Galois theory. | ||||
| Prerequisites: | MA3310 | ||||
| Restrictions: | None | ||||
| MA4330 | Linear Algebra | 3 | F | ||
| Description: | A study of fundamental ideas in linear algebra and its applications. Includes: review of basic operations, block computations: eigensystems of normal matrices: canonical forms and factorizations: singular value decompositions, pseudoinverses, least square applications: matrix exponentials and linear systems of ODE's: quadratic forms, extremal properties, bilinear forms. | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4410 | Complex Variables | 3 | S | ||
| Description: | A study of complex numbers, functions of a complex variable, analytic functions, elementary functions, integrals, Taylor and Laurent series, residues and poles, and conformal mapping. | ||||
| Prerequisites: | MA3150 or MA3160 | ||||
| Restrictions: | None | ||||
| MA4426 | Differential Geometry | 3 | S | ||
| Description: | Geometrical properties of curves and surfaces, including the Frenet formulas, natural equations of curves, first and second fundamental forms, normal and Gaussian curvature, lines of curvature, geodesics, covariant derivatives, and parallel displacement. Tensors or differential forms with possible applications to Riemannian geometry, general relativity or other physical applications. | ||||
| Prerequisites: | (MA3150 or MA3160) and (MA3520 or MA3530 or MA3560) | ||||
| Restrictions: | None | ||||
| MA4450 | Real Analysis | 3 | F | ||
| Description: | Real analysis on Euclidean n-space. Topics include real and vector valued functions, metric and normed linear spaces: an introduction to Lebesgue measure and convergence theorems. | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) and MA3450 | ||||
| Restrictions: | None | ||||
| MA4490 | Applied Wavelet Analysis | 3 | |||
| Description: | Introductory course with topics: review of Fourier transform, continuous wavelet transform, multi-resolution analysis, discrete wavelet transform, wavelet analysis of 1-D and 2-D signals, non-parametric estimation with wavelets, data compression by wavelet shrinkage, exploratory wavelet analysis, wavelet packet analysis, cosine packet analysis, variations on wavelet analysis, boundary conditions for wavelet analysis. | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4515 | Intro Partial Differential Equations | 3 | F S Su | ||
| Description: | An introduction to solution techniques for linear partial differential equations. Topics include: separation of variables, eigenvalue and boundary value problems, spectral methods and Green's functions. Applications in heat and mass transfer (diffusion eqn.), and mechanical vibrations (Wave and Beam eqns.) will be studied. | ||||
| Prerequisites: | MA3520 or MA3530 or PH2100 | ||||
| Restrictions: | None | ||||
| MA4520 | Integral Trans & Series Methods | 3 | S | ||
| Description: | Laplace, Fourier, and other integral transforms and methods: special functions: series methods to solve ordinary differential equations. | ||||
| Prerequisites: | MA3520 or MA3530 or MA3560 | ||||
| Restrictions: | None | ||||
| MA4525 | Applied Vector & Tensor Math | 3 | F | ||
| Description: | Introduction to vector and tensor mathematics with applications. Topics: Vectors: vector differential calculus, space curves: dyadic products and matrices: gradients, divergence, curl, Laplacians: Stokes's theorem, Gauss's divergence theorem, conservation laws: curvilinear coordinates: tensors, material derivatives: applications of potential theory in electricity and magnetism, heat transfer, solid and fluid mechanics. | ||||
| Prerequisites: | (MA3150 or MA3160) and (MA2320 or MA2330) | ||||
| Restrictions: | None | ||||
| MA4535 | Dynamic Sys: Control & Chaos | 3 | F | ||
| Description: | Ordinary differential equations and dynamical systems via a modern geometric approach, including physical and engineering applications. May include chaotic phenomena and fractals or elements of control theory. | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4540 | Waves and Solitons | 3 | S | ||
| Description: | A study of linear and nonlinear waves with a brief introduction to completely integrable systems. Topics include: Uni-directional wave equation, Burgers' equation, elementary numerical techniques, wave breaking and shock formation, dispersive waves, water waves and KdV equation, nonlinear optics, and scattering theory. | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4545 | Aerodynamics | 3 | |||
| Description: | This course is a mathematical study of the fundamental principles of aerodynamics. Topics include: elements of complex variable techniques, two dimensional potential flow theory, vorticity and circulation, lift and drag forces, pitching moment, analysis of two dimensional airfoils. | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4550 | Math Models in Biomathematics | 3 | |||
| Description: | Mathematical models from biology, biophysics, biomedical engineering, medicine, and ecology: models may include human physiology (heart, lung, brain, bones), population models (microorganisms, cells, animals), and diagnosis and treatment of disease (heart, cancer). | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4555 | Derivative Securities Models | 3 | S | ||
| Description: | Mathematical models to price derivative securities: stochastic calculus. Computational methods for computing option prices. May include study of mathematical models of risk analysis, portfolio selection theory, futures, options, and other derivative investment instruments. | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4610 | Numerical Linear Algebra | 3 | S | ||
| Description: | Derivation and analysis of algorithms for problems in linear algebra: floating point arithmetic, condition numbers, error analysis: solution of linear systems (direct and iterative methods), eigenvalue problems, least squares, singular value decomposition. Includes a review of elementary linear algebra and the use of MATLAB or software from NETLIB. | ||||
| Prerequisites: | MA2320 or MA2330 | ||||
| Restrictions: | None | ||||
| MA4620 | Finite Difference Meth & PDEs | 3 | F | ||
| Description: | Derivation, analysis, and implementation of finite difference methods: applications to fluid mechanics, elasticity, heat conduction, acoustics, or electromagnetism. Difference equations, Taylor series, stability, convergence: Runge-Kutta, multistep methods, etc., stiff systems. Finite difference methods for partial differential equations: alternate methods for discretizing space, such as spectral, finite element, or particle methods. | ||||
| Prerequisites: | (MA3520 or MA3530 or MA3560) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4625 | Finite Element Methods | 3 | S | ||
| Description: | Theory and practical applications of finite element methods in fluid mechanics, elasticity, heat transfer, and electricity and magnetism. Topics include: variational principles, elementary function space concepts, finite element methodology, convergence, errors, and element selection. | ||||
| Prerequisites: | (MA3520 or MA3530 or MA3560) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4630 | Comp Industrial Math I | 3 | F | ||
| Description: | Methods for solving industrial and financial problems involving: linear and nonlinear systems, eigen-analysis, discrete and numerical calculus, splines, mathematical models, well-posed problems and well-conditioned algorithms, stability and forward- and backward-error analyses, digital computer arithmetic, roundoff error, program design and development and debugging applications, simulations, efficacy, fidelity tests. | ||||
| Prerequisites: | MA3150 or MA3160 | ||||
| Restrictions: | None | ||||
| MA4631 | Comp Industrial Math II | 3 | S | ||
| Description: | Methods for solving industrial and financial problems involving: function approximation, data representation, curve fitting, constrained and unconstrained optimization, linear and nonlinear programming, ordinary and partial difference and differential equations, stability, convergence, consistency, well-posed problems and well-conditioned algorithms, Finite X Methods - X = Cell, Difference, Element, First-Principles, Interpolations, Volume. | ||||
| Prerequisites: | MA4630 and (MA3520 or MA3530 or MA3560) | ||||
| Restrictions: | None | ||||
| MA4635 | Numerical Meth for Integral Equations | 3 | F | ||
| Description: | This course includes quadrature and quadrature methods for solving integral equations which occur in many scientific disciplines (imaging, aerodynamics, ets.). | ||||
| Prerequisites: | (MA2320 or MA2330) and (MA3150 or MA3160) | ||||
| Restrictions: | None | ||||
| MA4710 | Regression Analysis | 3 | S | ||
| Description: | Simple, multiple, and polynomial regression. Estimation, testing, and prediction. Weighted least squares, matrix approach, dummy variables, multicollinearity, model diagnostics and variable selection. A statistical computing package is an integral part of the course. | ||||
| Prerequisites: | MA2720 or MA3710 or MA2710 | ||||
| Restrictions: | None | ||||
| MA4720 | Design/Analysis of Experiments | 3 | F | ||
| Description: | Construction and analysis of completely randomized, randomized block, incomplete block, Latin squares, factorial, fractional factorial, nested and split-plot designs. Fixed, random and mixed effects models and multiple comparisons and contrasts are also examined. The statistical package SAS is an integral part of the course. | ||||
| Prerequisites: | MA2720 or MA3710 or MA2710 | ||||
| Restrictions: | None | ||||
| MA4760 | Mathematical Statistics I | 3 | F | ||
| Description: | Probability set functions and distributions, multivariate distributions, special distributions, distributions of functions of random variables, limiting distributions. | ||||
| Prerequisites: | MA3720 | ||||
| Restrictions: | None | ||||
| MA4770 | Mathematical Statistics II | 3 | S | ||
| Description: | Point estimation, confidence intervals, sufficient statistics, Bayesian estimation, the Rao-Cramer inequality, hypothesis testing including optimal tests, non-parametric methods. | ||||
| Prerequisites: | MA4760 | ||||
| Restrictions: | None | ||||
| MA4810 | Life Contingencies | 3 | S | ||
| Description: | Measurement of mortality, life tables, commutation functions. Covers all basic forms of life insurance and life annuities, including gross and not premiums, reserves, cash values, and expense loadings. Advanced topics may include stationary populations, joint and multiple life functions, multiple decrement tables and dividends. | ||||
| Prerequisites: | MA3720 or MA3810 | ||||
| Restrictions: | None | ||||
| MA4820 | Loss Distribution/Credibility Theory | 3 | |||
| Description: | Credibility theory addresses methods for updating statistical estimates as new data becomes available. Loss distribution studies probability distributions that are used for modeling the outcomes of insurance claims. | ||||
| Prerequisites: | (MA3150 or MA3160) and MA3720 | ||||
| Restrictions: | None | ||||
| MA4830 | Risk Theory/Survival Models | 3 | |||
| Description: | Individual and collective risk models as they apply to the economics of insurance. Nature and properties of parametric and tabular survival models, estimated from complete or incomplete data. Includes actuarial, moment and maximum likelihood estimation techniques. Applications and extension of models. | ||||
| Prerequisites: | (MA3150 or MA3160) and MA3720 | ||||
| Restrictions: | None | ||||
| MA4900 | Mathematical Sciences Project | 1-4 | F S | ||
| Description: | Independent study in an area of mathematical sciences under the guidance of a faculty member. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA4908 | Theory of Numbers with Tech | 3 | S | ||
| Description: | Mathematical induction, Euclid's algorithm, prime and composite integers, algebra of congruences, Chinese Remainder Theorem, the Law of Quadratic Reciprocity, number theoretic functions, first degree Diophantine equations, Pythagorean triples, Fermat and Mersenne numbers, factoring algorithms, tests for primality and various applications. Projects will utilize Mathematica and EXCEL software packages. | ||||
| Prerequisites: | MA3160 | ||||
| Restrictions: | None | ||||
| MA4945 | History of Mathematics | 3 | F | ||
| Description: | Survey of the development of mathematics from ancient times to today. How cultural, mathematical, and technological developments have influenced one another throughout history. All necessary historical background is provided in the course. | ||||
| Prerequisites: | MA3150 or MA3160 | ||||
| Restrictions: | None | ||||
| MA4990 | Topics in Mathematics | 1-4 | F S | ||
| Description: | Students study in greater depth a particular area of mathematics not studied in existing courses. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5201 | Combinatorial Algorithms | 3 | |||
| Description: | Basic algorithmic and computational methods used in the solution of fundamental combinatorial problems. Topics may include but are not limited to, backtracking, hill climbing, combinatorial optimization, linear and integer programming, and network analysis. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5211 | Combinatorial Optimization I | 3 | |||
| Description: | Optimization problems (traveling salesman, minimal spanning tree, linear programming, scheduling, etc.), simplex algorithm, primal-dual algorithms, complexity, matching, weighted matching, spanning trees, matroid theory, integer linear programming, approximation algorithms, branch-and-bound, local search, polyhedral theory. | ||||
| Prerequisites: | None | ||||
| None | |||||
| MA5212 | Combinatorial Optimization II | 3 | |||
| Description: | Continuation of MA5211, Combinatorial Optimization I. | ||||
| Prerequisites: | MA5211 | ||||
| Restrictions: | None | ||||
| MA5221 | Combinatorics I | 3 | F | ||
| Description: | Counting principles, occupancy problems, recurrence relations, generating functions, applications. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5222 | Combinatorics II | 3 | S | ||
| Description: | Optimization, systems of distinct representatives, Polya's counting theorem, applications. Possible special topics include combinatorial designs, graph theory, and combinatorics on words. | ||||
| Prerequisites: | MA5221 | ||||
| Restrictions: | None | ||||
| MA5231 | Error-Correcting Codes | 3 | |||
| Description: | Basic concepts, motivation from information transmission, finite fields, bounds, optimal codes, projective spaces, duality and orthogonal arrays, important families of codes, MacWilliams' identities, applications. | ||||
| Prerequisites: | MA5301 | ||||
| Restrictions: | None | ||||
| MA5232 | Cryptography | 3 | S | ||
| Description: | Classical cryptography, public key systems, signature schemes, key exchange, authentication codes, secret sharing schemes, protocols. | ||||
| Prerequisites: | MA5221 | ||||
| Restrictions: | None | ||||
| MA5301 | Modern Algebra I | 3 | F | ||
| Description: | Groups, rings, and fields: Galois theory, ideal theory, introduction to algebraic geometry: representations of groups and algebras: multilinear algebra. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5302 | Modern Algebra II | 3 | S | ||
| Description: | A continuation of MA5302. Topics include rings and fields, ideal theory, polynomials, Galois theory, modules, and linear operators. | ||||
| Prerequisites: | MA5301 | ||||
| Restrictions: | None | ||||
| MA5330 | Topics in Linear Algebra | 3 | Su | ||
| Description: | A graduate level study of fundamental ideas in linear algebra and its applications. Includes a review of basic operations, block computations, vector spaces and decompositions, operators, eigenvalue problems, canonical forms, generalized inverses and singular value decompositions, functions of matrices, and applications. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5401 | Real Analysis I | 3 | F | ||
| Description: | A graduate level study of the Lebesgue integral including its comparison with the Riemann integral: the Lebesgue measure, measurable functions and measurable sets. Integrable functions, the Monotone Convergence theorem, the Dominated Convergence theorem and Fatou's Lemma. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5402 | Real Analysis II | 3 | S | ||
| Description: | Continuation of MA5401, including a study of L p - spaces, convergence in measure, almost uniform convergence, Egorov's and Vitali's convergence theorems. Decomposition of measures, the Radon- Nikodym theorem and the Riesz representation theorem. | ||||
| Prerequisites: | MA5401 | ||||
| Restrictions: | None | ||||
| MA5405 | Complex Variables | 3 | |||
| Description: | The Cauchy-Goursat theorem: the Argument principle and winding numbers: the Riemann Mapping theorem: conformal mappings and application in hydrodynamics: Poisson's formula and the Dirichlet problem for harmonic functions: analytic continuation: Infinite Products: the Gamma and Zeta functions and the distribution of primes. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5504 | Mathematical Modeling I | 3 | |||
| Description: | Construction, analysis, and testing of mathematical models (continuum, discrete, deterministic, or stochastic). Possible models: acoustical, biological, chemical, dynamical, ecological, economics, electromagnetics, financial, geological, mechanical, medical, metallurgical, optical, process, robotics, systems, thermal, material (solid, liquid, gas, plasma, multiphase) dynamics, etc. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5505 | Mathematical Modeling II | 3 | |||
| Description: | Continuation of MA5504. Construction of mathematical models involving approximating real world objects with ideal mathematical objects. Analysis of mathematical models including the investigation of whether or not they lead to well-posed mathematical problems. Testing of mathematical models including comparisons of them against reality. | ||||
| Prerequisites: | MA5504 | ||||
| Restrictions: | None | ||||
| MA5510 | Ordinary Differential Equations I | 3 | |||
| Description: | First order equations, general theory of linear equations, constant coefficient equations, matrix methods, singular points, infinite series methods, plane autonomous systems. | ||||
| Prerequisites: | MA4520 | ||||
| Restrictions: | None | ||||
| MA5511 | Ordinary Differential Equations II | 3 | |||
| Description: | Asymptotic solutions, solutions in terms of integrals, boundary and eigenvalue problems, Green's functions, non-linear equations. | ||||
| Prerequisites: | MA5510 | ||||
| Restrictions: | None | ||||
| MA5524 | Functional Analysis | 3 | On Demand | ||
| Description: | Metric spaces, Banach spaces, Hilbert spaces, fundamental convergence and mapping theorems, spectral theory, weak topologies and weak compactness, unbounded operators and their adjoints, fixed point theorems. | ||||
| Prerequisites: | (MA4330 or MA4610) and MA4450 | ||||
| Restrictions: | None | ||||
| MA5531 | Asymptotic & Perturbation Meth | 3 | F | ||
| Description: | Asymptotic expansions for integrals, method of steepest descent, stationary phase, etc., asymptotic expansions for differential equations, regular perturbation methods, Linstedt-Poincare expansions, multiple scales, and averaging, singular perturbation methods, matched asymptotic expansions, composite expansions, etc., specific applications in mechanical vibrations and boundary layer heat transfer and fluid flows are addressed. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5532 | Bifurcation & Stability Theory | 3 | On Demand | ||
| Description: | Study of the branching of solutions to nonlinear problems and their stability. Asymptotic and functional and analytic techniques are employed to study stationary (steady), and Hopf (time-periodic) bifurcations. Specific applications in elastic buckling, Benard convection, hydrodynamic stability, and chemical reaction-diffusion systems will be analyzed. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5545 | Applied Integral Equations | 3 | F | ||
| Description: | Linear integral equations of the first and second kind, Fredholm theory with applications, Hilbert-Schmidt theory with applications, computational methods for approximate solutions of integral equations. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5548 | Math Continuum Mechanics | 3 | S | ||
| Description: | Lagrangian and Eulerian coordinate systems, stress and strain in elastic, viscoelastic, and plastic materials. Constitutive equations, viscosity, balance laws of fluid and solid mechanics, elasticity, Euler, and Navier-Stokes equations. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5560 | Symbolic Comp for Res in Math | 3 | F | ||
| Description: | An introduction to the effective use of symbolic computation in mathematical research using a computer algebra system for simulation, discovering patterns, forming conjectures, scientific visualization, and algebraic manipulation. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5565 | Partial Differential Equations I | 3 | |||
| Description: | Theory and practice of partial differential equations: classification, appropriate boundary conditions and initial conditions, PDE's of mathematical physics, characteristics, Green's functions, variational principles. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5566 | Partial Differential Equations II | 3 | |||
| Description: | Continuation of MA5565. | ||||
| Prerequisites: | MA5565 | ||||
| Restrictions: | None | ||||
| MA5626 | Numerical Approximation Theory | 3 | On Demand | ||
| Description: | Analysis and design of algorithms (for the numerical solution of industrial and financial problems) using the following bodies of theory: difference calculus and interpolation, summation calculus and quadrature, function approximation and data representation, linear and nonlinear optimization and mathematical programming. | ||||
| Prerequisites: | MA4630 or MA3520 or MA3530 | ||||
| Restrictions: | None | ||||
| MA5627 | Numerical Linear Algebra | 3 | S | ||
| Description: | Analysis and design of algorithms for the numerical solutions of linear systems of equations using direct and iterative methods: eigenvalue problems. | ||||
| Prerequisites: | MA3520 or MA3530 or MA4630 | ||||
| Restrictions: | None | ||||
| MA5628 | Numerical ODEs | 3 | F | ||
| Description: | Analysis and design of algorithms for the numerical solutions of ordinary differential equations. | ||||
| Prerequisites: | MA3520 or MA3530 or MA4631 | ||||
| Restrictions: | None | ||||
| MA5629 | Numerical PDEs | 3 | S | ||
| Description: | Analysis and design of algorithms for the numerical solution of partial differential equations. | ||||
| Prerequisites: | MA4631 or MA5628 or MA4515 | ||||
| Restrictions: | None | ||||
| MA5701 | Statistical Methods | 3 | F | ||
| Description: | Introduction to design, conduct and analysis of statistical studies, with an introduction to statistical computing and preparation of statistical reports. Topics covered include: design, descriptive and graphical methods, probability models, parameter estimation and hypothesis testing. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5711 | Mathematical Statistics I | 3 | |||
| Description: | Review of distribution theory and transformation theory of random variables. Topics include sufficiency: exponential and Bayesian models: estimation methods, including optimality theory: basics of confidence procedures and hypothesis testing, including the Neyman-Pearson framework. | ||||
| Prerequisites: | MA4450 and MA4760 | ||||
| Restrictions: | None | ||||
| MA5712 | Mathematical Statistics II | 3 | |||
| Description: | Optimal tests and decision theory. Other topics may include regression and analysis of variance: discrete data analysis: non-parametric models. | ||||
| Prerequisites: | MA5711 | ||||
| Restrictions: | None | ||||
| MA5721 | Stochastic Processes | 3 | F | ||
| Description: | Markov chains and their stationary distributions, Markov processes, second order processes including Gaussian processes and Brownian motion, differentiation and integration of second order processes, white noise, stochastic differential equations. | ||||
| Prerequisites: | MA3710 | ||||
| Restrictions: | None | ||||
| MA5731 | Linear Models | 3 | S | ||
| Description: | A unified development of linear statistical models that includes the following topics: matrices and quadratic forms, normal and chi-square distribution theory, ordinary and generalized least squares modeling, estimability, estimation and tests of hypothesis. | ||||
| Prerequisites: | MA4710 and MA4720 and MA4760 and MA4330 | ||||
| Restrictions: | None | ||||
| MA5741 | Multivariate Stat Methods | 3 | |||
| Description: | Survey of methods used to analyze multivariate data. Topics include graphical and descriptive analyses, inference for the multivariate normal model, multivariate linear models, classification, dimension reduction, cluster analysis, additional topics as time permits. | ||||
| Prerequisites: | (MA4710 or MA4720) and MA5701 | ||||
| Restrictions: | None | ||||
| MA5781 | Time Series Analysis | 3 | On Demand | ||
| Description: | Analysis of data collected over time. Topics include graphical and descriptive methods, spectral analysis: identification, fitting and implementation of Box-Jenkins ARIMA models: intervention and transfer function models, additional topics as time permits. | ||||
| Prerequisites: | MA4710 | ||||
| Restrictions: | None | ||||
| MA5791 | Categorical Data Analysis | 3 | On Demand | ||
| Description: | Structure of 2-way contingency tables. Goodness-of-fit tests and Fisher's exact test for categorical data. Fitting models including logistic regression, logic models, profit and extreme value models for binary response variables. Building and applying log-linear models for contingency tables. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5980 | Special Topics in Mathematics | 1-10 | F S Su | ||
| Description: | Special topics in mathematics. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA5999 | Graduate Research in Math | 1-10 | F S Su | ||
| Description: | Original investigation in theoretical, or applied mathematics, and submission of a thesis in partial fulfillment of the requirements for the master's degree in mathematics. | ||||
| Prerequisites: | None | ||||
| Restrictions: | Graduate students only; | ||||
| MA6200 | Advanced Topics in Discrete Math | 1-3 | On Demand | ||
| Description: | This course reflects the current research interests of the Discrete Mathematics faculty. Topics may include but are not limited to: Finite Fields, Permutation Groups, Projective Geometries, Design Theory, Graph Theory, Coding Theory, Probabilistic Methods, Extremal Set Theory and Combinatorial Matrix Theory. | ||||
| Prerequisites: | None | ||||
| Restrictions: | Graduate students only; | ||||
| MA6700 | Advanced Topics in Statistics | 1-30 | On Demand | ||
| Description: | Topics may include but are not limited to: Experimental Designs, Methods of Quality Improvement, Discrete Data Analysis, Regression Analysis, Sampling Theory, Multivariate Methods, Resampling Methods, Statistical Computing, Integral and Measure Theory, Stochastic Processes, Asymptotic Methods, Optimization, Modeling, Non-parametric and Parametric Statistics. | ||||
| Prerequisites: | None | ||||
| Restrictions: | Graduate students only; | ||||
| MA6701 | Probability | 3 | On Demand | ||
| Description: | Review of discrete probability, probability measures, random variables, distribution functions, expectation as a Lebesgue-Stieltjes integral, independence, modes of convergence, laws of large numbers and iterated logarithms, characteristic functions, central limit theorems, conditional expectation, martingales, introduction to stochastic processes. | ||||
| Prerequisites: | MA3720 and MA4450 | ||||
| Restrictions: | None | ||||
| MA6980 | Special Topics in Mathematics | 1-15 | F S | ||
| Description: | Special topics in mathematics. | ||||
| Prerequisites: | None | ||||
| Restrictions: | None | ||||
| MA6999 | Math Sci Doctoral Research | 1-30 | F S Su | ||
| Description: | Taken in partial fulfillment of the doctoral thesis requirement. | ||||
| Prerequisites: | None | ||||
| Restrictions: | Graduate students only; Dept. Perm. Reqd. | ||||