Graduate Courses in Mathematical Sciences

Course:	MA4208: Optimization Graph Algorithms / 3 cr. / Spring
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
Course:	MA4209: Combinatorics and Graph Theory / 3 cr. / Fall
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
Course:	MA4211: Information Theory / Data Compression / 3 cr. /
	Spring (odd years)
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
Course:	MA4308: Theory of Numbers / 3 cr. / On demand
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
Course:	MA4310: Abstract Algebra / 3 cr. / Spring
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

Course:	MA4330: Linear Algebra / 3 cr. / Fall
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 ODEs;
	quadratic forms, extremal properties, bilinear forms.
Prerequisites:	(MA2320 or MA2330) and (MA3150 or MA3160)
Course:	MA4410: Complex Variables / 3 cr. / Spring
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
Course:	MA4426: Differential Geometry / 3 cr. / Spring (odd years)
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 MA3521 or MA3530 or MA3560)
Course:	MA4450: Real Analysis / 3 cr. / Fall
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
Course:	MA4490: Applied Wavelet Analysis / 3 cr. / Fall (odd years)
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)

Course:	MA4515: Intro to Partial Differential Equations / 3 cr. / Spring, Summer
Description:	An introduction to solution techniques for linear partial differential
	equations. Topics include: separation of variables, eigenvalue and
	boundary value problems, spectral methods, Fourier series, and
	Green's functions. Applications in heat and mass transfer
	(diffusion eqn.), and mechanical vibrations (Wave and Beam eqns.)
	will be studied.
Prerequisites:	(MA3150 or MA3160) and (MA3520 or MA3530 or PH2100)
Course:	MA4520: Integral Transforms and Series Methods / 3 cr. / Spring (odd years)
Description:	Laplace, Fourier, and other integral transforms and methods: special
	functions: series methods to solve ordinary differential equations.
Prerequisites:	(MA3520 or MA3521 or MA3530 or MA3560) and (MA3150 or MA3160)
Course:	MA4525: Applied Vector and Tensor Math / 3 cr. / Fall
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' 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) or (MA2320 or MA2330)
Course:	MA4535: Dynamic Systems: Control and Chaos / 3 cr. / Fall (even years)
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:	(MA3520 or MA3521 or MA3530 or MA3560) and (MA3150 or MA3160)
Course:	MA4540: Waves and Solitons / 3 cr. / Spring (odd years)
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:	(MA3520 or MA3521 or MA3530 or MA3560) and (MA3150 or MA3160)

Course:	MA4545: Aerodynamics / 3 cr. / Spring (even years)
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:	(MA3520 or MA3521 or MA3530 or MA3560) and (MA3150 or MA3160)
Course:	MA4550: Math Models in Biomathematics / 3 cr. / Fall (odd years)
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:	(MA3520 or MA3521 or MA3530 or MA3560) and (MA3150 or MA3160)
Course:	MA4555: Derivative Securities Models / 3 cr. / Spring (odd years)
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:	(MA3520 or MA3512 or MA3530 or MA3560) and (MA3150 or MA3160)
Course:	MA4610: Numerical Linear Algebra / 3 cr. / Spring
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 MA2321 or MA2330
Course:	MA4620: Finite Difference Methods and PDEs / 3 cr. /
	Fall (even years)
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 MA3521 or MA3530 or MA3560) and (MA3150 or MA3160)

Course:	MA4625: Finite Element Methods / 3 cr. / Spring (odd years)
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 MA3521 or MA3530 or MA3560) and (MA3150 or MA3160)
Course:	MA4630:Comp. Industrial Math I / 3 cr. / Fall (odd years)
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
Course:	MA4631: Comp. Industrial Math II . 3 cr. / Spring (even years)
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 MA3521 or MA3530 or MA3560)
Course:	MA4635: Numerical Methods for Integral Equations / 3 cr. / Fall (even years)
Description:	This course includes quadrature and quadrature methods for solving
	integral equations which occur in many scientific disciplines (imaging,
	aerodynamics, etc.).
Prerequisites:	(MA3520 or MA3521 or MA3530 or MA3560) and (MA3150 or MA3160)
Course:	MA4710: Regression Analysis / 3 cr. / Spring
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 and MA3730

Course:	MA4720: Design / Analysis of Experiments / 3 cr. / Fall
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 and MA3730
Course:	MA4730: Nonparametric statistics / 3 cr. / Spring
Description:	Survey of distribution-free statistical inference procedures.
	Topics include a review of probability and distribution theory;
	one sample, paired samples, and multi-sample location tests;
	tests of independence and related measures of association; goodness-of fit
	tests and test based on the cumulative distribution function.
Prerequisites:	MA2710 or MA2720 or MA3710
Course:	MA4740: Sampling methods / 3 cr. / On demand
Description:	Topics include survey construction, sources of errors in surveys,
	estimation of population parameters from simple random, stratified,
	systematics, and multi-stage samples, effects of and remedies for
	non-response, hypothesis testing with survey data, and other topics
	as time permits.
Prerequisites:	MA3730 or MA5701
Restrictions:	Students cannot receive credit for both MA4740 and MA5740
Course:	MA4760: Mathematical Statistics I / 3 cr. / Fall
Description:	Probability set functions and distributions, multivariate distributions,
	special distributions, distributions of functions of random variables,
	limiting distributions.
Prerequisites:	MA3720
Course:	MA4770: Mathematical Statistics II / 3 cr. / Spring
Description:	Point estimation, confidence intervals, sufficient statistics, Bayesian
	estimation, the Rao-Cramer inequality, hypothesis testing including
	optimal tests, non-parametric methods.
Prerequisites:	MA4760

Course:	MA4810: Life Contingencies / 3 cr. / Spring (odd years)
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
Course:	MA4820: Loss Distribution / Credibility Theory / 3 cr. / Fall (odd years)
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:	MA3720
Course:	MA4830: Risk Theory / Survival Models / 3 cr. / Spring (even years)
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:	MA3720
Course:	MA4900: Mathematical Sciences Project / 1-4 cr. / Fall, Spring
Description:	Independent study in an area of mathematical sciences under the guidance
	of a faculty member.
Prerequisites:	None
Course:	MA4908: Theory of Numbers with Technology / 3 cr. / Spring
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:	MA3210 or MA3310 or MA3924

Course:	MA4945: History of Mathematics / 3 cr. / Fall
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:	Junior standing; MA3150 or MA3160 recommended
Course:	MA4990: Topics in Mathematics / 1-4 cr. / Fall, Spring
Description:	Students study in greater depth a particular area of mathematics not
	studied in existing courses.
Prerequisites:	None
Course:	MA5201: Combinatorial Algorithms / 3 cr. / Fall (odd years)
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
Course:	MA5211: Discrete Optimization / 3 cr. / Fall (even years)
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
Course:	MA5221: Graph Theory / 3 cr. / Fall (odd years)
Description:	Review of basic graph theory, followed by one or more advanced topics,
	which may include topological graph theory, algebraic graph theory,
	graph decomposition, graph coloring.
Prerequisites:	MA5301 and MA4209, or consent of instructor
Course:	MA5222: Design Theory / 3 cr. / Spring
Description:	Methods for the construction of different combinatorial structures, such
	as difference sets, symmetric designs, projective geometries, orthogonal
	Latin squares, transversal designs, Steiner systems, and tournements.
Prerequisites:	MA5301 and MA4209, or consent of instructor

Course:	MA5231: Error-Correcting Codes / 3 cr. / Spring (odd years)
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
Course:	MA5232: Cryptography / 3 cr. / Fall (even years)
Description:	Classical cryptography, public key systems, signature schemes, key
	exchange, authentication codes, secret sharing schemes,
	protocols.
Prerequisites:	MA5221
Course:	MA5301: Finite Groups and Fields / 3 cr. / Fall
Description:	Basic theory of finite groups (subgroups, normality, homomorphisms,
	Abelian groups, cyclic groups, commutators, order, cosets, index,
	conjugacy, simply groups, Sylow theorems), basic theory of finite fields
	(prime fields, irreducible polynomials, Galois groups, trace), families
	of groups defined over finite fields (linear groups).
Prerequisites:	MA4310 or consent of instructor
Course:	MA5302: Rings and Modules / 3 cr. / On demand
Description:	A continuation of MA5301. Topics include rings and fields, ideal theory,
	polynomials, Galois theory, modules, and linear operators.
Prerequisites:	MA5301
Course:	MA5330: Topics in Linear Algebra / 3 cr. / On demand
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

Course:	MA5401: Real Analysis / 3 cr. / Fall (even years)
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
Course:	MA5405: Complex Variables / 3 cr. / Fall (odd years)
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
Course:	MA5504: Mathematical Modeling / 3 cr. / Spring (even years)
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
Course:	MA5510: Ordinary Differential Equations / 3 cr. / Spring (even years)
Description:	First order equations, general theory of linear equations, constant
	coefficient equations, matrix methods, singular points,
	infinite series methods, plane autonomous systems.
Prerequisites:	MA4450 and MA5330 or consent of instructor
Course:	MA5524: Functional Analysis / 3 cr. / Spring (odd years)
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

Course:	MA5531: Asymptotic and Perturbation Methods / 3 cr. / On demand
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
Course:	MA5532: Bifurcation and Stability Theory / 3 cr. / 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
Course:	MA5545: Applied Integral Equations / 3 cr. / Fall (even years)
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
Course:	MA5548: Mathematical Continuum Mechanics / 3 cr. / Fall (odd years)
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
Course:	MA5565: Partial Differential Equations / 3 cr. / Spring (even years)
Description:	Theory and practice of partial differential equations: classification,
	appropriate boundary conditions and initial conditions, PDEs of
	mathematical physics, characteristics, Green's functions, variational
	principles.
Prerequisites:	None

Course:	MA5626: Numerical Approximation Theory / 3 cr. / 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 MA3521 or MA3530 or MA3560
Course:	MA5627: Numerical Linear Algebra / 3 cr. / Spring
Description:	Analysis and design of algorithms for the numerical solutions of linear
	systems of equations using direct and iterative methods; eigenvalue
	problems.
Prerequisites:	MA4330 or MA4630 or consent of instructor
Course:	MA5628: Numerical ODEs / 3 cr. / Fall (even years)
Description:	Analysis and design of algorithms for the numerical solutions of
	ordinary differential equations.
Prerequisites:	MA3520 or or MA3521 or MA3530 or MA3560 or MA4631
Course:	MA5629: Numerical PDEs / 3 cr. / Fall (odd years)
Description:	Analysis and design of algorithms for the numerical solution of partial
	differential equations.
Prerequisites:	MA4631 or MA5628 or MA4515
Course:	MA5630: Numerical Optimization / 3 cr. / Spring (odd years)
Description:	Numerical solution of unconstrained and constrained optimization
	problems and nonlinear equations. Topics include optimality conditions,
	local convergence of Newton and Quasi-Newton methods, line search and
	trust region globalization techniques, quadratic penalty and
	augmented Lagrangian methods for equality-constrained problems,
	logarithmic barrier method for inequality-constrained problems, and
	Sequential Quadratic Programming.
Prerequisites:	MA4330 or MA4610 or MA5627 or MA4630 or consent of instructor

Course:	MA5640: Computational Fluid Dynamics / 3 cr. / Spring (even years)
Description:	Equations of continuum mechanics, principles and applications of numerical
	methods to discretize equations, stabilitiy and error analysis, linear
	and nonlinear solvers, boundary conditions, incompressible and
	compressible flow, transient and stationary flows, pre- and post-processing,
	and applications.
Prerequisites:	Consent of instructor
Course:	MA5701: Statistical Methods / 3 cr. / Fall
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
Course:	MA5711: Mathematical Statistics I / 3 cr. / Fall
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 and MA4770
Course:	MA5712: Mathematical Statistics II / 3 cr. / Spring
Description:	Optimal tests and decision theory. Other topics may include regression
	and analysis of variance; discrete data analysis; non-parametric models.
Prerequisites:	MA5711
Course:	MA5721: Stochastic Processes / 3 cr. / Fall (odd years)
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

Course:	MA5731: Linear Models / 3 cr. / Spring (odd years)
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
Course:	MA5740: Advanced Sampling Methods / 3 cr. / On demand
Description:	Runs concurrently with MA4740. Same topics as MA4740, but students meet
	an additional one hour per week to prove results and discuss advanced
	topics.
Prerequisites:	MA5701 and MA4770
Course:	MA5741: Multivariate Statistical Methods / 3 cr. / Spring (even years)
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
Course:	MA5750: Statistical Genetics / 3 cr. / On demand
Description:	Application of statistical methods to solve problems
	in genetics such as locating genes. Topics include basic concepts of
	genetics, linkage analysis, and association studies of family data,
	association tests based on population samples (for both qualitative
	and quantitative traits), gene mapping methods based on family data
	and population samples.
Prerequisites:	MA2710 or MA3710
Course:	MA5781: Time Series Analysis / 3 cr. / Spring (even years)
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

Course:	MA5791: Categorical Data Analysis / 3 cr. / Spring (odd years)
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
Course:	MA5980: Special Topics in Mathematics / 1-12 cr. / Fall, Spring, Summer
Description:	Special topics in mathematics.
Prerequisites:	None
Course:	MA5999: Graduate Research in Math / 1-12 cr. / Fall, Spring, Summer
Description:	Original investigation in theoretical, or applied mathematics, and
	submission of a thesis in partial fulfillment of the requirements for the MS
	degree in mathematics.
Prerequisites:	None
Course:	MA6200: Advanced Topics in Discrete Math / 1-3 cr. / 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
Course:	MA6201: Finite Geometries / 3 cr. / Spring (even years)
Description:	Introduction to finite geometries and its links to groups and codes.
	Topics include projective and affine geometries over finite fields,
	geometric description of error-correcting codes, bilinear forms and
	their groups (the classical groups, geometric algebra), group
	geometries (Dynkin diagrams, projective planes, generalized quadrangles),
	coordinatization of projective planes.
Prerequisites:	MA5301 or consent of instructor

Course:	MA6301: Permutation Groups and Enumeration / 3 cr. / Spring (even years)
Description:	Introduction to finite groups, permutations and their applications.
	Covers a review of finite group theory (Lagrange's theorem, simple groups,
	p-groups, Sylow theorems), permutation groups (Burnside's lemma, orbit
	formula, primitivity, t-fold transitivity, linear groups, the Mathieu
	groups). Applications include Polya theory (counting group orbits) and
	its use in chemistry, construction of combinatorial designs.
Prerequisites:	MA5301 or consent of instructor
Course:	MA6302: Algebraic Curves and Codes / 3 cr. / Spring (odd years)
Description:	Introduction to the theory of algebraic curves, equivalent algebraic
	function fields (main theorems Riemann-Roch theorem and Hasse-Weil
	theorem) and the construction of error-correcting codes from algebraic
	curves with finite fields of constants.
Prerequisites:	MA5301 or consent of instructor
Course:	MA6700: Advanced Topics in Statistics / 1-12 cr. / 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
Course:	MA6701: Probability / 3 cr. / 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
Course:	MA6980: Special Topics in Mathematics / 1-12 cr. / Fall, Spring
Description:	Special topics in mathematics.
Prerequisites:	None

Course:	MA6999: Mathematical Sciences Doctoral Research/ 1-12 cr./ Fall,
	Spring, Summer
Description:	Taken in partial fulfillment of the doctoral thesis requirement.
Prerequisites:	None
Restrictions:	Graduate students only; department permission required.