# Course Descriptions

Students who have credit for one or more upper division mathematics courses will not receive repeat credit for a mathematics course numbered below MA 2000. Students who have credit for MA 1713 are not permitted to enroll in any mathematics course numbered below MA 1713 without departmental approval.

## MA 0003. Developmental Mathematics. (3)

(MA 0003 is a developmental course designed to prepare a student for university mathematics courses at the level of MA 1313 College Algebra: credit received for this course will not be applicable toward a degree). Three hours lecture. Real numbers fractions, decimal fractions, percent, algebraic expressions, factoring, algebraic fractions, linear equations/inequalities, integral exponents, quadratic equations.

## MA 0103. Intermediate Algebra. (3)

(MA 0103 is designed to prepare a student for MA 1313 College Algebra) Two hours lecture. Two hours laboratory. Real numbers, algebraic expressions, factoring, algebraic fractions, linear equations/inequalities, quadratic equations, Pythagorean Theorem. Does not count toward any degree.

## MA 1313. College Algebra. (3)

(Students with credit in MA 1713 will not receive credit for this course. Prerequisite: ACT Math sub-score 19, or grade of C or better in MA 0103). Two hours lecture. Two hours laboratory. Review of fundamentals; linear and quadratic equations; inequalities; functions; simultaneous equations; topics in the theory of equations. For college algebra placement exam go to: www.math.msstate.edu/capt/.

## MA 1323. Trigonometry. (3)

(Students with credit in MA 1713 will not receive credit for this course. Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Three hours lecture. The trigonometric functions: identities; trigonometric equations: applications.

## MA 1413. Structure of the Real Number System. (3)

(Prerequisite: a C or better in MA 1313 or an ACT Math sub-score of 24). Three hours lecture. The nature of mathematics; introductory logic; structure and development of the real number system. (Course is meant primarily for Elementary and Special Education majors).

## MA 1423. Problem Solving with Real Numbers. (3)

(Prerequisite: a C or better in MA 1413). Three hours lecture. Proportions, percent problems, probability, counting principles, statistics. (Course is meant primarily for Elementary or Special Education majors).

## MA 1433. Informal Geometry and Measurement. (3)

(Prerequisites: a C or better in both MA 1413 and MA 1423). Three hours lecture. Measurements and informal geometry. (Course is meant primarily for Elementary and Special Education majors).

## MA 1453. Precalculus with Graphing Calculators. (3)

(Prerequisites: Math ACT 24 or C or better in MA 1323 or score of at least 70 on the Precalculus Qualifying Exam). Three hours lecture. Properties, applications, and graphs of linear, quadratic, polynomial, exponential, logarithmic, and trigonometric functions; trigonometric identities, equations and inverses; inequalities. (Degree credit will not be granted for MA 1453 and either MA 1313 or MA 1323. This course is intended to prepare students to take MA 1713 Calculus I).

## MA 1463. Finite Mathematics and Introduction to Calculus.

(Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Three hours lecture. Matrices and systems of linear equations; introduction to calculus.

## MA 1613. Calculus for Business and Life Sciences I. (3)

(Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Three hours lecture. Algebraic and some transcendental functions, solutions of systems of linear equations, limits, continuity, derivatives, applications.

## MA 1623. Calculus for Business and Life Sciences II. (3)

(Prerequisite: MA 1613). Three hours lecture. Anti-derivatives, the definite integral, applications of the definite integral, functions of two or more variables, partial derivatives, maxima and minima, applications.

## MA 1713. Calculus I. (3)

(Prerequisite: ACT Math subscore 26, or grade of C or better in MA 1323 or MA 1453). Three hours lecture. Analytic geometry; functions; limits; continuity; derivatives of algebraic functions. Application of the derivative. Honors section available through invitation.

## MA 1723. Calculus II. (3)

(Prerequisite: Grade of C or better in MA 1713). Three hours lecture. Antidifferentiation; the definite integral; applications of the definite integral; differentiation and integration of transcendental functions. Honors section available through invitation.

## MA 2113. Introduction to Statistics. (3)

(Prerequisite: ACT Math subscore 24, or a grade of C or better in MA 1313). Two hours lecture. Two hours laboratory. Introduction to statistical techniques: descriptive statistics, random variables, probability distributions, estimation, confi dence intervals, hypothesis testing, and measurement of association. Computer instruction for statistical analysis. (Same as ST 2113).

## MA 2733. Calculus III. (3)

(Prerequisite: Grade of C or better in MA 1723). Three hours lecture. Further methods of integration; polar coordinates; vectors; infinite series. Honors section available through invitation.

## MA 2743. Calculus IV. (3)

(Prerequisite: Grade of C or better in MA 2733). Three hours lecture. Differential calculus of functions of several variables; multiple integration; vector calculus. Honors section available through invitation.

## MA 3053. Foundations of Mathematics. (3)

(Prerequisite: MA 1723). Three hours lecture. The logical structure of mathematics; the nature of a mathematical proof; applications to the basic principles of algebra and calculus.

## MA 3113. Introduction to Linear Algebra. (3)

(Prerequisite: MA 1723). Three hours lecture. Vector spaces; matrices; linear transformations; systems of linear equations; characteristic values and characteristic vectors.

## MA 3123. Introduction to Statistical Inference. (3)

(Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Two hours lecture. Two hours laboratory. Basic concepts and methods of statistics, including descriptive statistics, probability, random variables, sampling distribution, estimation, hypothesis testing, introduction to analysis of variance, simple linear regression. (Same as ST 3123).

## MA 3163. Introduction to Modern Algebra. (3)

(Prerequisite: MA 3113 and MA 3053). Three hours lecture. Rings, integral domains, and fields with special emphasis on the integers, rational numbers, real numbers and complex numbers; theory of polynomials.

## MA 3253. Differential Equations I. (3)

(Prerequisite: MA 2743 or co-registration in MA 2743). Origin and solution of differential equations; series solutions; Laplace Transform methods; applications.

## MA 3353. Differential Equations II. (3)

(Prerequisite: MA 3253). Three hours lecture. Systems of differential equations; matrix representations; infinite series solution of ordinary differential equations; selected special functions; boundary-value problems; orthogonal functions: Fourier series.

## MA 3463. Foundations of Geometry. (3)

(Prerequisite: MA 1723 and MA 3053). Three hours lecture. The structural nature of geometry; modern methods in geometry: finite geometrics.

## MA 3513. History of Mathematics. (3)

(Prerequisite: MA 2733 or co-registration in MA 2733). Three hours lecture. A historical development of mathematicians and their most important contributions will be emphasized.

## MA 4133/6133. Discrete Mathematics. (3)

(Prerequisites: MA 3163 or consent of instructor). Three hours lecture. Sets, relations, functions, combinatorics, review of group and ring theory, Burnside’s theorem, Polya’s counting theory, group codes, fi nite fi elds, cyclic codes, and error-correcting codes.

## MA 4143/6143. Graph Theory. (3)

(Prerequisites: MA 3113 or consent of instructor). Three hours lecture. Basic concepts, graphs, and matrices, algebraic graph theory, planarity and nonplanarity, Hamiltonian graphs, digraphs, network fl ows, and applications.

## MA 4153/6153. Matrices and Linear Algebra. (3)

(Prerequisites: MA 3113 and MA 3253). Three hours lecture. Linear transformations and matrices; eigenvalues and similarity transformations; linear functionals, bilinear and quadratic forms; orthogonal and unitary transformations; normal matrices; applications of linear algebra.

## MA 4163/6163. Group Theory. (3)

(Prerequisite: MA 3163 or consent of the instructor). Three hours lecture. Elementary properties: normal subgroups; factor groups; homomorphisms and isomorphisms; Abelian groups; Sylow theorems; composition series; solvable groups.

## MA 4173/6173. Number Theory. (3)

(Prerequisite: MA 3113). Three hours lecture. Divisibility: congruences; quadratic reciprocity; Diophantine equations; continued fractions.

## MA 4213. Senior Seminar in Mathematics. (3)

(Prerequisites: MA 3163 and MA 3253 and MA 4633). Three hours lecture. Students explore topics in current mathematical research, write expository articles, and give oral presentations. Refi nement of specialized writing skills needed for effective mathematical communication.

## MA 4243/6243 Data Analysis I. (3)

(Prerequisite: MA 2743. Co-requisite: MA 3113). Three hours lecture. Data description and descriptive statistics, probability and probability distributions, parametric one-sample and two-sample inference procedures, simple linear regressions, one-way ANOVA. Use of SAS. (Same as ST 4243/6243.)

## MA 4253/6253 Data Analysis II. (3)

(Prerequisites: MA 4243/6243 and MA 3113). Three hours lecture. Multiple linear regression; fi xed, mixed and random effect models; block designs; two-factor analysis of variance; three-factor analysis of variance; analysis of covariance. Use of SAS. (Same as ST 4253/6253.)

## MA 4313/6313. Numerical Analysis I. (3)

(Prerequisites: CSE 1213, MA 3113, and MA 2743). Three hours lecture. Matrix operations; error analysis; norms of vectors and matrices; transformations; matrix functions; numerical solutions of systems of linear equations; stability; matrix inversion; eigen value problems; approximations.

## MA 4323/6323. Numerical Analysis II. (3)

(Prerequisites: CSE 1213 or equivalent. MA 3113 and MA 3253). Three hours lecture. Numerical solution of equations; error analysis; finite difference methods; numerical differentiation and integration; series expansions; difference equations; numerical solution of differential equations.

## MA 4373/6373. Introduction to Partial Differential Equations. (3)

(Prerequisite: MA 3253). Three hours lecture. Linear operators: linear fi rst order equations; the wave equation; Green’s function and Sturm—Liouville problems; Fourier series; the heat equation; Laplace’s equation.

## MA 4513/6513. Applied Probability and Statistics for Secondary Teachers. (3)

(Prerequisite: MA 1723). Three hours lecture. (Credit not available for students with credit in MA-ST 4543/6543). Graphical methods of presenting data; analysis of data; probability, binomial distribution, normal distribution; random sampling; linear regression and correlation.

## MA 4523/6523. Introduction to Probability. (3)

(Prerequisite: MA 2733). Three hours lecture. Basic concepts of probability, conditional probability, independence, random variables, discrete and continuous probability distributions, moment generating function, moments, special distributions, central limit theorem. (Same as ST 4523/6523).

## MA 4533/6533. Introductory Probability and Random Processes. (3)

(Prerequisites: MA 3113 and MA 2743). Three hours lecture. Probability, law of large numbers, central limit theorem, sampling distributions, confidence intervals, hypothesis testing, linear regression, random processes, correlation functions, frequency and time domain analysis. (Credit can not be earned for this course and MA/ST 4523/6523.)

## MA 4543/6543. Introduction to Mathematical Statistics I. (3)

(Prerequisite: MA 2743.) Three hours lecture. Combinatorics; probability, random variables, discrete and continuous distributions, generating functions, moments, special distributions, multivariate distributions, independence, distributions of functions of random variables. (Same as ST 4543/6543.)

## MA 4573/6573. Introduction to Mathematical Statistics II. (3)

(Prerequisite: MA 4543/6543.) Three hours lecture. Continuation of MA-ST 4543/6543. Transformations, sampling distributions, limiting distributions, point estimation, interval estimation, hypothesis testing, likelihood ratio tests, analysis of variance, regression, chi-square tests. (Same as ST 4573/6573.)

## MA 4633/6633. Advanced Calculus I. (3)

(Prerequisite: MA 2743 and MA 3053). Three hours lecture. Theoretical investigation of functions; limits; differentiability and related topics in calculus.

## MA 4643/6643. Advanced Calculus II. (3)

(Prerequisite: MA 4633/6633). Three hours lecture. Rigorous development of the defi nite integral; sequences and series of functions; convergence criteria; improper integrals.

## MA 4733/6733. Linear Programming. (3)

(Prerequisites: MA 3113). Three hours lecture. Theory and application of linear programming; simplex algorithm, revised simplex algorithm, duality and sensitivity analysis, transportation and assignment problem algorithms, integer and goal programming. (Same as IE 4733/6733).

## MA 4753/6753. Applied Complex Variables. (3)

(Prerequisite: MA 2743). Three hours lecture. Analytic functions: Taylor and Laurent expansions; Cauchy theorems and integrals; residues; contour integration; introduction to conformal mapping.

## MA 4933/6933. Mathematical Analysis I. (3)

(Prerequisite: MA 4633/6633 or equivalent). Three hours lecture. Metric and topological spaces; functions of bounded variation and differentiability in normed spaces.

## MA 4943/6943. Mathematical Analysis II. (3)

(Prerequisite: MA 4933/6933). Three hours lecture. Riemann-Stieltjes integration, sequences and series of functions; implicit function theorem; multiple integration.

## MA 4953/6953. Elementary Topology. (3)

(Prerequisite: MA 4633/6633). Three hours lecture. Defi nition of a topological space, metric space, continuity in metric spaces and topological spaces; sequences; accumulation points.

## MA 8113. Modern Higher Algebra I. (3)

(Prerequisite: MA 4163/6163). Three hours lecture. A study of the basic mathematical systems with emphasis on rings, fi elds, and vector spaces.

## MA 8123. Modern Higher Algebra II. (3)

(Prerequisite: MA 8113). Three hours lecture. A continuation of the topics introduced in MA 8113.

## MA 8203. Foundations of Applied Mathematics I. (3)

(Prerequisites: MA 3113, MA 3253 or consent of instructor.) Three hours lecture. Principles of applied mathematics including topics from perturbation theory, calculus of variations, and partial differential equations. Emphasis of applications from heat transfer, mechanics, fluids.

## MA 8213. Foundations of Applied Mathematics II. (3)

(Prerequisite: MA 8203). Three hours lecture. A continuation of MA 8203 including topics from wave propagation, stability, and similarity methods.

## MA 8253. Operational Mathematics. (3)

(Prerequisite: MA 4753/6753). Three hours lecture. Theory and applications of Laplace, Fourier, and other integral transformations: introduction to the theory of generalized functions.

## Courses numbered MA 8273, 8283, 8293 and 8313 have as prerequisites at least one of the courses MA 4633/6633, MA 4153/6153, 4753/6753.

## MA 8273. Special Functions. (3)

Three hours lecture. Infi nite products: asymptotic series; origin and properties of the special functions of mathematical physics.

## MA 8283. Calculus of Variations. (3)

Three hours lecture. Functionals: weak and strong extrema; necessary conditions for extrema; suffi cient conditions for extrema; constrained extrema; direct methods; applications.

## MA 8293. Integral Equations. (3)

Three hours lecture. Equations of Fredholm type: symmetric kernels; Hilbert-Schmidt theory; singular integral equations; applications; selected topics.

## MA 8313. Ordinary Differential Equations I. (3)

Three hours lecture. Linear systems of differential equations; existence and uniqueness; second order systems; systems with constant coeffi cients; periodic systems; matrix comparison theorems; applications and selected topics.

## MA 8323. Ordinary Differential Equations II. (3)

(Prerequisite: MA 8313). Three hours lecture. Existence, uniqueness, continuation of solutions of nonlinear systems; properties of solutions of linear and nonlinear equations including boundedness, oscillation, asymptotic behavior, stability, and periodicity; application.

## MA 8333. Partial Differential Equations I. (3)

(Prerequisite: MA 4373/6373 or consent of instructor). Three hours lecture. Solution techniques; existence and uniqueness of solutions to elliptic, parabolic, and hyperbolic equations; Green’s functions.

## MA 8343. Partial Differential Equations II. (3)

(Prerequisite: MA 8333). Three hours lecture. A continuation of the topics introduced in MA 8333.

## MA 8363. Numerical Solution of Systems of Nonlinear Equations. (3)

(Prerequisites: MA 4313/6313 and MA 4323/6323). Three hours lecture. Basic concepts in the numerical solution of systems of nonlinear equations with applications to unconstrained optimization.

## MA 8383. Numerical Solution of Ordinary Differential Equations I. (3)

(Prerequisites: MA 4313/6313 and MA 4323/6323). Three hours lecture. General single-step, multistep, multivalue, and extrapolation methods for systems of nonlinear equations; convergence; error bounds; error estimates; stability; methods for stiff systems; current literature.

## MA 8443. Numerical Solution of Partial Differential Equations I. (3)

(Prerequisites: MA 4313/6313, MA 4323/6323, and MA 4373/6373 or consent of instructor). Three hours lecture. Basic concepts in the fi nite difference and fi nite element methods; methods for parabolic, hyperbolic and elliptic equations; analysis of stability and convergence.

## MA 8453. Numerical Solution of Partial Differential Equations II. (3)

(Prerequisite: MA 8443). Three hours lecture. Methods for elliptic equations; iterative procedures; integral equation methods; methods for hyperbolic equations; stability; dissipation and dispersion.

## MA 8463. Numerical Linear Algebra. (3)

(Prerequisite: MA 4323/6323). Three hours lecture. Basic concepts of numerical linear algebra.

## MA 8633. Real Analysis I. (3)

(Prerequisite: MA 4943/6943). Three hours lecture. Lebesgue measure and Lebesgue integrals; convergence theorems, differentiation and L spaces.

## MA 8643. Real Analysis II. (3)

(Prerequisite: MA 8633). Three hours lecture. General measures; the Radon-Nikodym theorem and other topics.

## MA 8663. Functional Analysis I. (3)

(Prerequisite: MA 8643). Three hours lecture. Hilbert spaces; Banach spaces; locally convex spaces; Hahn-Banach and closed graph theorems; principle of uniform boundedness; weak topologies.

## MA 8673. Functional Analysis II. (3)

(Prerequisite: MA 8663). Three hours lecture. Continuation of topics introduced in MA 8663.

## MA 8713. Complex Analysis I. (3)

(Prerequisite MA 4943/6943 or consent of instructor). Three hours lecture. Complex numbers: functions of a complex variable; continuity; differentiation and integration of complex functions; transformations in the complex plane.

## MA 8723. Complex Analysis II. (3)

(Prerequisite: MA 8713). Three hours lecture. Series; analytic continuation; Riemann surfaces; theory of residues.

## MA 8913. Introduction to Topology I. (3)

(Prerequisite: MA 4643/6643 or MA 4953/6953). Three hours lecture. Basic general topology; introduction of homotopy and homology groups.

## MA 8923. Introduction to Topology II. (3)

(Prerequisite: MA 8913). Three hours lecture. Continuation of topics introduced in MA 8913.

## MA 8981. Teaching Seminar. (1)

One hour lecture. Preparation for service as instructors in mathematics and statistics courses; includes practice lectures and exam preparation. (May be taken for credit more than once.)

## MA 9313. Selected Topics in Ordinary Differential Equations. (3)

(Prerequisite: MA 8313 and consent of instructor). (May be taken for credit more than once). Three hours lecture. Topics to be chosen from such areas as Bifurcation Theory, Biological Modeling, Control Theory, Dynamical Systems, Functional Differential Equations, Nonlinear Oscillations, and Quantitative Behavior.

## MA 9333. Selected Topics in Partial Differential Equations. (3)

(Prerequisite: MA 8333 and consent of instructor). (May be taken for credit more than once). Three hours lecture. Topics to be chosen from such areas as Bifurcation Theory, Boundary Integral Methods, Evolution Equations, Maximum and Variational Principles, and Spectral Methods.

## MA 9413. Selected Topics in Numerical Analysis. (3)

(Prerequisite: Consent of instructor). (May be taken for credit more than once). Three hours lecture. Current topics in Numerical Analysis. The subject matter may vary from year to year.

## MA 9633. Selected Topics in Analysis. (3)

(Prerequisite: MA 8643 and consent of instructor). (May be taken for credit more than once). Three hours lecture. Topics will be chosen from areas of analysis of current interest.

## ST 2113. Introduction to Statistics. (3)

(Prerequisite: ACT Math subscore 24, or grade of C or better in MA 1313). Two hours lecture. Two hours laboratory. Introduction to statistical techniques: descriptive statistics, random variables, probability distributions, estimation, confi dence intervals, hypothesis testing, and measurement of association. Computer instruction for statistical analysis. (Same as MA 2113).

## ST 3123. Introduction to Statistical Inference. (3)

(Prerequisite: ACT Math subscore of 24 or grade of C or better in MA 1313). Two hours lecture. Two hours laboratory. Basic concepts and methods of statistics, including descriptive statistics, probability, random variables, sampling distributions, estimation, hypothesis testing, introduction to analysis of variance, simple linear regression. (Same as MA 3123).

## ST 4111/6111. Seminar in Statistical Packages. (1)

One hour lecture. Introduction to the statistical computer packages available at MSU.

## ST 4211/6211. Statistical Consulting. (1)

(Prerequisite: Consent of the department). (May be repeated for credit.) Provides students with the opportunity to participate as statistical consultants on real projects; consultants are required to attend a weekly staff meeting.

## ST 4213/6213. Nonparametric Methods. (3)

(Prerequisite: An introductory course in statistical methods). Three hours lecture. Nonparametric and distribution-free methods, including inferences for proportions, contingency table analysis, goodness of fi t tests, statistical methods based on rank order, and measures of association.

## ST 4243/6243 Data Analysis I. (3)

(Prerequisite: MA 2743. Co-requisite: MA 3113). Three hours lecture. Data description and descriptive statistics, probability and probability distributions, parametric one-sample and two-sample inference procedures, simple linear regressions, one-way ANOVA. Use of SAS. (Same as MA 4243/6243.)

## ST 4253/6253 Data Analysis II. (3)

(Prerequisites: MA 4243/6243 and MA 3113). Three hours lecture. Multiple linear regression; fi xed, mixed and random effect models; block designs; two-factor analysis of variance; three-factor analysis of variance; analysis of covariance. Use of SAS. (Same as MA 4253/6253.)

## ST 4313/6313. Introduction to Spatial Statistics. (3)

(Prerequisite: Grade of C or better in ST 3123 or equivalent). Two hours lecture. Two hours laboratory. Spatial data analysis: kriging, block kriging, cokriging; variogram models; median polish and universal kriging for mean-nonstationary data; spatial autoregressive models; estimation and testing; spatial sampling.

## ST 4523/6523. Introduction to Probability. (3)

(Prerequisite: MA 2733). Three hours lecture. Basic concepts of probability, conditional probability, independence, random variables, discrete and continuous probability distributions, moment generating function, moments, special distributions, central limit theorem. (Same as MA 4523/6523).

## ST 4543/6543. Introduction to Mathematical Statistics I. (3)

(Prerequisite: MA 2743). Three hours lecture. Combinatorics; probability, random variables, discrete and continuous distributions, generating functions, moments, special distributions, multivariate distributions, independence, distributions of functions of random variables. (Same as MA 4543/6543).

## ST 4573/6573. Introduction to Mathematical Statistics II. (3)

(Prerequisite: ST 4543/6543). Three hours lecture. Continuation of ST 4543/6543. Transformations, sampling distributions, limiting distributions, point estimation, interval estimation, hypothesis testing, likelihood ratio tests, analysis of variance, regression, chi-square tests. (Same as MA 4573/6573).

## ST 8114. Statistical Methods. (4)

(Prerequisite: MA 1313). Three hours lecture. Two hours laboratory. Fall and Spring semesters. Descriptive statistics; sampling distributions; inferences for one and two populations; completely random, block, Latin square, split-plot designs; factorials; simple linear regression; chi-square tests.

## ST 8214. Design and Analysis of Experiments. (4)

(Prerequisite: ST 8114) Three hours lecture. Three hours laboratory. Offered spring semester. Procedures in planning and analyzing experiments; simple, multiple, and curvilinear regression; factorial arrangement of treatments; confounding; fractional replication; block designs; lattices; split-plots.

## ST 8253. Regression Analysis. (3)

(Prerequisite: ST 8114 or equivalent). Three hours lecture. Fall and Spring semesters. Simple linear regression analysis and related inferences, remedial measures, multiple and polynomial regression, use of indicator variables, variable selection methods, and use of computer.

## ST 8263. Advanced Regression Analysis. (3)

(Prerequisite: ST 8253). Three hours lecture. Continuation of ST 8253, including variable selection methods, optimization techniques, biased estimation methods such as ridge regression, non-linear regression, model validation methodology, indicator variables, design models.

## ST 8313. Introduction to Survey Sampling. (3)

(Prerequisite: ST 8114). Three hours lecture. Topics include: design, planning, execution, and analysis of sample surveys; simple random, stratifi ed random, cluster, and systematic sampling; ratio and regression estimation.

## ST 8353. Statistical Computations. (3)

(Prerequisite: ST 8114). Three hours lecture. Applications of computer packages, including data screening, t-tests and Hotelling's T", analysis of designed experiments, regression analysis, contingency table analysis, projects, and report writing.

## ST 8413. Multivariate Statistical Methods. (3)

(Prerequisite: ST 8253). Three hours lecture. Multivariate normal; multiple and partial correlation; principal components; factor analysis; rotation; canonical correlation; discriminant analysis; Hotelling's T"; cluster analysis; multidimensional scaling; multivariate analysis of variance.

## ST 8533. Applied Probability. (3)

(Prerequisite: ST 4543/6543). Three hours lecture. An introduction to the applications of probability theory. Topics include Markov Chains, Poisson Processes, and Renewal, Queueing, and Reliability theories. Other topics as time permits.

## ST 8553. Advanced Probability Theory. (3)

(Prerequisites: ST 6543 and MA 8633 or consent of instructor). Three hours lectures. A measure-theoretic presentation of the theory of probability including independence and conditioning, convergence theorems, characteristics functions, and limit theorems.

## ST 8563. Advanced Stochastic Processes. (3)

(Prerequisite: ST 8553 or consent of instructor). Three hours lecture. Continuation of ST 8553, including Markov processes, second-order processes, stationary Processes, Ergodic theory, martingales, stopping times, and Brownian motion.

## ST 8603. Applied Statistics. (3)

(Prerequisite: ST 4253/6253 or equivalent). Three hours lecture. Advanced analysis of experimental data. Topics include mixed and random models, incomplete block design, changeover trials, experiments, analysis of covariance, and repeated measures design.

## ST 8613. Linear Models I. (3)

(Prerequisites: ST 4253/6253 and 4573/6573). Three hours lecture. Random vectors, multivariate normal, distribution of quadratic forms, estimation and statistical inferences relative to the general linear model of full rank, theory of hypothesis testing.

## ST 8633. Linear Models II. (3)

(Prerequisite: ST 8613). Three hours lecture. Continuation of ST 8613, including generalized inverses; general linear model not of full rank, related inferences, applications; computing techniques; design models, analyses, hypothesis testing; variance-component models.

## ST 8733. Advanced Statistical Inference I

(Prerequisites: MA/ST 4573/6573 or consent of instructor). Three hours lecture. Theoretical statistics, including sufficiency and completeness, UMVU estimators, likelihood estimation, Bayesian estimation, UMP tests, likelihood-based tests, sequential tests, optimality, and asymptotic properties.

## ST 8743 Advanced Statistical Inference II. (3)

(Prerequisites: ST 8733 or consent of instructor). Three hours lecture. Theoretical statistics, including order statistics, power functions, efficiency, asymptotic theory, nonparametric rank-based hypothesis testing, permutation testing, M estimation, jackknife procedure, and bootstrap procedure.

## ST 8853. Advanced Design of Experiments I. (3)

(Prerequisite: ST 8603 or ST 8214). Three hours lecture. Noise reducing designs; incomplete block designs; factorial experiments, Yates' algorithms, confounding systems; fractional replication; pooling of experiments; nested designs; repeated measurement designs; messy data analyses.

## ST 8863. Advanced Design of Experiments II. (3)

(Prerequisites: ST 8853 and ST 8613). Three hours lecture. Continuation of ST 8853, including analysis of covariance, splitplot designs and variants, applications of the general linear model, response surface methodology, randomization models, pseudo-factors, and cross-over design.

## ST 8913. Recent Developments in Statistics. (3)

(Prerequisite: Consent of instructor). New results in statistical theory and/or statistical methodology; advanced work organized around topics not usually considered in the other courses.

## ST 8951. Seminar in Statistics. (1)

(Prerequisite: Consent of instructor). (May be repeated for credit). Review of literature on assigned topics; discussions and presentations of papers.

## ST 9423. Multivariate Statistical Analysis. (3)

(Prerequisites: ST 8413 and ST 8613 or consent of instructor). Three hours lecture. Theory of multivariate statistical methodology, including multivariate normal and Wishart distributions, Hotelling’s T2 , classification, multivariate analysis of variance and covariance, canonical correlation, principal components analysis.