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Mathematics Courses

Mathematics Courses MATH 1100. Basic Algebra. (3). Review of Real number system; exponents; rational roots; graphs using graphing calculators; partial fractions; synthetic division; theory of equations; inequalities; applications. NOTE: does not satisfy any part of mathematics requirements for any degree; not applicable toward fulfulling credit hour minimum for degrees in The College of Arts and Sciences. PREREQUISITE: two years of high school algebra or DSPM 0850 with C- or better. MATH 0990. Foundations of Geometry. (3). Axiomatic development of plane geometry; emphasis on concepts of symmetry, congruence and similarity, Pythagorean Theorem and special right triangle properties, area and volumes of special right triangle properties; area and volumes of special two- and three-dimensional figures. NOTE: will not count toward the 120-semester hour degree requirement for any degree. PREREQUISITE: two units of high school algebra or DSPM 0850. MATH 1710. College Algebra. (3). (1211). Analysis of functions (linear, quadratic, polynomial, root, rational, exponential, logarithmic) using graphing calculators; partial fractions; synthetic division; conic sections; theory of equations; inequalities; applications. NOTE: only one of MATH 1710 or MATH 1730 may be used to satisfy degree requirements. PREREQUISITE: two years of high school algebra , or DSPM 0850. [G] MATH 1720. Trigonometry. (3). (1212). Circular functions; inverse circular functions, graphs of circular and inverse functions, identities, equations, angles, trigonometric functions, solution of triangles, elementary application of vectors; trigonometric form of complex numbers. NOTE: MATH 1720 and MATH 1730 will not satisfy a six semester hour degree requirement. PREREQUISITE: placement test recommended but not required; MATH 1710. MATH 1730. College Algebra and Trigonometry. (4). (1213). Exponents, radicals, quadratic functions, inequalities; relations and functions; inverse, exponential and logarithmic functions; solution of algebraic systems; trigonometric functions, identities, equations and graphs; angle measurements; sum, difference, half-angle and double-angle formulas; solution of triangles, laws of sines and cosines. NOTE: MATH 1710 and 1730, or 1720 and 1730 will not satisfy a six semester hour degree requirement. PREREQUISITE: two units of high school algebra, or DSPM 0850. MATH 1530. Introduction to Statistical Reasoning and Application. (3). (1601). Underlying ideas of statistical and quantitative thinking; randomization in sample survey methods and design of experiments; double blind experiments and observational studies; descriptive and summary statistics; measurement errors; probability models; normal approximation; tests of significance and p-values, basic concepts of correlation and regression analyses; MINITAB. NOTE: Math majors may not use this course as part of the major. PREREQUISITE: Two years of high school algebra or DSPM 0850. [G] MATH 1480. Mathematics for Elementary School Teachers. (3). Examination of mathematics taught at the elementary school level; problem solving, sets, algebraic thinking, number theory, rational numbers, real numbers. PREREQUISITE: two units of high school algebra or DSPM 0850. MATH 1420. Foundations of Mathematics II. (3). (1182). Algebra review and applications; functions, graphs, permutations, combinations; introduction to probability and statistics; problem solving. PREREQUISITE: two units of high school algebra or DSPM 0850. [G] w MATH 1830. Elementary Calculus. (3). (1312). Introduction to concepts and methods of elementary calculus of one real variable as related to rational, exponential, and logarithmic functions; nature of derivatives; differentiation; application of derivative; nature of integration: definite integral; applications of definite integral. NOTE: only one of MATH 1830 or 1910 may be used to satisfy degree requirements. PREREQUISITE: MATH 1710 (with a minimum grade of C), ACT Math subscore of at least 24, or equivalent SAT Math score. [G] w MATH 1910. Calculus I. (4). (1321). Introduction to calculus of one real variable; limits; continuity; derivatives; applications of derivatives including Newton’s method, graphing techniques, optimization, indeterminate forms and l’Hospital’s rule; antiderivatives; includes transcendental functions. NOTE: only one of MATH 1830 or MATH 1910 may be used to satisfy degree requirements. Students may not receive credit for both MATH 1910 and MATH 1421. PREREQUISITE: MATH 1720 (with a minimum grade of C) or MATH 1730 (with a minimum grade of C), or satisfactory score on placement exam. [G] w MATH 1421. Honors Calculus I. (4). (1401). Concepts of differential calculus with emphasis on theory; limits, continuous functions, applications of the derivative. NOTE: students may not receive credit for both MATH 1421 and MATH 1910. PREREQUISITE: permission of instructor. MATH 2000. Experiences in Mathematics. (3). Introduction to selected areas of mathematical sciences through application to modeling and solution of problems involving networks, circuits, trees, linear programming, random samples, regression, probability, inference, voting systems, game theory symmetry and tilings, geometric growth, conics, comparison of algorithms, codes and data management. PREREQUISITE: three years of high school mathematics, including two years of algebra and one year of geometry. [G]w MATH 1900. Experiences with Calculus. (1). In-depth study of concepts introduced in MATH 1830 with focus on use of transcendental function. Students completing both MATH 1830 and 1900 will fulfill the required prerequisites for MATH 1920. PREREQUISITE: MATH 1830 with a grade of A, and permission of instructor. MATH 1920. Calculus II. (4). (2321). Integration and applications of the definite integral; techniques of integration and improper integrals; curves defined by Parametric equations; arc length and surface area; polar coordinates; infinite series, Taylor and McLaurin series. NOTE: students may not receive credit for both MATH 1920 and MATH 2421. PREREQUISITE: MATH 1910 or both MATH 1830 and 1900. w MATH 2421. Honors Calculus II. (4). (1402). Differential and integral calculus with emphasis on theory; anti-derivatives, definite integrals, techniques of integration, sequences, and series. NOTE: Students may not receive credit for both MATH 2421 and 1920. PREREQUISITES: MATH 1421 or MATH 1920, and permission of instructor. MATH 2701. Discrete Structures. (3). Elementary logic; sets, relations, functions, orderings, equivalence relations, partitions: finite sets, modular arithmetic; natural numbers, mathematical induction, strings, string programs, connectedness, traversals, graph algorithms. NOTE: students may not receive credit for both MATH 2701 and MATH 2702. PREREQUISITE: MATH 1910. COREQUISITE: COMP 2701. MATH 2702. Introduction to Proofs and Fundamentals of Mathematics. (3). Logic, algebra of sets; forms of proof including mathematical induction; elementary combinatorics and binomial theorem; paradoxes, basic number theory, cardinality. PREREQUISITE: MATH 1910. MATH 3581. College Geometry. (3). Axiomatic systems; major results from plane geometry; affine, projective, elliptic, and hyperbolic geometry; applications of differential calculus. PREREQUISITE: MATH 1910 and 2702. MATH 2110. Calculus III. (4). Multivariable calculus including three-dimensional analytic geometry and vectors, quadratic surfaces, arc length and curvature, limits and continuity, partial derivatives and their applications, tangent planes, optimization problems and Lagrange multipliers, multiple integrals, vector fields, line and surface integrals, Green’s theorem, Stokes' theorem, the divergence theorem. PREREQUISITE: MATH 1920. MATH 2422. Honors Calculus III. (4). Multivariable calculus; vectors and matrices, partial derivative and applications, multiple integrals, line and surface integrals, Green’s and Stokes’ theorem. NOTE: Students may not receive credit for both MATH 2422 and 2110. PREREQUISITE: MATH 2421. MATH 4082. Mathematics for Middle School Teachers. (3). Capstone course consisting of more thorough study of fundamental concepts involving numbers, operations, functions, spatial relationships, data analysis; Excel, graphing calculators, modern software. PREREQUISITE: permission of instructor. MATH 3221. Elementary Number Theory. (3). Divisibility properties of integers; prime numbers; congruences; Diophantine equations; quadratic residues; number theoretic functions; Fermat’s theorem and Euler’s generalization; applications to cryptography; quadratic reciprocity law. PREREQUISITE: MATH 3242 , or one of MATH 2701, MATH 2702, or permission of instructor. MATH 3242. Introduction to Linear Algebra. (3). (4241). Systems of linear equations, matrices, elementary row and column operations, determinants; vector spaces and subspaces; linear transformations. PREREQUISITE: MATH 2110, or MATH 1920 and one of MATH 2701, 2702, or permission of instructor. [C] MATH 3120. Differential Equations. (3). (3391). Ordinary differential equations including series solutions. PREREQUISITE: MATH 2110. MATH 3402. Honors Mathematics IV. (4). (2402). Linear algebra and differential equations; vector spaces, bases, linear transformations, matrices, first and second order ordinary differential equations, systems, phase plane methods. NOTE: students with credit for this course cannot receive credit for MATH 3242 or MATH 3120. PREREQUISITE: MATH 2422. MATH 4020-6020. Actuarial Mathematics. (3). Preparation for SOA Exam P, CAS Exam 1. Conditional probability, dependence, combinatorial principles, random variables, discrete and continuous probability distributions, expectation, marginal distributions, risk management concepts. COREQUISITE: MATH 4635. MATH 4151-6151. History of Mathematics. (3). Development of mathematics from earliest times to present; problem studies; parallel reading and class reports. PREREQUISITE: 21 hours in MATH courses including MATH 2110 and one of MATH 2701, MATH 2702, or permission of instructor. [I] MATH 4361-6361. Complex Variables. (3). Complex numbers; analytic functions; Cauchy-Riemann conditions; Taylor and Laurent series; integration. PREREQUISITE: MATH 2110. MATH 4391-6391. Partial Differential Equations I. (3). Laplace transforms; Fourier series; introduction to partial differential equations. PREREQUISITE: MATH 3120. MATH 4721-6721. Numerical Analysis. (3). Derivation and application of computer-oriented, numerical methods for functional approximation, differentiation, quadrature, and solution of ordinary differential equations. PREREQUISITE: MATH 1920 and knowledge of some structured programming language. MATH 4261-6261. Abstract Algebra. (3). Groups; homomorphisms; rings; integral domains; polynomials; fields. PREREQUISITE: MATH 3242, or permission of instructor. MATH 4411-6411. Topology. (3). Introductory set theory; metric spaces; topological spaces; continuous functions; separation axioms; separability and countability axioms; connectedness and compactness. PREREQUISITE: MATH 2702 and either MATH 3242 or MATH 4350. MATH 4350-6350. Introduction to Real Analysis I. (3). (3111). Real number system, functions and sequences, limits, continuity, differentiation; Riemann-Stieltjes integration, series of functions. PREREQUISITE: MATH 2110, MATH 2702 and MATH 3242. [W] MATH 4242-6242. Linear Algebra. (3). Linear transformations, polynomials, determinants, direct-sum decompositions, diagonalizable operators, rational and Jordan forms, inner product spaces, the spectral theorem. PREREQUISITE: MATH 3242. MATH 4392-6392. Partial Differential Equations II. (3). Methods of characteristics; Green’s functions; existence and regularity of solutions of boundary value and Cauchy problems. PREREQUISITE: MATH 4391-6391. MATH 7721. Advanced Numerical Analysis. (3). A continuation of MATH 6721; specialized methods and techniques in field of numerical analysis. PREREQUISITE: MATH 6721. MATH 7261. Algebraic Theory I. (3). Studies in group theory and ring theory, including Sylow theory and factorization theory. PREREQUISITE: MATH 6261. MATH 7411. Point Set Topology. (3). An axiomatic approach to compactness, separability, connnectedness, metrizability and other topological properties. PREREQUISITE: MATH 6411. MATH 4351-6351. Introduction to Real Analysis II. (3). Integration theory; Riemann and Lebesgue integrals; partial differentiation, implicit function theorem. PREREQUISITE: MATH 4350-6350, or permission of instructor. MATH 7237-8237. Graph Theory. (3). Connectivity, Euler tours, and Hamilton cycles, matchings, coloring problems, planarity, and network flows; study of classical theorems due to Brooks, Menger, Kuratowski, Schur, Tutte, and Vizing. PREREQUISITE: MATH 6242 or permission of instructor. MATH 7395-8395. Theory of Differential Equations. (3). Qualitative aspects of linear and nonlinear differential equations including asymptotic behavior and regularity; geometric, functional analytic, and harmonic analytic methods. The asymptotic could include ergodic limits and chaos. The regularity might range from analyticity to discontinuous solutions (shocks, liquid crystals etc.). PREREQUISITES: MATH 6350 and 6242. MATH 7321. Modeling and Computation. (3). Introduction to process of formulating, solving, and interpreting mathematical models of real phenomena; both formal analysis and numerical techniques for variety of models. PREREQUISITE: MATH 3120, 6721. MATH 7262. Algebraic Theory II. (3). A continuation of Math 7261. Studies in field theory and modules, including free algebras, Galois theory, tensor products. PREREQUISITE: MATH 7261. MATH 7361. Complex Analysis. (3). Analytic functions, power series, mapping properties, complex integration, Cauchy’s theorem and its consequences, sequences of analytic functions. PREREQUISITE: MATH 6351. MATH 7350. Real Variables I. (3). s-algebra, outer measure, Lebesgue measure, measurable functions, differentiation, absolute continuity, Lp-spaces. PREREQUISITE: MATH 6351. MATH 7016. Fourier Analysis. (3). Facilitates understanding of some important facts abut Fourier series, Fourier transforms, and finite Fourier analysis, including applications to other sciences (optics, acoustics, particle physics, uncertainty principle) as well as links within mathematics (infinitude of primes, isoperimetric inequality). May be repeated for a maximum of 6 credit hours when topics change. PREREQUISITE: MATH 6350 or equivalent, or permission of instructor. MATH 7375. Methods of Mathematical Physics I. (3). Vector spaces, matrices, tensors, vector fields, function spaces, differential and integral operators, transform theory, partial differential equations. PREREQUISITE: MATH 3120, 4242, and 4350; or permission of instructor. MATH 7393-8393. Differential Equations and Applications. (3). Basic concepts in ordinary and partial differential equations (possibly functional or stochastic differential equations); existence, uniqueness, continuous dependence theorems. Application areas could include diffusion, wave propagation, population dynamics, neural networks, mathematical biology and ecology, quantum theory, kinetic theory, depending on interests of class. PREREQUISITE: MATH 3120 or consent of instructor. MATH 7356-8356. Functional Analysis II. (3). A continuation of MATH 7355-8355. PREREQUISITE: MATH 7355-8355. MATH 7355-8355. Functional Analysis I. (3). Vector spaces, Banach spaces, Hilbert spaces; linear functionals and operators in such spaces; spectral theory. PREREQUISITE: MATH 7350. MATH 7351. Real Variables II. (3). Metric spaces, Baire category theorem, Hahn Banach theorem, uniform boundedness principle, closed graph theorem, general measure, signed measures, Radon-Nikodym theorem, product measures, Fubini theorem. PREREQUISITE: MATH 7350. MATH 7235-8235. Combinatorics. (3). (7793). Principles and techniques of combinatorial mathematics with a view toward applications in computer science; methods of enumeration, matching theory, paths and cycles, planarity, coloring problems, extremal problems. PREREQUISITE: Permission of instructor. MATH 7376. Methods of Mathematical Physics II. (3). Complex variables, asymptotic expansions, special functions, calculus of variations, additional topics on matrices and operators, topics in non-linear analysis. PREREQUISITE: MATH 7375 or permission of the instructor. MATH 7371. Calculus of Variations. (3). Introduction to calculus of variations, Euler-Lagrange equations, and optimization in infinite dimensional spaces. Applications could include various topics in science, engineering, economics, or geometry, such as ground state density theories, Dirichlet’s principle and differential equations, theory of least action, depending on interests of class. PREREQUISITE: Permission of instructor.

Statistics Courses

Statistics Courses MATH 4607-6607. Introduction to SAS Programming. (3). SAS program statement syntax and flow control; selecting and summarizing observations; combing, dividing and updating SAS dataset; input tailoring and output customization; SAS built-in functions SAS Macro Language Programming and other SAS packages such as SAS/GRAPH and SAS/IML. PREREQUISITE: Introductory course in statistics. MATH 7607. Advanced Programming in SAS. (3). Covers SAS macro language and SAS SOL; topics include macro variables, macro processing, Marco expressions, Marco quoting; Proc SQL, retrieving data from tables, creating and updating tables and views; applications in statistics. PREREQUISITE: MATH 6607. MATH 7613. Probability Theory. (3). Probability measures; distribution functions; independence; mathematical expectation, modes of convergence; Borel-Cantelli Lemma, weak and strong laws of large numbers; Glinvenko-Cantelli lemma; characteristic functions inversion theorems; Slustky’s theorem, central limit theorem, Liapounov and Lindberg-Levy and Lindberg-Feller theorems; multivariate extensions; Berry-Esseen theorem. PREREQUISITES: MATH 6350. Knowledge of MATH 6613 recommended. MATH 4614-6614. Probability and Statistics. (3). Probability distribution; statistical methods of parameter estimation and hypothesis testing; comparisons of two population means, proportions, and variances; analysis of variance, linear models and multiple regression. Students may not receive credit for both MATH 4614 and MATH 4635. PREREQUISITE: MATH 1920 and 2701. MATH 4635-6635. Introduction to Probability Theory. (3). Basic probability theory, random variables, expectation, variance, covariance, moment generating functions; binomial, hypergeometric, Poisson, geometric, negative binomial, uniform, normal, exponential, Cauchy. chi-square, t, and F distributions; central limit theorem. functions of a random variable; bivariate, marginal, and conditional distributions. NOTE: Students may not receive credit for both MATH 4614-6614 and MATH 4635-6635. PREREQUISITE: MATH 1920. MATH 4611-6611. Introduction to Applied Statistics. (3). Binomial, hypergeometric, Poisson, multinomial and normal distributions, test of hypotheses, chi-square test, t-test. F-test, etc, nonparametric tests; correlation analysis. PREREQUISITE: 6 hours in mathematics at level of MATH 1710 or above (except MATH 1601). NOTE: Students majoring in Mathematical Sciences may not apply credit for this course to their degree requirements. Students majoring in other areas such as Physics or Engineering and who have a calculus background should take MATH 4635-6635. MATH 7643. Least Squares and Regression Analysis. (3). Basic concepts of hypothesis testing and confidence intervals; simple and multiple regression analyses, model selection, Mallow’s Cp, examination of residuals, Box-Cox transformation, influence diagnostics, multicolinearity, ridge-regression, probit, logit, and log-linear analyses; intensive use of SAS or other statistical packages. PREREQUISITE: MATH 6635. MATH 7645. Sampling Techniques. (3). Planning, execution, and analysis of sampling from finite populations; simple, stratified, multistage cluster and systematic sampling; ratio and regression estimates, estimation of variance. PREREQUISITE: MATH 6635; COREQUISITE: MATH 6636. MATH 7647. Nonparametric Statistical Methods. (3). Use of distribution-free statistics for estimation, hypothesis testing, and correlation measures in designing and analyzing experiments. PREREQUISITE: MATH 6635; COREQUISITE: MATH 6636. MATH 4636-6636. Introduction to Statistical Theory. (3). Functions of two random variables; gamma, beta, multinomial, and bivariate normal distributions; Bayes estimators; maximum likelihood and methods of moments estimators; sufficient statistics, unbiasedness, confidence intervals, and hypothesis testing. PREREQUISITE: MATH 4635-6635. MATH 4640-6640. Introduction to Probability Models. (3). Basic concepts of discrete Markov chains; branching processes; Poisson processes; applications to modelling of population growth; applications to modelling of spread of infectious disease. PREREQUISITE: MATH 4635-6635. MATH 4637-6637. Statistical Methods. (3). Basic concepts of hypothesis testing; comparisons of two population means, proportions, and variances; analysis of variance; completely randomized designs, randomized block designs, Latin square designs; multiple comparisons; simple linear model and multiple regression; analysis of covariance. PREREQUISITE: MATH 4611-6611 or 4635-6635. MATH 7221-8221. Statistical Methods for Analyzing Gene Expression Data. (3). Design of microarray experiements; normalization procedures for Oligonucleotide and cDNA microarrays; clustering procedures: hierarchical clustering, principal compenents and analysis, discriminant analysis, eigenvalue decomposition discriminant analysis and nonparametric clustering methods; controlling error rates in multiple testing through resampling methods, false discovery rates, Bayesian and empirical Bayes techniques, Support Vector Machines. PREREQUISITE: MATH 7643. MATH 7695-8695. Bootstrap and Other Resampling Methods. (3). Empirical distribution and plug-in principle; bias reduction; bootstraping regression models; the jackknife; balanced repeated replication; bootstrap confidence intervals; parametric bootstrap; permutation tests. PREREQUISITE: MATH 7645 and MATH 7647. MATH 7657-8657. Multivariate Statistical Methods. (3). Basic contents: multivariate normal distributions; Wishart distribution, Hotelling-T2, Matric-t and Beta distributions; generalized regression models and growth curve models; multivariate analysis of variance; principal component analysis; discriminant analysis; factor analysis; curve fitting procedures in multivariate cases. All topics will be illustrated by practical examples. PREREQUISITE: MATH 6636 or permission of the instructor. MATH 7660-8660. Applied Time Series Analysis. (3). Basic concepts and examples of stationary and nonstationary time series; random harmonic analysis; spectral density functions, model building procedures for time series models; model identification; diagnostic checking, smooth, forecasting and control; Box-Jenkin approach of time series analysis; some seasonal models. PREREQUISITE: MATH 6636. MATH 7680-8680. Bayesian Inference. (3). Nature of Bayesian inference; formulation and choice of prior distributions; advantages and disadvantages of Bayesian approach; applications of Bayesian approach to Behren-Fisher problems, to regression analysis and to the analysis of random effect models; applications of Bayesian approach to the assessment of statistical assumptions; Bayesian prediction procedures. PREREQUISITE: MATH 6636. MATH 7692-8692‡. Statistical Consulting. (3). Methods and techniques of statistical consulting; students will participate in consulting practice supervised by graduate faculty in statistics. May be repeated for a total of 6 credit hours. PREREQUISITES: MATH 6611 and MATH 6637. MATH 7651. Linear Models. (3). Multivariate normal distributions, distribution of quadratic forms, general linear hypothesis of full rank, optimal point and interval estimations, applications to regression models; elements of generalized linear models, applications to logistic regression and log-linear models; use of SAS procedures. PREREQUISITE: MATH 7643. MATH 7642-8642. Experimental Design. (3). Fundamental concepts in designing experiments, justification of linear models, randomization, principle of blocking, use of concomitant observations, principle of confounding, fractional replication, composite designs, incomplete block designs. PREREQUISITE: MATH 7641 or 7643. MATH 7641. Analysis of Variance. (3). Basic concepts of ANOVA, partitioning of the sums of squares, fixed effects models, t- and F-tests, multiple comparison procedures, random effect models, variance component models, analysis of covariance and introduction to MANOVA (SAS or comparable statistical packages used extensively to analyze different types of designs). PREREQUISITE: MATH 7643 or MATH 6636. MATH 7654. Inference Theory. (3). Bayes and maximum likelihood estimators, sufficient statistics; Rao-Blackwell Theorem, sampling distributions; unbiasedness, completeness and UMVU estimators; efficient estimators, Cramer-Rao inequality; simple robust estimators; UMP-tests; likelihood ratio tests, t-tests and F-tests. PREREQUISITE: MATH 6636. MATH 7670-8670. Applied Stochastic Models. (3). Markov chains with discrete time; classification of states, stationary distributions, absorption probabilities and absorption time; Markov chains with continuous time; birth-death processes, waiting time distributions, queuing models, population growth models, Kolmogorov forward and backward equations, diffusion processes, Fokker-Planck equation; applications to genetic problems, etc. PREREQUISITES: MATH 6636 and 6640. MATH 7691-8691. Seminar in Statistical Research. (1-3). Recent developments in statistical methods and their applications. Basic topics cover "multivariate method," growth curve models, robustness and effects of departure from basic statistical assumptions on common inference procedures, multivariate contingency tables, bioassay, etc. PREREQUISITE: MATH 6636. MATH 7759-8759. Categorical Data Analysis. (3). Exponential family of distributions and generalized linear models; binary variables and logistic regression; contingency tables and log-linear models; quasi-likelihood functions; estimating functions. PREREQUISITES: MATH 7643 and MATH 7654. MATH 7762-8762. Survival Analysis. (3). Nonparametric estimation and comparison of survival functions: Kaplan-Meier Estimator and other estimators of hazard functions; parametric survival models; Gehan test, Mantel-Haenszel test and their extensions; Cox proportional hazard model: conditional likelihood, partial likelihood analysis, identification of prognostic and risk factors; applications to life-testing and analysis of survival data using statistical packages such as SAS. PREREQUISITES: MATH 7643 and MATH 7654. MATH 7764-8764. Statistical Methods for Biomedical and Environmental Research. (3). Penalized likelihood method, spline and nonparametric regression, use of E-M algorithm, Fourier transform method, error-in-variables, longitudinal models and repeated measures; generalized estimating equations; analysis and modeling of AIDS data; statistical risks assessment. PREREQUISITES: MATH 7643 and MATH 7654. MATH 7656-8656. Advanced Techniques in Statistical Inference. (3). Limit theorems; uniformly minimum variance unbiased and maximum likelihood estimators; information inequalities; large sample theory; robust estimators; uniformly most powerful unbiased and invariant tests; sequential and robust tests. PREREQUISITE: MATH 7654. MATH 7765-8765. Advanced Stochastic Models in Biomedical Sciences. (3). Stochastic models of the AIDS epidemic; chain multinomial models, Markov models, Non-Markov marker processes, diffusion processes for AIDS, stochastic models of carcinogenesis; two-stage, multi-event and multiple path models. PREREQUISITES: MATH 7654 and MATH 7670-8670. MATH 7685-8685. Statistical Simulation and Computing. (3). Uniform random number generation and testing, generation of non-uniform random variables, approximating tail probabilities and percentage points in common distributions, computational methods for multiple regression analysis. PREREQUISITE: MATH 6636 and knowledge of FORTRAN.

Courses for Teachers

Courses for Teachers MATH 7681. Probability for Teachers. (3). Probability spaces, theory of statistical inference physical interpretations of probability. PREREQUISITE MATH 1920. MATH 7281. Linear Algebra for Teachers. (3). Euclidean n-space; vector spaces; subspaces; linear independence and bases; linear transformations; matrices; systems of linear conditions; characteristic values and vectors of linear transformations. PREREQUISITE: MATH 1920. MATH 7282. Abstract Algebra for Teachers. (3). A basic abstract algebra course designed especially for teachers. Topics will include: groups, rings, integral domains, fields; an axiomatic approach to the development of algebra; concepts of proof. PREREQUISITE: MATH 7281 or equivalent. MATH 7381. Real Analysis for Teachers I. (3). Properties of real number system; elementary functions; plane analytic geometry; nature of the derivative; techniques of differentiation; periodic functions; differentiation of trigonometric functions; applications of the derivative; concepts of integration. PREREQUISITE: MATH 1920. MATH 7382. Real Analysis for Teachers II. (3). Continuation of MATH 7381; definite integral with applications; integration of elementary transcendental functions; techniques of integration; indeterminate forms and improper integrals; infinite sequences and infinite series with tests for convergence. PREREQUISITE: MATH 7381 or equivalent. MATH 6151. History of Mathematics. (3). The development of mathematics from the earliest times to the present; problem studies; parallel reading and class reports. PREREQUISITE: 21 hours in MATH courses including MATH 2110 and one of MATH 2701, 2702, or permission of instructor. MATH 7171. Workshop in Junior High Mathematics. (3). This course is designed to provide in-service training, with emphasis on new course content. MATH 7174. Workshop in Senior High Mathematics. (3). This course is designed to provide in-service training, with emphasis on transformation geometry.


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