2004-06 IUPUI Campus Bulletin

Courses in Mathematical Sciences (MATH)

Note: Statistics courses (STAT) follow MATH listings. P-prerequisite; C-corequisite; R-recommended; Fall-offered fall semester; Spring-offered spring semester; Summer-offered in the summer session. For courses with no designated semester, consult the Schedule of Classes. Equiv.-course is equivalent to the indicated course taught at Indiana University Bloomington, or the indicated course taught at Purdue University, West Lafayette.

Special Developmental Courses

M001 Introductory Algebra (6 cr.) P: placement test or self elect for students who need more time on task. Fall, spring, summer. This is a first course in the study of algebra. Real numbers, algebraic expressions, solving equations, graphing equations, operations with polynomials, factoring polynomials, rational expressions and equations, solutions of systems of equations, radical expressions and problem solving strategies are taught.

001 Introduction to Algebra (4 cr.) P: M010 (minimum grade of C-) or placement. Fall, spring, summer. Covers the material in the first year of high school algebra. Numbers and algebra, integers, rational numbers, equations, polynomials, graphs, systems of equations, inequalities, radicals. Credit does not apply toward any degree.

002 Geometry (3 cr.) P or C: 001 or M001 or equivalent. This course is intended to provide one unit of geometry as a first encounter or as a review for those students with little or no geometry background and needing this prerequisite to pursue higher-level course work. Covers plane and solid geometry, right triangle trigonometry, and mathematical logic through a structure focused on problem-solving and critical thinking skills.

Undergraduate Level

Lower-Division Courses

110 Fundamentals of Algebra (4 cr.) P: 001 or M001 (minimum grade of C-) or placement. Intended primarily for liberal arts and business majors. Integers, rational and real numbers, exponents, decimals, polynomials, equations, word problems, factoring, roots and radicals, logarithms, quadratic equations, graphing, linear equations in more than one variable, and inequalities. This course satisfies the prerequisites needed for M118, M119, 130, and STAT 301.

111 Algebra (4 cr.) P: 001 or M001 (minimum grade of C) or placement. Fall, spring, summer. Real numbers, linear equations and inequalities, systems of equations, polynomials, exponents, logarithmic functions. Covers material in the second year of high school algebra.

M118 Finite Mathematics1 (3 cr.) P: 111 or 110 (minimum grade of C-) or equivalent. Fall, spring, summer. Set theory, logic, permutations, combinations, simple probability, conditional probability, Markov chains. An honors option is available in this course.

M119 Brief Survey of Calculus I (3 cr.) P: 111 or 110 (minimum grade of C-) or equivalent. Fall, spring, summer. Sets, limits, derivatives, integrals, and applications. An honors option is available in this course.

123 Elementary Concepts of Mathematics (3 cr.) P: None. Mathematics for liberal arts students; experiments and activities that provide an introduction to inductive and deductive reasoning, number sequences, functions and curves, probability, statistics, topology, metric measurement, and computers.

130 Mathematics for Elementary Teachers I1 (3 cr.) P: 111 or 110 (minimum grade of C-) or equivalent; one year of high school geometry. Fall, spring, summer. Numeration systems, mathematical reasoning, integers, rationals, reals, properties of number systems, decimal and fractional notations, problem solving.

132 Mathematics for Elementary Teachers II1 (3 cr.) P: 130. Fall, spring, summer. Rationals, reals, geometric relationships, properties of geometric figures, one-, two-, and three-dimensional measurement and problem solving.

136 Mathematics for Elementary Teachers1 (6 cr.) P: 111 or 110 (minimum grade of C) or equivalent; one year of high school geometry. Fall, spring, summer. 136 is a one-semester version of 130 and 132. Not open to students with credit in 130 or 132.

151 Algebra and Trigonometry (5 cr.) P: 111 (minimum grade of B) or placement. Fall, spring, summer I. 151 is a one-semester version of 153-154. Not open to students with credit in 153 or 154. 151 covers college-level algebra and trigonometry and provides preparation for 163 and 164.

153 Algebra and Trigonometry I (3 cr.) P: 111 (minimum grade of C) or two years of high school algebra. Fall, spring, summer. 153-154 is a two-semester version of 151. Not open to students with credit in 151. 153 covers college-level algebra and provides preparation for 163 and 221. 1The sequence MATH M118, 130, 132 or MATH M118, 136 fulfills the mathematics requirement for elementary education majors.

154 Algebra and Trigonometry II (3 cr.) P: 153 (minimum grade of C) or five semesters of high school algebra. Fall, spring, summer. 153-154 is a two-semester version of 151. Not open to students with credit in 151. 154 covers college-level trigonometry and provides preparation for 163 and 221.

163 Integrated Calculus and Analytic Geometry I (5 cr.) P: 151 or 154 (minimum grade of C) or equivalent, and one year of geometry. Equiv. IU MATH M211. Fall, spring, summer I. Review of plane analytic geometry and trigonometry, functions, limits, differentiation, applications of differentiation, integration, the fundamental theorem of calculus, and applications of integration. An honors option is available in this course.

164 Integrated Calculus and Analytic Geometry II (5 cr.) P: 163 (minimum grade of C-). Equiv. IU MATH M212. Fall, spring, summer I. Transcendental functions, techniques of integration, indeterminate forms and improper integrals, conics, polar coordinates, sequences, infinite series, and power series. An honors option is available in this course.

179 Computers and Mathematics (3 cr.) P: 163. Exploration of some modern mathematical concepts, using the computer as an experimental tool. Possible topics include iteration, fixed points, convergence, stability/instability, chaos, fractals. Function approximation: polynomials, splines, computer graphics. Calculus: numerical approximations, symbolic manipulations. Arithmetic with large integers: prime numbers, factorization, encryption, unsolved problems in number theory.

190 Topics in Applied Mathematics for Freshmen (3 cr.) Treats applied topics in mathematics at the freshman level. Prerequisites and course material vary with the applications.

221 Calculus for Technology I (3 cr.) P: 151 or 154 (minimum grade of C-) or equivalent, and one year of geometry. Fall, spring, summer. Analytic geometry, the derivative and applications, the integral and applications.

222 Calculus for Technology II (3 cr.) P: 221 (minimum grade of C-). Fall, spring, summer. Differentiation of transcendental functions, methods of integration, power series, Fourier series, differential equations.

261 Multivariate Calculus (4 cr.) P: 164. Equiv. IU MATH M311. Fall, spring, summer. Spatial analytic geometry, vectors, curvilinear motion, curvature, partial differentiation, multiple integration, line integrals, Green's theorem. An honors option is available in this course.

262 Linear Algebra and Differential Equations (4 cr.) P: 164. R: 261. Fall, spring, summer. First-order equations, higher-order linear equations, initial and boundary value problems, power series solutions, systems of first-order equations, Laplace transforms, applications. Requisite topics of linear algebra: vector spaces, linear independence, matrices, eigenvalues, and eigenvectors.

290 Topics in Applied Mathematics for Sophomores (3 cr.) Treats applied topics in mathematics at the sophomore level. Prerequisites and course material vary with the applications.

Upper-Division Courses

300 Logic and the Foundations of Algebra (3 cr.) P: 163. Fall. Logic and the rules of reasoning, theorem proving. Applications to the study of the integers; rational, real, and complex numbers; and polynomials. Bridges the gap between elementary and advanced courses. Recommended for prospective high school teachers.

351 Elementary Linear Algebra (3 cr.) P: 261. Not open to students with credit in 511. Fall, spring. Systems of linear equations, matrices, vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, applications.

375 Theory of Interest (3 cr.) P: 261. An introduction to the theory of finance including such topics as compound interest, annuities certain, amortization schedules, sinking funds, bonds, and related securities.

390 Topics in Applied Mathematics for Juniors (3 cr.) Treats applied topics in mathematics at the junior level. Prerequisites and course material vary with the applications.

414 Numerical Methods (CSCI 414) (3 cr.) P: 262 and a course in a high-level programming language. Not open to students with credit in CSCI 512. Error analysis, solution of nonlinear equations, direct and iterative methods for solving linear systems, approximation of functions, numerical differentiation and integration, numerical solution of ordinary differential equations.

417 Discrete Modeling and Game Theory (3 cr.) P: 262 and 351 or 511 or consent of instructor. Linear programming; mathematical modeling of problems in economics, management, urban administration, and the behavioral sciences.

424 The Teaching of Mathematics in Middle and Junior High Schools (2 cr.) Designed to prepare the prospective teacher to plan, present, and evaluate mathematics lessons, determine goals, manage instruction, and use a variety of instructional strategies.

425 The Teaching of Mathematics in Secondary Schools (2-3 cr.) Designed to prepare the prospective teacher to plan, present, and evaluate mathematics lessons, determine goals, manage instruction, and use a variety of instructional strategies.

426 Introduction to Applied Mathematics and Modeling (3 cr.) P: 262 and PHYS 152. Introduction to problems and methods in applied mathematics and modeling. Formulation of models for phenomena in science and engineering, their solution, and physical interpretation of results. Examples chosen from solid and fluid mechanics, mechanical systems, diffusion phenomena, traffic flow, and biological processes.

441 Foundations of Analysis (3 cr.) P: 261. Set theory, mathematical induction, real numbers, completeness axiom, open and closed sets in Rm, sequences, limits, continuity and uniform continuity, inverse functions, differentiation of functions of one and several variables.

442 Foundations of Analysis II (3 cr.) P: 441. Continuation of differentiation, the mean value theorem and applications, the inverse and implicit function theorems, the Riemann integral, the fundamental theorem of calculus, point-wise and uniform convergence, convergence of infinite series, series of functions.

453 Beginning Abstract Algebra (3 cr.) P: 351 or consent of the instructor. Basic properties of groups, rings, and fields, with special emphasis on polynomial rings.

456 Introduction to the Theory of Numbers (3 cr.) P: 261. Divisibility, congruences, quadratic residues, Diophantine equations, the sequence of primes.

462 Elementary Differential Geometry (3 cr.) P: 351. Calculus and linear algebra applied to the study of curves and surfaces. Curvature and torsion, Frenet-Serret apparatus and theorem, fundamental theorem of curves. Transformation of R2, first and second fundamental forms of surfaces, geodesics, parallel translation, isometries, fundamental theorem of surfaces.

463 Intermediate Euclidean Geometry for Secondary Teachers (3 cr.) P: 002 (or one year of high school geometry), and 300, or consent of instructor. History of geometry. Ruler and compass constructions, and a critique of Euclid. The axiomatic method, models, and incidence geometry. Presentation, discussion and comparison of Hilbert's, Birkhoff's, and SMSG's axiomatic developments.

490 Topics in Mathematics for Undergraduates (1-5 cr.) By arrangement. Open to students only with the consent of the department. Supervised reading and reports in various fields.

S490 Senior Seminar (3 cr.)

491 Seminar in Competitive Math Problem-Solving (1-3 cr.) Approval of the director of undergraduate programs is required. This seminar is designed to prepare students for various national and regional mathematics contests and examinations such as the Putnam Mathematical Competition, the Indiana College Mathematical Competition and the Mathematical Contest in Modeling (MCM), among others. May be repeated twice for credit.

492 Capstone Experience (1-3 cr.) By arrangement.

495 TA Instruction (0 cr.) For teaching assistants. Intended to help prepare TAs to teach by giving them the opportunity to present elementary topics in a classroom setting under the supervision of an experienced teacher who critiques the presentations.

Undergraduate and Graduate Level

504 Real Analysis (3 cr.) P: 441 or consent of the instructor. Completeness of the real number system, basic topological properties, compactness, sequences and series, absolute convergence of series, rearrangement of series, properties of continuous functions, the Riemann-Stieltjes integral, sequences and series of functions, uniform convergence, the Stone-Weierstrass theorem, equicontinuity, the Arzela-Ascoli theorem.

505 Intermediate Abstract Algebra (3 cr.) P: 453 or consent of the instructor. Group theory with emphasis on concrete examples and applications. Field theory: ruler and compass constructions, Galois theory, solvability of equations by radicals.

510 Vector Calculus (3 cr.) P: 261. Calculus of functions of several variables and of vector fields in orthogonal coordinate systems. Optimization problems, implicit function theorem, Green's theorem, Stokes' theorem, divergence theorems, applications to engineering and the physical sciences.

511 Linear Algebra with Applications (3 cr.) P: 261. Not open to students with credit in 351. Matrices, rank and inverse of a matrix, decomposition theorems, eigenvectors, unitary and similarity transformations on matrices.

519 Introduction to Probability (STAT 519) (3 cr.) P: 262. See STAT 519.

520 Boundary Value Problems of Differential Equations (3 cr.) P: 261 and 262. Sturm-Liouville theory, singular boundary conditions, orthogonal expansions, separation of variables in partial differential equations, spherical harmonics.

522 Qualitative Theory of Differential Equations (3 cr.) P: 262 and 351. Laplace transforms, systems of linear and nonlinear ordinary differential equations, brief introduction to stability theory, approximation methods, other topics.

523 Introduction to Partial Differential Equations (3 cr.) P: 262 and 510, or consent of instructor. Method of characteristics for quasilinear first-order equations; complete integral; Cauchy-Kowalewsky theory; classification of second-order equations in two variables; canonical forms; difference methods of hyperbolic and parabolic equations; Poisson integral method for elliptic equations.

525 Introduction to Complex Analysis (3 cr.) P: 261 and 262. Complex numbers and complex-valued functions; differentiation of complex functions; power series, uniform convergence; integration, contour integrals; elementary conformal mapping.

526 Principles of Mathematical Modeling (3 cr.) P: 262 and 510, or consent of instructor. Ordinary and partial differential equations of physical problems, simplification, dimensional analysis, scaling, regular and singular perturbation theory, variational formulation of physical problems, continuum mechanics, and fluid flow.

527 Advanced Mathematics for Engineering And Physics I (3 cr.) P: 262. R: 511. Linear algebra, systems of ordinary differential equations, Laplace transforms, Fourier series and transforms, and partial differential equations.

528 Advanced Mathematics for Engineering and Physics II (3 cr.) P: 262. R: 510. Divergence theorem, Stokes' Theorem, complex variables, contour integration, calculus of residues and applications, conformal mapping, and potential theory.

530 Functions of a Complex Variable I (3 cr.) P or C: 544. Complex numbers, holomorphic functions, harmonic functions, linear transformations. Power series, elementary functions, Riemann surfaces, contour integration, Cauchy's theorem, Taylor and Laurent series, residues. Maximum and argument principles. Special topics.

531 Functions of a Complex Variable II (3 cr.) P: 530. Compactness and convergence in the space of analytic functions, Riemann mapping theorem, Weierstrass factorization theorem, Runge's theorem, Mittag-Leffler theorem, analytic continuation and Riemann surfaces, Picard theorems.

532 Elements of Stochastic Processes (STAT 532) (3 cr.) P: 519. See STAT 532.

535 Theoretical Mechanics (3 cr.) P: 262 and PHYS 152. Kinematics and dynamics of systems of particles and of rigid bodies; Lagrange and Hamilton-Jacobi equations; oscillations about equilibrium; Hamiltonian systems; integral invariants; transformation theory.

536 Perturbation and Asymptotic Analysis (3 cr.) P: 525 or 530, and 523. Matched asymptotic expansions, inner and outer expansions, strained coordinates and multiple scales, turning point analysis.

537 Applied Mathematics for Scientists and Engineers I (3 cr.) P: 261, 262, and consent of instructor. Covers theories, techniques, and applications of partial differential equations, Fourier transforms, and Laplace transforms. Overall emphasis is on applications to physical problems.

544 Real Analysis and Measure Theory (3 cr.) P: 441 or consent of instructor. Algebras of sets, real number system, Lebesgue measure, measurable functions, Lebesgue integration, differentiation, absolute continuity, Banach spaces, metric spaces, general measure and integration theory, Riesz representation theorem.

545 Principles of Analysis II (3 cr.) P: 544. Continues the study of measure theory begun in 544.

546 Introduction to Functional Analysis (3 cr.) P: 545. By arrangement. Banach spaces, Hahn-Banach theorem, uniform boundedness principle, closed graph theorem, open mapping theorem, weak topology, Hilbert spaces.

547 Analysis for Teachers I (3 cr.) P: 261. Set theory, logic, relations, functions, Cauchy's inequality, metric spaces, neighborhoods, Cauchy sequence.

548 Analysis for Teachers II (3 cr.) P: 547. Functions on a metric space, continuity, uniform continuity, derivative, chain rule, Riemann integral, fundamental theorem of calculus, double integrals.

549 Applied Mathematics for Secondary School Teachers (3 cr.) P: 262 and 351. Summer, odd-numbered years. Applications of mathematics to problems in the physical sciences, social sciences, and the arts. Content varies. May be repeated for credit with the consent of the instructor.

550 Algebra for Teachers I (3 cr.) P: 351. Definitions and elementary properties of groups, rings, integral domains, fields. Intended for secondary school teachers.

551 Algebra for Teachers II (3 cr.) P: 550. Polynomial rings, fields, vector spaces, matrices.

552 Applied Computational Methods II (3 cr.) P: 559 and consent of instructor. The first part of the course focuses on numerical integration techniques and methods for ODEs. The second part concentrates on numerical methods for PDEs based on finite difference techniques with brief surveys of finite element and spectral methods.

553 Introduction to Abstract Algebra (3 cr.) P: 453 or consent of instructor. Group theory: finite abelian groups, symmetric groups, Sylow theorems, solvable groups, Jordan-Hölder theorem. Ring theory: prime and maximal ideals, unique factorization rings, principal ideal domains, Euclidean rings, factorization in polynomial and Euclidean rings. Field theory: finite fields, Galois theory, solvability by radicals.

554 Linear Algebra (3 cr.) P: 351. Review of basics: vector spaces, dimension, linear maps, matrices, determinants, linear equations. Bilinear forms; inner product spaces; spectral theory; eigenvalues. Modules over principal ideal domain; finitely generated abelian groups; Jordan and rational canonical forms for a linear transformation.

559 Applied Computational Methods I (3 cr.) P: 262 and 351 or 511. Computer arithmetic, interpolation methods, methods for nonlinear equations, methods for solving linear systems, special methods for special matrices, linear least square methods, methods for computing eigenvalues, iterative methods for linear systems; methods for systems of nonlinear equations.

561 Projective Geometry (3 cr.) P: 351. Projective invariants, Desargues' theorem, cross-ratio, axiomatic foundation, duality, consistency, independence, coordinates, conics.

562 Introduction to Differential Geometry and Topology (3 cr.) P: 351 and 442. Smooth manifolds, tangent vectors, inverse and implicit function theorems, submanifolds, vector fields, integral curves, differential forms, the exterior derivative, DeRham cohomology groups, surfaces in E3, Gaussian curvature, two-dimensional Riemannian geometry, Gauss-Bonnet and Poincaré theorems on vector fields.

563 Advanced Geometry (3 cr.) P: 300 or consent of instructor. Topics in Euclidean and non-Euclidean geometry.

571 Elementary Topology (3 cr.) P: 441. Topological spaces, metric spaces, continuity, compactness, connectedness, separation axioms, nets, function spaces.

572 Introduction to Algebraic Topology (3 cr.) P: 571. Singular homology theory, Ellenberg-Steenrod axioms, simplicial and cell complexes, elementary homotopy theory, Lefschetz fixed point theorem.

578 Mathematical Modeling of Physical Systems I (3 cr.) P: 262, PHYS 152 and 251 and consent of Instructor. Linear systems modeling, mass-spring-damper systems, free and forced vibrations, applications to automobile suspension, accelerometer, seismograph, etc., RLC circuits, passive and active filters, applications to crossover networks and equalizers, nonlinear systems, stability and bifurcation, dynamics of a nonlinear pendulum, van der Pol oscillator, chemical reactor, etc., introduction to chaotic dynamics, identifying chaos, chaos suppression and control, computer simulations and laboratory experiments.

581 Introduction to Logic for Teachers (3 cr.) P: 351. Not open to students with credit in 385. Logical connectives, rules of sentential inference, quantifiers, bound and free variables, rules of inference, interpretations and validity, theorems in group theory, introduction to set theory.

583 History of Elementary Mathematics (3 cr.) P: 261. A survey and treatment of the content of major developments of mathematics through the eighteenth century, with selected topics from more recent mathematics, including non-Euclidean geometry and the axiomatic method.

585 Mathematical Logic I (CSCI 585) (3 cr.) P: 351. Formal theories for propositional and predicate calculus with study of models, completeness, compactness. Formalization of elementary number theory; Turing machines, halting problem, and the undecidability of arithmetic.

587 General Set Theory (3 cr.) P: 351. Informal axiomatization of set theory, cardinal numbers, countable sets, cardinal arithmetic, order types, well-ordered sets and ordinal numbers, axiom of choice and equivalences, paradoxes of intuitive set theory, Zermelo-Fraenkel axioms.

588 Mathematical Modeling of Physical Systems II (3 cr.) P: 578. Depending on the interests of the students, the content may vary from year to year. Emphasis will be on mathematical modeling of a variety of physical systems. Topics will be chosen from the volumes "Mathematics in Industrial Problems" by Avner Friedman. Researchers from local industries will be invited to present real-world applications. Each student will undertake a project in consultation with one of the instructors or an industrial researcher.

598 Topics in Mathematics (1-5 cr.) By arrangement. Directed study and reports for students who wish to undertake individual reading and study on approved topics.

Graduate Level

611 Methods of Applied Mathematics I (3 cr.) P: Consent of Instructor. Introduction to Banach and Hilbert spaces, linear integral equations with Hilbert-Schmidt kernels, eigenfunction expansions, and Fourier transforms.

612 Methods of Applied Mathematics II (3 cr.) P: 611. Continuation of theory of linear integral equations; Sturm-Liouville and Weyl theory for second-order differential operators, distributions in n dimensions, and Fourier transforms.

626 Mathematical Formulation of Physical Problems I (3 cr.) P: Graduate standing and consent of instructor. Topics to be chosen from the following: Tensor formulation of the field equations in continuum mechanics, fluid dynamics, hydrodynamic stability, wave propagation, and theoretical mechanics.

627 Mathematical Formulation of Physical Problems II (3 cr.) P: 626. Continuation of 626.

642 Methods of Linear and Nonlinear Partial Differential Equations I (3 cr.) P: 520, 523, and 611. Topics from linear and nonlinear partial differential equations, varied from time to time.

646 Functional Analysis (3 cr.) P: 546. Advanced topics in functional analysis, varying from year to year at the discretion of the instructor.

672 Algebraic Topology I (3 cr.) P: 572. Continuation of 572; cohomology, homotopy groups, fibrations, further topics.

673 Algebraic Topology II (3 cr.) P: 672. Sequel to 672 covering further advanced topics in algebraic and differential topology such as K-theory and characteristic classes.

692 Topics in Applied Mathematics (1-3 cr.)

693 Topics in Analysis (1-3 cr.)

694 Topics in Differential Equations (1-3 cr.)

697 Topics in Topology (1-3 cr.)

699 Research Ph.D. Thesis (cr. arr.)

Courses in Statistics (STAT)

Undergraduate Level

Upper-Division Courses

STAT 301 Elementary Statistical Methods I (3 cr.) P: MATH 111 or 110 or equivalent. Not open to students in the Department of Mathematical Sciences. Fall, spring. Introduction to statistical methods with applications to diverse fields. Emphasis on understanding and interpreting standard techniques. Data analysis for one and several variables, design of samples and experiments, basic probability, sampling distributions, confidence intervals and significance tests for means and proportions, correlation and regression. Software is used throughout.

STAT 302 Elementary Statistical Methods II (3 cr.) P: 301 or equivalent. Continuation of 301. Multiple regression and analysis of variance, with emphasis on statistical inference and applications to various fields.

STAT 311 Introductory Probability (3 cr.) P: MATH 261 or equivalent. Not open to students with credit in 416. Fall. Fundamental axioms and laws of probability; finite sample spaces and combinatorial probability; conditional probability; Bayes theorem; independence; discrete and continuous random variables; univariate and bivariate distributions; binomial, negative binomial, Poisson, normal, and gamma probability models; mathematical expectation; moments and moment generating functions.

STAT 350 Introduction to Statistics (3 cr.) P: MATH 163 or equivalent. Fall, spring. A data-oriented introduction to the fundamental concepts and methods of applied statistics. STAT 350 is intended primarily for majors in the mathematical sciences (mathematics, actuarial sciences, mathematics education). The objective is to acquaint the students with the essential ideas and methods of statistical analysis for data in simple settings. It covers material similar to that of STAT 511 but with emphasis on more data-analytic material. Includes a weekly computing laboratory using Minitab.

STAT 416 Probability (3 cr.) P: MATH 261 or equivalent. Not open to students with credit in 311. Fall, spring. An introduction to mathematical probability suitable as preparation for actuarial science, statistical theory, and mathematical modeling. General probability rules, conditional probability, Bayes theorem, discrete and continuous random variables, moments and moment generating functions, continuous distributions and their properties, law of large numbers, and central limit theorem.

STAT 417 Statistical Theory (3 cr.) P: 416. R: 350 or equivalent. Spring. An introduction to the mathematical theory of statistical inference, emphasizing inference for standard parametric families of distributions. Properties of estimators. Bayes and maximum likelihood estimation. Sufficient statistics. Properties of test of hypotheses. Most powerful and likelihood-ratio tests. Distribution theory for common statistics based on normal distributions.

STAT 490 Topics in Statistics for Undergraduates (1-5 cr.) Supervised reading and reports in various fields.

Undergraduate and Graduate Level

STAT 511 Statistical Methods I (3 cr.) P: MATH 164. Descriptive statistics; elementary probability; random variables and their distributions; expectation; normal, binomial, Poisson, and hypergeometric distributions; sampling distributions; estimation and testing of hypotheses; one-way analysis of variance; correlation and regression.

STAT 512 Applied Regression Analysis (3 cr.) P: STAT 511. Inference in simple and multiple linear regression, estimation of model parameters, testing and prediction. Residual analysis, diagnostics and remedial measures. Multicollinearity. Model building, stepwise and other model selection methods. Weighted least squares. Nonlinear regression. Models with qualitative independent variables. One-way analysis of variance. Orthogonal contrasts and multiple comparison tests. Use of existing statistical computing package.

STAT 513 Statistical Quality Control (3 cr.) P: 511. Control charts and acceptance sampling, standard acceptance plans, continuous sampling plans, sequential analysis, and response surface analysis. Use of existing statistical computing packages.

STAT 514 Designs of Experiments (3 cr.) P: 512. Fundamentals, completely randomized design, randomized complete blocks. Latin squares, multiclassification, factorial, nested factorial, incomplete blocks, fractional replications, confounding, general mixed factorial, split-plot and optimum design. Use of existing statistical computing packages.

STAT 515 Statistical Consulting Problems (1-3 cr.) P: Consent of advisor. Consultation on real-world problems involving statistical analysis under the guidance of a faculty member. A detailed written report and an oral presentation are required.

STAT 516 Basic Probability and Applications (3 cr.) P: MATH 261 or equivalent. A first course in probability intended to serve as a foundation for statistics and other applications. Intuitive background; sample spaces and random variables; joint, conditional, and marginal distributions; special distributions of statistical importance; moments and moment generating functions; statement and application of limit theorems; introduction to Markov chains.

STAT 517 Statistical Inference (3 cr.) P: 511 or 516. A basic course in statistical theory covering standard statistical methods and their applications. Includes unbiased, maximum likelihood, and moment estimation; confidence intervals and regions; testing hypotheses for standard distributions and contingency tables; introduction to nonparametric tests and linear regression.

STAT 519 Probability Theory (3 cr.) P: MATH 261 or equivalent. Sample spaces and axioms of probability, conditional probability, independence, random variables, distribution functions, moment generating and characteristics functions, special discrete and continuous distributions - univariate and multivariate cases, normal multivariate distributions, distribution of functions of random variables, modes of convergence and limit theorems including laws of large numbers and central limit theorem.

STAT 520 Time Series and Applications (3 cr.) P: 519. A first course in stationary time series with applications in engineering, economics, and physical sciences. Stationarity, autocovariance function and spectrum; integral representation of a stationary time series and interpretation; linear filtering; transfer function models; estimation of spectrum; multivariate time series. Use of existing statistical computing packages.

STAT 521 Statistical Computing (3 cr.) C: STAT 512 or equivalent. A broad range of topics involving the use of computers in statistical methods. Collection and organization of data for statistical analysis; transferring data between statistical applications and computing platforms; techniques in exploratory data analysis; comparison of statistical packages.

STAT 522 Sampling and Survey Techniques (3 cr.) P: 512 or equivalent. Survey designs; simple random, stratified, and systematic samples; systems of sampling; methods of estimation; ratio and regression estimates; costs. Other related topics as time permits.

STAT 523 Categorical Data Analysis (3 cr.) P: 528 or equivalent, or consent of instructor. Models generating binary and categorical response data, two-way classification tables, measures of association and agreement, goodness-of-fit tests, testing independence, large sample properties. General linear models, logistic regression, probit and extreme value models. Loglinear models in two and higher dimensions; maximum likelihood estimation, testing goodness-of-fit, partitioning chi-square, models for ordinal data. Model building, selection, and diagnostics. Other related topics as time permits. Computer applications using existing statistical software.

STAT 524 Applied Multivariate Analysis (3 cr.) P: 528 or equivalent, or consent of instructor. Extension of univariate tests in normal populations to the multivariate case, equality of covariance matrices, multivariate analysis of variance, discriminant analysis and misclassification errors, canonical correlation, principal components, factor analysis. Strong emphasis on the use of existing computer programs.

STAT 525 Intermediate Statistical Methodology (3 cr.) C: 528 or equivalent, or consent of instructor. Generalized linear models, likelihood methods for data analysis, diagnostic methods for assessing model assumptions. Methods covered include multiple regression, analysis of variance for completely randomized designs, binary and categorical response models, and hierarchical loglinear models for contingency tables.

STAT 528 Mathematical Statistics (3 cr.) P: STAT 519 or equivalent. Sufficiency and completeness, the exponential family of distributions, theory of point estimation, Cramer-Rao inequality, Rao-Blackwell Theorem with applications, maximum likelihood estimation, asymptotic distributions of ML estimators, hypothesis testing, Neyman-Pearson Lemma, UMP tests, generalized likelihood ratio test, asymptotic distribution of the GLR test, sequential probability ratio test.

STAT 529 Applied Decision Theory and Bayesian Analysis (3 cr.) C: STAT 528 or equivalent. Foundation of statistical analysis, Bayesian and decision theoretic formulation of problems; construction of utility functions and quantifications of prior information; methods of Bayesian decision and inference, with applications; empirical Bayes; combination of evidence; game theory and minimax rules, Bayesian design and sequential analysis. Comparison of statistical paradigms.

STAT 532 Elements of Stochastic Processes (MATH 532) (3 cr.) P: 519 or equivalent. A basic course in stochastic models including discrete and continuous time processes, Markov chains, and Brownian motion. Introduction to topics such as Gaussian processes, queues and renewal processes, and Poisson processes. Application to economic models, epidemic models, and reliability problems.

STAT 533 Nonparametric Statistics (3 cr.) P: 516 or equivalent. Binomial test for dichotomous data, confidence intervals for proportions, order statistics, one-sample signed Wilcoxon rank test, two-sample Wilcoxon test, two-sample rank tests for dispersion, Kruskal-Wallis test for one-way layout. Runs test and Kendall test for independence, one- and two-sample Kolmogorov-Smirnov tests, nonparametric regression.

STAT 536 Introduction to Survival Analysis (3 cr.) P: 517 or equivalent. Deals with the modern statistical methods for analyzing time-to-event data. Background theory is provided, but the emphasis is on the applications and the interpretations of results. Provides coverage of survivorship functions and censoring patterns; parametric models and likelihood methods, special life-time distributions; nonparametric inference, life-tables, estimation of cumulative hazard functions, the Kaplan-Meier estimator; one- and two-sample nonparametric tests for censored data; and semiparametric proportional hazards regression (Cox Regression), parameters' estimation, stratification, model fitting strategies, and model interpretations. Heavy use of statistical software such as Splus and SAS.

STAT 598 Topics in Statistical Methods (1-3 cr.) P: Consent of instructor. Directed study and reports for students who wish to undertake individual reading and study on approved topics.

STAT 698 Research M.S. Thesis (6 cr.) P: Consent of advisor. M.S. thesis in applied statistics.