For current class offerings, times, and additional information, visit the Office of the Registrar.

 

Mathematics Course Descriptions

Review of algebra, sets, linear equations and inequalities, nonlinear inequalities, interest problems, systems of linear equations, functions and graphs, and elementary data analysis. Usually offered every term. Prerequisite: three years of high school mathematics or equivalent. Note: For students who need extra work on mathematical skills. No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

 

Review of algebra, sets, linear equations and inequalities, nonlinear inequalities, interest problems, systems of linear equations, functions and graphs, and elementary data analysis. Usually offered every term. Prerequisite: three years of high school mathematics or equivalent. Note: No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

 

This course explores a sample of beautiful branches of modern mathematics, concentrating on conceptual underpinnings rather than technical aspects. Includes study of infinity, number theory, fractals, and modern geometry, among other mathematical ideas. The course focuses on verbal and written communication skills and problem solving. Prerequisite: three years of high school mathematics or equivalent. Note: No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

 

Study of mathematical subjects including linear, quadratic, polynomial, rational, exponential, and logarithmic functions, in the context of difference equations models. Emphasizes concepts and applications using numerical, graphical, and theoretical methods. Also includes an introduction to the mathematical subject of chaos. Usually offered every term. Prerequisite: three years of high school mathematics or equivalent. Note: No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

  

Fundamentals of algebraic, exponential, and logarithmic functions with emphasis on applications to problems in business and economics and the natural sciences. Usually offered every term. Prerequisite: three years of high school mathematics or equivalent. Note: Intended primarily for students planning to take MATH-211 Applied Calculus I. No credit toward mathematics major. Students may not receive credit for more than one course numbered MATH-15x.

 

Fundamentals of algebraic, logarithmic, exponential, and trigonometric functions for students planning to take MATH-221. MATH-15x and MATH-170 may not both be used to fulfill the mathematics requirements for any major program. Usually offered every term. Prerequisite: three years of high school mathematics, or MATH-15x, or permission of department.

 

Topics vary by section, may be repeated for credit with different topic.

 

Continuity, limits, differentiation, and integration. Applications to biological, social, and environmental sciences and business. Usually offered every term. Prerequisite: MATH-15x or four years of high school mathematics. Note: No credit toward mathematics or applied mathematics major, but together with MATH-212 meets calculus requirement for applied statistics. Students may not receive credit toward a degree for both MATH-211 and MATH-221.

 

Calculus of several variables, matrices, series, and differential equations. Applications to biological, social, and environmental sciences and business. Usually offered every spring. Prerequisite: MATH-211 or MATH-221. Note: No credit toward mathematics or applied mathematics major, but together with MATH-211 meets calculus requirement for applied statistics. Students may not receive credit toward a degree for both MATH-212 and MATH-222 or MATH-313.

 

Real numbers; coordinate systems; functions; limits and continuity; differentiation and applications; trigonometric functions; indefinite and definite integration and applications; fundamental theorem of integral calculus. Usually offered every term. Prerequisite: MATH-170 or four years of high school mathematics. Note: Students may not receive credit toward a degree for both MATH-221 and MATH-211.

 

Techniques of integration, calculus of exponential and logarithmic functions, infinite series, power series representations, and analytic geometry. Usually offered every term. Prerequisite: MATH-211 or MATH-221, or permission of department. Note: Students may not receive credit toward a degree for both MATH-222 and MATH-212.

 

Topics vary by section, may be repeated for credit with different topic.

 

Vector spaces, systems of linear equations, solutions by matrices, determinants, linear transformations, and algebraic forms. Usually offered every term. Prerequisite: MATH-212 or MATH-222 (may be taken concurrently).

 

Vectors, functions of several variables, partial differentiation, and multiple integrals. Usually offered every term. Prerequisite: MATH-222.

 

First order equations, linear equations of higher order, solutions in series, Laplace transforms, numerical methods, and applications to mechanics, electrical circuits, and biology. Usually offered every fall. Prequisite: MATH-313 and MATH-310 (which may be both taken concurrently).

This course explores applications such as auctions, firm competition, and voting with mathematical analysis. It includes Nash equilibrium, subgame perfect equilibrium, evolutionary stability, repeated games, signaling, mechanism design, uncertainty, and behavioral game theory. Meets with ECON-345. Usually offered every fall. Prerequisite: ECON-200, and MATH-211 or MATH-221. Note: this course does not fulfill the University Mathematics Requirement.

Designed to teach scientific rigor in the use of computers and/or computational tools. Techniques from mathematics are introduced which lead to efficient algorithm design, algorithm analysis, data classification, data manipulation, and scientific computation. Includes data types, induction, recursion, sorting, searching, summation, optimization, asymptotic analysis, basic number theory, discrete probability, and parallel computing. Meets with CSC-360. Usually offered every fall. Prerequisite: CSC-280, CSC-281, MATH-221, and MATH-222.

 

Prerequisite: permission of instructor and department chair.

 

Prerequisite: permission of instructor and department chair.

 

Topics vary by section, may be repeated for credit with different topic.

  

Algebra of sets; probability in discrete sample spaces; combinatorial analysis; random variables; binomial, Poisson, normal, and other distributions; and applications. Usually offered every fall. Prerequisite: MATH-313 or permission of instructor.

 

An introduction to the proof-based methodology of advanced mathematics courses, with emphasis on the fundamentals of logic and set theory (truth-tables and quantifiers, Boolean operations, functions, relations, and cardinally); elementary number theory (mathematical induction and modular arithmetic), and structural properties of the fields of real and complex numbers. Usually offered every semester. Prerequisite: MATH-222.

 

MATH-504: Advanced Calculus of Several Variables (3)

Vector-functions of several variables, limits and continuity, differentials and tangent plane, implicit and inverse functions, line and surface integrals, gradient, divergent, curl, Stoke's and Green's theorems. Usually offered alternate springs. Prerequisite: MATH-310 and MATH-313 and MATH-503, or permission of instructor. 

 

The mathematical study of the scope and limits of deductive reasoning with special attention to propositional and first order logic, leading to results concerning completeness, compactness, and the existence of decision procedures for various logical systems, culminating in the incompleteness theorems of Godel. Usually offered alternate springs. Prerequisite: MATH-503 or permission of instructor.

  

Euclidean and non-Euclidean (spherical, elliptic and hyperbolic) geometries from axiomatic and analytic points of view. Includes isometrics, transformation groups, symmetry groups, quadratic forms, projective geometry, as well as some historical background. Usually offered alternate falls. Prerequisite: MATH-310 or equivalent.

 

Groups, rings vector spaces and modules, fields, and Galois theory. Usually offered every fall. Prerequisite:Math -503 or permission of instructor

 

An advanced study of rings and fields with a focus on polynomials and their roots. Includes ring theory, factorization, polynomials, field theory, ruler and compass constructions, Galois theory, and solvability of polynomials. Usually offered alternate springs (odd years). Prerequisite: MATH-512.

 

Divisibility, fundamental theorem of arithmetic, congruences, arithmetic functions, Diophantine equations, quadratic residues, sums of squares, and partitions. Usually offered alternate falls . Prerequisite: MATH-222.

 

This course develops the foundations of mathematical analysis by focusing on the real numbers as a complete ordered field, infinite sequences and series, limits and continuity, and key theorems of the differential and integral calculus. Usually offered every fall. Prerequisite: MATH-503 or permission of instructor.

 

This course presents the fundamental concepts and techniques of measure theory. It includes Borel sets, measures, measurable sets and functions, integrals as measures, Lp soaces, modes of convergence, and decomposition ans generation of measures (including product measure). Usually offered alternate springs. Prerequisite: MATH-503 and MATH-520 or permission of instructor.

 

Topological spaces, continuity, compactness, connectedness, and metric spaces. Usually offered alternate falls. Prerequisite: MATH-503 or permission of instructor.

 

Complex functions, Cauchy's theorem and integral formulae, Taylor and Laurent series, residue calculus and contour integration, and conformal mapping. Usually offered every spring. Prerequisite: MATH-503 and MATH-504, or permission of instructor.

 

Fourier series, orthonormal systems, wave equation, vibrating strings and membranes, heat equation, Laplace's equation, harmonic and Green functions. Usually offered alternate springs . Prerequisite: MATH-321.

 

Computer arithmetic and error analysis in computation, matrix decomposition methods in solving systems of linear equations and linear least squares problems, polynomial approximation and polynomial data fitting, iterative algorithms for solving nonlinear equations, and numerical differentiation and integration. Usually offered alternate falls. Prerequisite: CSC-280, MATH-222, and MATH-310, or permission of instructor.

 

This course surveys aspects of historical development or mathematics form ancient to modern times and examines the ideological,social, and cultural forces which shaped this development. By providing historical continuity. the course interrelates and unifies the major subject areas such as algebra, calculus and analysis, geometry,number theory, probability, set theory, and the foundation of mathematics. usually offered alternate springs. Prerequisite: Calculus I - III.

 

Topics vary by section, may be repeated for credit with different topic. Topics include foundations/set theory/logic, matrix theory, algebraic topology, measure and integration, functional analysis, ring theory, modern geometry, and advanced modern linear algebra. Usually offered every spring.

 

Curriculum construction and program design, instructional effectiveness, and methods and technology for teaching mathematics. Different approaches for students with a variety of mathematical and cultural backgrounds. Required of all students in mathematics education. Usually offered every fall. Prerequisite: MATH-313.

 

Prerequisite: permission of instructor and department chair.

 

Topics vary by section, may be repeated for credit with different topic.

 

Harmonic analysis on the circle, the real line, and on groups. The main concepts are: periodic functions, Fourier series, Fourier transform and spherical harmonics. The course includes a brief account of the necessary ingredients from the theory of the Lebesgue integral. Usually offered alternate springs (even years). Prerequisite: MATH-503 or permission of instructor.

 

Measure theoretical treatment of probability, convergence of random variables, conditional probability and expectation, laws of large numbers, infinitely divisible distributions, general central limit theorem. Usually offered alternate springs (even years). Prerequisite: MATH-574.

 

MATH-680: Advanced Topics in Mathematics (3)

Topics vary by section , may be repeated for credit with different topic. Intensive courses in a specialized area of mathematics.

 

MATH-685: Practicum in Mathematics Education (3)

May be repeated for credit but not in the same term. Seminar course in researching, implementing, and writing in publishable form an innovative teaching methodology, educational contribution, or internship in cooperating school system, college, or other organization involving teaching. Required of all students in the Ph.D. program in mathematics education. Usually offered alternate springs (odd years).

 

Prerequisite: permission of instructor and department chair.

 

Topics vary by section, may be repeated for credit with different topic.

 

In-dept exploration of current issues in mathematics education. A research paper and presentation are required. Course required of all students in the Ph.D program in mathematics education. May be repeated for credit, but not withing the same term: topic must be different. Usually offered alternative springs.

 

Usually offered every term.

 

Usually offered every term.

 

Statistics Course Descriptions

Topics vary by section, may be repeated for credit with different topic.

 

Classification of data, averages, dispersion, probability, frequency distributions, confidence intervals, tests of significance, nonparametric techniques, simple regression, and correlation. A package of computer programs is used to demonstrate various statistical techniques. Separate sections are available for biology, business, economics, psychology, education, sociology, and government majors. Usually offered every term. Prerequisite: MATH-15x or permission of department.

A calculus-based introduction to basic statistics including data presentation, display and summary, correlation, development of least squares regression models, probability, independence, probability density functions, moments, use of moment generating functions, sampling distributions, confidence intervals, and tests of significance. Concepts are explored through simulation and the use of the calculus tools of finding maxima and minima of a function and the area under a curve. Usually offered every term. Prerequisite: MATH-221 or one semester of calculus.

 

Topics vary by section, may be repeated for credit with different topic.

 

Estimation, inference, multiple regression, and correlation. Elementary decision theory. Usually offered every fall. Prerequisite: STAT-202 with a grade of C or higher, or permission of department. Note: students may not receive credit for STAT-300 and either STAT-302 or STAT-514.

 

Acquisition and development of statistical methods that are used commonly throughout the social sciences, the physical sciences, and governments for research as well as for routine planning and forecasting. Methods include techniques for estimation and inference with qualitative and quantitative data focusing on regression, correlation, analysis of variance and nonparametric statistics. Usually offered every spring. Prerequisite: a grade of C or higher in STAT-202, or permission of department. Note: students may not receive credit for STAT-302 and either STAT-300 or STAT-514.

 

This course examines how statistical methods are utilized within the fields of biology, medicine, and public health. Advanced statistical methods, including ANOVA, multiple regression, analysis of covariance, survival analysis, and nonparametric methods are discussed, with emphasis on their applicability to public health. Usually offered every spring. Prerequisite: STAT-202.

 

Prerequisite: permission of instructor and department chair.

 

Topics vary by section, may be repeated for credit with different topic.

 

Prerequisite: permission of instructor and department chair.

 

Topics vary by section, may be repeated for credit with different topic.

 

Probability, probability distributions, sampling, sampling distributions, and introduction to the theory of point estimation and statistical inference, including confidence intervals and hypothesis testing. Usually offered alternate springs (even years). Prerequisite: MATH-212 or equivalent and MATH-501, or permission of instructor.

 

This course introduces the basic approaches to surveys,including simple random, systematic and stratified sampling, also included is the design of questionnaires and the analysis of sample data, Emphasis is on the practical application of sampling. Usually offered alternate falls. Prerequisite: STAT-202, STAT 514, or equivalent, or permission of instructor.

 

This course cover the mathematical development of principles of survey design, including methods for determining expected value, bias, variance, and mean square error; simple random, systematic, stratified, cluster, multistage, and double sampling; unbiased, ratio, regression, and composite estimation; optimum allocation of resources; controlled and other nonsimple methods of selection; introduction to measurement error; and comparison of alternative designs. Usually offered alternate springs. Prerequisite: STAT-502 and STAT 510,or equivalent, or permission of instructor.

 

Averages, dispersion, probability, sampling, and approach to normality; simple and multiple regression; tests and confidence intervals for means, proportions, differences, and regression coefficients; nonparametric statistics; and analysis of variance. Usually offered every term. Prerequisite: STAT-202 or equivalent. Note: does not carry credit for majors in mathematics or statistics; students may not receive credit for STAT-514 and either STAT-300 or STAT-302.

 

Simple and multiple regression, least squares, curve fitting, graphic techniques, and tests and confidence intervals for regression coefficients. Usually offered every fall and summer. Prerequisite: STAT-302 or STAT-514 or equivalent.

 

Design and analysis of the results of balanced experiments, simple analysis of variance, components of variance, analysis of covariance, and related subjects. Usually offered every spring. Prerequisite: STAT-302 or STAT-514 or equivalent.

 

Topics vary by section, may be repeated for credit with different topic. Alternating topics in statistics from an applied viewpoint. Topics include sampling, multivariate techniques, factor analysis, and time series. Usually offered alternate summers (odd years). Prerequisite: STAT-302 or STAT-514 or equivalent.

 

Application of nonparametric techniques in the analysis of social-science data, with emphasis on tests appropriate for data having interval, nominal, and ordinal scales. Usually offered alternate falls (even years). Prerequisite: STAT-302 or STAT-514 or equivalent.

 

Introduction to multivariate analysis emphasizing statistical applications. Includes matrix theory, multivariate distributions, tests of hypotheses, multivariate analysis of variance, principal components, discriminant analysis, canonical correlation, multivariate regression, and related subjects. Usually offered alternate falls (odd years). Prerequisite: STAT-302 or STAT-514 or equivalent.

 

Chi-square tests, contingency tables (2 X 2, r X c, and multidimensional), loglinear models, and other special models. Usually offered alternate springs (even years). Prerequisite: STAT-302 or STAT-514 or equivalent.

 

An introduction to the theory of time-dependent data. The analysis includes modeling, estimation, and testing; alternating between the time domain; using autoregressive and moving average models and the frequency domain; and using spectral analysis. Usually offered alternate springs (odd years). Prerequisite: STAT-515 or STAT-520 or permission of instructor.

 

An introduction to exploratory data analysis, including resistant or robust techniques, study of residuals, transformations, graphical displays, and related topics. Usually offered every fall. Prerequisite: STAT-515 or STAT-520 or equivalent.

 

Introduction to the use of the SAS language to prepare, modify, and analyze data, interpret output and final preparation of results. Emphasis on practical programming principles and use of built-in procedures in both personal computer and main frame environments. Comparisons with other programming languages. Usually offered every fall. Prerequisite: STAT-514 or two statistics courses, or permission of instructor.

 

Distribution and functions of random variables, generating functions, order statistics, point estimation, maximum likelihood, confidence intervals, tests of hypotheses (Neyman-Pearson, likelihood ratio, etc.), linear regression, and analysis of variance. Usually offered every fall. Prerequisite: MATH-310, MATH-313, and STAT-502 or equivalent.

 

Distribution and functions of random variables, generating functions, order statistics, point estimation, maximum likelihood, confidence intervals, tests of hypotheses (Neyman-Pearson, likelihood ratio, etc.), linear regression, and analysis of variance. Usually offered every spring. Prerequisite: MATH-313, STAT-502 or equivalent, and MATH-310.

 

Introduction to random walks, Markov chains and processes, Poisson processes, recurrent events, birth and death processes, and related subjects. Usually offered alternate springs (odd years). Prerequisite: MATH-501 or STAT-530.

 

Prerequisite: permission of instructor and department chair.

 

Topics vary by section, may be repeated for credit with different topic.

 

Theory of estimation, properties of estimators, large-sample properties and techniques, and applications. Usually offered every fall. Prerequisite: STAT-531 and MATH-574 (may be taken concurrently).

 

Topics vary by section, may be repeated for credit with different topic. Mathematical foundations of statistical theory. Special topics in probability and mathematical statistics. Usually offered alternate springs (odd years). Prerequisite: permission of instructor.

 

The mathematical foundations of statistical inference; the Theory of Estimation including minimum risk-, Bayes-, minimax-, and equivariant estimation; decision theory; and large sample behavior. Usually offered alternate falls (even years). Prerequisite: STAT-600.

 

Extension of regression methodology to more general settings where standard assumptions for ordinary least squares are violated. Generalized least squares, robust regression, bootstrap, regression in the presence of auto-correlated errors, generalized linear models, logistic and Poisson regression. Usually offered every spring. Prerequisite: STAT-515.

 

Multivariate normal distribution, Hotelling's T2, Wilks's likelihood ratio criterion, other test statistics, classification problems, principal components, canonical correlation, general multivariate regression and experimental designs, and related subjects. Usually offered alternate falls (even years). Prerequisite: STAT-600 (may be taken concurrently).

 

Multivariate normal distribution, Hotelling's T2, Wilks's likelihood ratio criterion, other test statistics, classification problems, principal components, canonical correlation, general multivariate regression and experimental designs, and related subjects. Usually offered alternate springs (even years). Prerequisite: STAT-600 (may be taken concurrently).

 

An introduction to numerical analysis, computer science, and statistical theory as they apply to random number generation, the Monte Carlo method, simulations, and other aspects of statistical computing. Usually offered every spring. Prerequisite: permission of instructor.

 

General linear hypothesis, least-squares estimation, Gauss-Markov theorem, regression, analysis of variance, multiple comparisons, analysis of covariance, factorial designs, randomized blocks, other experimental designs, and effects of departures from assumptions. Usually offered alternate falls (odd years). Prerequisite: STAT-600 (may be taken concurrently).

 

General linear hypothesis, least-squares estimation, Gauss-Markov theorem, regression, analysis of variance, multiple comparisons, analysis of covariance, factorial designs, randomized blocks, other experimental designs, and effects of departures from assumptions. Usually offered alternate springs (even years). Prerequisite: STAT-600 (may be taken concurrently).

 

Prerequisite: permission of instructor and department chair.

 

Individual placement and supervision in an approved organization involving statistical analysis, methodology, or theory. Prerequisite: permission of instructor and department chair.

 

Topics vary by section, may be repeated for credit with different topic.

 

Prerequisite: permission of department.

 

Topics vary by section, may be repeated for credit with different topic. Topics chosen from recent research in statistics. Through written reviews and oral presentations, students investigate advances in statistical theory and applications in recent journals. Through interaction with other departments, students learn to formulate statistically problems expressed in the language of another discipline and interact in a consulting role with researchers outside of statistics. Usually offered every fall. Prerequisite: permission of department.

 

Prerequisite: permission of department.