Course Descriptions

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 00100

Introduction to Algebra

Credit Hrs:4

P: Placement. Covers the material taught 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.

Course Materials

MATH- 11000

Fundamentals of Algebra

Credit Hrs:4

P: MATH 00100 with a 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 prerequisite needed for MATH M118, M119, 13000, 13600, and STAT 30100.

Course Materials

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 11100

Algebra

Credit Hrs:4

P: MATH 00100 with a minimum grade of C or placement. Real numbers, linear equations and inequalities, systems of equations, polynomials, exponents, and logarithmic functions. Covers material in the second year of high school algebra. This course satisfies the prerequisite needed for MATH M118, M119, 13000, 13600, 15300, and STAT 30100.

Course Materials

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

STAT- 11300

Statistics and Society

Credit Hrs:3

Intended to familiarize the student with basic statistical concepts and some of their applications in public and health policies as well as in social and behavioral sciences. No mathematics beyond simple algebra is needed, but quantitative skills are strengthened by constant use. Involves much reading, writing, and critical thinking through discussions on such topics as data ethics, public opinion polls and the political process, the question of causation the role of government statistics, and dealing with chance in everyday life. Applications include public opinion polls, medical experiments, smoking and health, the consumer price index, state lotteries, and the like. STAT 11300 can be used for general education or as preparation for later methodology courses.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH-M 118

Finite Mathematics

Credit Hrs:3

P: MATH 11100 or 11000 with a minimum grade of C- or placement. Set theory, logic, permutations, combinations, simple probability, conditional probability, Markov chains. An honors option is available in this course.

Course Materials

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH-M 119

Brief Survey of Calculus I

Credit Hrs:3

P: MATH 11100 or 11000 with a minimum grade of C- or placement. Sets, limits, derivatives, integrals, and applications. An honors option is available in this course.

Course Materials

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 13000

Mathematics for Elementary Teachers I

Credit Hrs:3

P: MATH 11100 or 11000 with a minimum grade of C- or placement. Numeration systems, mathematical reasoning, integers, rationals, reals, properties of number systems, decimal and fractional notations, and problem solving.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 13100

Mathematics for Elementary Teachers II

Credit Hrs:3

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 13200

Mathematics for Elementary Teachers II

Credit Hrs:3

P: MATH 13000. Rationals, reals, geometric relationships, properties of geometric figures, one-, two-, and three-dimensional measurement, and problem solving.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 13600

Mathematics for Elementary Teachers

Credit Hrs:6

P: MATH 11100 or 11000 with a minimum grade of C or placement. MATH 13600 is a one-semester version of MATH 13000 and 13200. Not open to students with credit in 13000 or 13200.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 15300

Algebra and Trigonometry I

Credit Hrs:3

P: MATH 11100 with a minimum grade of C or placement. MATH 15300-15400 is a two-semester version of 15900. Not open to students with credit in MATH 15900. 15300 covers college-level algebra and provides preparation for MATH 16500, 22100, and 23100.

Course Materials

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 15400

Algebra and Trigonometry II

Credit Hrs:3

P: MATH 15300 with a minimum grade of C. MATH 15300-15400 is a two-semester version of 15900. Not open to students with credit in MATH 15900. MATH 15400 covers college-level trigonometry and provides preparation for MATH16500, 22100, and 23100.

Course Materials

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 15900

Precalculus

Credit Hrs:5

P: MATH11100 with a minimum grade of B or placement. MATH 15900 is a one-semester version of 15300-15400. Not open to students with credit in MATH 15300 or 15400. 15900 covers college-level algebra and trigonometry and provides preparation for MATH 16500, 22100, and 23100.

Course Materials

MATH-S 165

Honors Integrated Calculus and Analytic Geometry I

Credit Hrs:4

P: Precalculus or trigonometry and consent of instructor. This course covers the same topics as MATH 16500. However, it is intended for students having a strong background in mathematics who wish to study the concepts of calculus in more depth and who are seeking mathematical challenges.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 16500

Analytic Geometry and Calculus I

Credit Hrs:4

P: MATH15900 or 15400 (minimum grade of C) or placement. Introduction to differential and integral calculus of one variable, with applications. The Fundamental Theorem of Calculus.

Course Materials

MATH-S 166

Honors Analytic Geometry and Calculus II

Credit Hrs:4

P: MATH S16500 with a minimum grade of B- or MATH 16500 with a minimum grade of A-, and consent of instructor. This course covers the same topics as Math 16600. However, it is intended for students having a strong interest in mathematics who wish to study the concepts of calculus in more depth and who are seeking a mathematical challenge.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 16600

Analytic Geometry and Calculus II

Credit Hrs:4

P: MATH16500 with a minimum grade of C-. Continuation of Math 16500. Inverse functions: exponential, logarithmic and inverse trigonometric functions. Techniques of integration, applications of integration, differential equations and infinite series.

Course Materials

MATH- 17100

Multidimensional Mathematics

Credit Hrs:3

P: MATH 15900 or 15400 with a minimum grade of C or placement. An introduction to mathematics in more than two dimensions. Graphing of curves, surfaces and functions in three dimensions. Two and three dimensions vector spaces with vector operations. Solving systems of linear equations using matrices. Basic matrix operations and determinants.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 22100

Calculus for Technology I

Credit Hrs:3

P: MATH 15400 or 15900 with a minimum grade of C- or placement. Analytic geometry, the derivative and applications, and the integral and applications.

Course Materials

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 22200

Calculus for Technology II

Credit Hrs:3

P: MATH 22100 with a minimum grade of C-. Differentiation of transcendental functions, methods of integration, power series, Fourier series, and differential equations.

Course Materials

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 23100

Calculus for Life Sciences I

Credit Hrs:3

P: MATH 15400 or 15900 or placement. Limits, derivatives and applications. Exponential and logarithmic functions. Integrals, antiderivatives and the Fundamental Theorem of Calculus. Examples and applications are drawn from the life sciences.

Course Materials

Syllabus

MATH- 23200

Calculus for Life Sciences II

Credit Hrs:3

P: MATH 23100 with a minimum grade of C-. Matrices, functions of several variables, differential equations and solutions with applications. Examples and applications are drawn from the life sciences.

Course Materials

Syllabus

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 26100

Multivariate Calculus

Credit Hrs:4

P: MATH 16600 and 17100. Spatial analytic geometry, vectors, curvilinear motion, curvature, partial differentiation, multiple integration, line integrals, and Green's theorem. An honors option is available in this course.

MATH- 26600

Ordinary Differential Equations

Credit Hrs:3

P: MATH 16600 and 17100. R: MATH 26100. First order equations, second and n'th order linear equations, series solutions, solution by Laplace transform, systems of linear equations.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 27600

Discrete Math

Credit Hrs:3

P or C: MATH 16500. Logic, sets, functions, integer algorithms, applications of number theory, mathematical induction, recurrence relations, permutations, combinations, finite probability, relations and partial ordering, and graph algorithms.

MATH- 30000

Logic and the Foundations of Algebra

Credit Hrs:3

P: MATH 16500. 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.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

STAT- 30100

Elementary Statistical Methods I

Credit Hrs:3

P: MATH 11000 or 11100 or placement. Not open to students in the Department of Mathematical Sciences. 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, and correlation and regression. Software is used throughout. See Course Web Site for more information.

MATH- 33300

Chaotic Dynamical Systems

Credit Hrs:3

P: MATH 16600, 22200 or 23200. The goal of the course is to introduce some of the spectacular new discoveries that have been made in the past twenty years in the field of mathematics known as dynamical systems. It is intended for undergraduate students in mathematics, science or engineering. It will include a variety of computer experiments using software that is posted on the web.

STAT- 35000

Introduction to Statistics

Credit Hrs:3

P: MATH 16500. 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 51100 but with emphasis on more data-analytic material. Includes a weekly computing laboratory using Minitab.

MATH- 35100

Elementary Linear Algebra

Credit Hrs:3

P: MATH 26100. Not open to students with credit in MATH 51100. Systems of linear equations, matrices, vector spaces, linear transformations, determinants, inner product spaces, eigenvalues, and applications.

STAT- 37100

Prep for Actuarial Exam I

Credit Hrs:2

This course is intended to help actuarial science students prepare for the SOA/CAS Exam P/1.

MATH- 37300

Financial Mathematics

Credit Hrs:3

P: MATH26100. Fundamental concepts of financial mathematics and economics, and their application to business situations and risk management. Valuing investments, capital budgeting, valuing contingent cash flows, modified duration, convexity, immunization, financial derivatives. Provides preparation for the SOA/CAS Exam FM/2.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 39800

Internship in Professional Practice

Credit Hrs:1-3

P: Approval of Department of Mathematical Sciences. Professional work experience involving significant use of mathematics or statistics. Evaluation of performance by employer and Department of Mathematical Sciences. May count toward major requirements with approval of the Department of Mathematical Sciences. May be repeated with approval of the Department of Mathematical Sciences for a total of 6 credits.

MATH- 41400

Numerical Methods CSCI 41400

Credit Hrs:3

P: MATH 26600 and a course in a high-level programming language. Not open to students with credit in CSCI 51200. Error analysis, solution of nonlinear equations, direct and iterative methods for solving linear systems, approximation of functions, numerical differentiation and integration, and numerical solution of ordinary differential equations.

STAT- 41600

Probability

Credit Hrs:3

P: MATH 26100. Not open to students with credit in STAT 31100. 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.

MATH- 41700

Discrete Modeling and Game Theory

Credit Hrs:3

P: MATH 26600 and MATH 35100 or 51100, or consent of instructor. Linear programming; mathematical modeling of problems in economics, management, urban administration, and the behavioral sciences.

STAT- 41700

Statistical Theory

Credit Hrs:3

P: STAT 41600. R: STAT 35000. 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.

MATH- 42600

Introduction to Applied Mathematics and Modeling

Credit Hrs:3

P: MATH 26600 and PHYS 15200. 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.

MATH- 44400

Foundations of Analysis I

Credit Hrs:3

P: MATH 26100. Set theory, mathemtical induction, real numbers, completeness axiom, open and closed sets in Rm, sequences, limits, continuity and uniform continuity, inverse fuctions, differentiation of functions of one and several variables. See Course Web Site for more information.

MATH- 44500

Foundations of Analysis II

Credit Hrs:3

P: MATH 44400. 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.

MATH- 45300

Beginning Abstract Algebra

Credit Hrs:3

P: MATH 35100. Basic properties of groups, rings, and fields, with special emphasis on polynomial rings.

MATH- 45600

Introduction to the Theory of Numbers

Credit Hrs:3

P: MATH 26100. Divisibility, congruences, quadratic residues, Diophantine equations, and the sequence of primes.

MATH- 46200

Elementary Differential Geometry

Credit Hrs:3

P: MATH 35100. Calculus and linear algebra applied to the study of curves and surfaces. Curvature and torsion, Frenet-Serret apparatus and theorem, and fundamental theorem of curves. Transformation of R^2, first and second fundamental forms of surfaces, geodesics, parallel translation, isometries, and fundamental theorem of surfaces.

MATH- 46300

Intermediate Euclidean Geometry for Secondary Teachers

Credit Hrs:3

P: MATH 30000. 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.

STAT- 47200

Actuarial Models I

Credit Hrs:3

P: STAT 41700 or equivalent. Mathematical foundations of actuarial science emphasizing probability models for life contingencies as the basis for analyzing life insurance and life annuities and determining premiums. This course, together with its sequel, STAT 47300, provides most of the background for Exams MLC and MFE of the Society of Actuaries.

STAT- 47300

Actuarial Models II

Credit Hrs:3

P: STAT 47200. Continuation of STAT 47200. Together, these courses cover contingent payment models, survival models, frequency and severity models, compound distribution models, simulation models, stochastic process models, and ruin models.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 49000

Topics in Mathematics for Undergraduates

Credit Hrs:1-5

By arrangement. Open to students only with the consent of the department. Supervised reading and reports in various fields.

MATH- 49100

Seminar in Competitive Math Problem-Solving

Credit Hrs:1-3

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.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 49200

Capstone Experience

Credit Hrs:1-3

By arrangement.

MATH- 49500

TA Instruction

Credit Hrs:0

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.

Offered in Summer of 2009 Offered in Spring of 2010

STAT-N 501

Statistical Methods for Health Sciences

Credit Hrs:3

P: Math 15300. An introductory statistical methods course, with emphasis on applications in the health sciences. Topics include descriptive statistics, probability distributions, sampling distributions, confidence interval estimation, hypothesis testing, analysis of variance, linear regression, goodness-of-fit tests, and contingency tables. Credit cannot be given for more than one of STAT 30100, 35000 or 51100; or STAT N501.

MATH- 50400

Real Analysis

Credit Hrs:3

P: MATH 44400. 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, and the Arzela-Ascoli theorem.

MATH- 50500

Intermediate Abstract Algebra

Credit Hrs:3

P: MATH 45300. Group theory with emphasis on concrete examples and applications. Field theory: ruler and compass constructions, Galois theory, and solvability of equations by radicals.

MATH- 51000

Vector Calculus

Credit Hrs:3

P: MATH 26100. 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, and applications to engineering and the physical sciences.

MATH- 51100

Linear Algebra with Applications

Credit Hrs:3

P: MATH 26100. Not open to students with credit in MATH 35100. Matrices, rank and inverse of a matrix, decomposition theorems, eigenvectors, unitary and similarity transformations on matrices.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

STAT- 51100

Statistical Methods I

Credit Hrs:3

P: MATH 16500. 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; and correlation and regression.

STAT- 51200

Applied Regression Analysis

Credit Hrs:3

P: STAT 51100. 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- 51300

Statistical Quality Control

Credit Hrs:3

P: STAT 51100. Control charts and acceptance sampling, standard acceptance plans, continuous sampling plans, sequential analysis, and response surface analysis. Use of existing statistical computing packages.

STAT- 51400

Designs of Experiments

Credit Hrs:3

P: STAT 51200. Fundamentals, completely randomized design, and 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.

BIOS-S 515

Biostatistical Practicum

Credit Hrs:1-3

Real-world projects in biostatistics involving participation in consulting sessions, directed reading in the literature, research ethics, design of experiments, collection of data and applications of biostatistical methods. Detailed written and oral reports required. May be repeated, up to 6 credits.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

STAT- 51500

Statistical Consulting Problems

Credit Hrs:1-3

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- 51600

Basic Probability and Applications

Credit Hrs:3

P: MATH 26100. 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; and introduction to Markov chains.

STAT- 51700

Statistical Inference

Credit Hrs:3

P: STAT 51100 or 51600. 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; and introduction to nonparametric tests and linear regression.

MATH- 51800

Advanced Discrete Mathematics

Credit Hrs:3

P: MATH 26600. This course covers mathematics useful in analyzing computer algorithms. Topics include recurrence relations, evaluation of sums, integer functions, elementary number theory, binomial coefficients, generating functions, discrete probability, and asymptotic methods.

MATH- 51900

Introduction to Probability STAT 51900

Credit Hrs:3

P: 26100. See course listing for STAT 51900.

STAT- 51900

Probability Theory

Credit Hrs:3

P: MATH 26100. 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.

MATH- 52000

Boundary Value Problems of Differential Equations

Credit Hrs:3

P: MATH26100 and 26600. Sturm-Liouville theory, singular boundary conditions, orthogonal expansions, separation of variables in partial differential equations, and spherical harmonics.

STAT- 52000

Time Series and Applications

Credit Hrs:3

P: STAT 51900. 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; and multivariate time series. Use of existing statistical computing packages.

STAT- 52100

Statistical Computing

Credit Hrs:3

MATH- 52200

Qualitative Theory of Differential Equations

Credit Hrs:3

P: MATH 26600 and 35100. Nonlinear ODEs, critical points, stability and bifurcations, perturbations, averaging, nonlinear oscillations and chaos, and Hamiltonian systems.

STAT- 52200

Sampling and Survey Techniques

Credit Hrs:3

P: STAT 51200. Survey designs; simple random, stratified, and systematic samples; systems of sampling; methods of estimation; ratio and regression estimates; and costs. Other related topics as time permits.

MATH- 52300

Introduction to Partial Differential Equations

Credit Hrs:3

P: MATH 26600 and 51000. 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, and Poisson integral method for elliptic equations.

STAT- 52300

Categorical Data Analysis

Credit Hrs:3

P: STAT 52800. 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, and probit and extreme value models. Loglinear models in two and higher dimensions; maximum likelihood estimation, testing goodness-of-fit, partitioning chi-square, and models for ordinal data. Model building, selection, and diagnostics. Other related topics as time permits. Computer applications using existing statistical software.

STAT- 52400

Applied Multivariate Analysis

Credit Hrs:3

P: STAT 52800. 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, and factor analysis. Strong emphasis on the use of existing computer programs.

MATH- 52500

Introduction to Complex Analysis

Credit Hrs:3

P: MATH 26100 and 26600. Complex numbers and complex-valued functions; differentiation of complex functions; power series, uniform convergence; integration, contour integrals; and elementary conformal mapping.

STAT- 52500

Intermediate Statistical Methodology

Credit Hrs:3

C: STAT 52800. Generalized linear models, likelihood methods for data analysis, and 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.

BIOS-S 527

Introduction to Clinical Trials

Credit Hrs:3

Prepares biostatisticians for support of clinical trial projects. Topics: fundamental aspects of the appropriate design and conduct of medical experiments involving human subjects including ethics, design, sample size calculation, randomization, monitoring, data collection analysis and reporting of the results.

MATH- 52800

Advanced Mathematics for Engineering and Physics II

Credit Hrs:3

P: 53700 or consent of instructor. Divergence theorem, Stokes' Theorem, complex variables, contour integration, calculus of residues and applications, conformal mapping, and potential theory.

STAT- 52800

Mathematical Statistics

Credit Hrs:3

P: STAT 51900. 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, and sequential probability ratio test.

STAT- 52900

Applied Decision Theory and Bayesian Analysis

Credit Hrs:3

C: STAT 52800. 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; and game theory and minimax rules, Bayesian design, and sequential analysis. Comparison of statistical paradigms.

MATH- 53000

Functions of a Complex Variable I

Credit Hrs:3

P or C: MATH 54400. Complex numbers, holomorphic functions, harmonic functions, and linear transformations. Power series, elementary functions, Riemann surfaces, contour integration, Cauchy's theorem, Taylor and Laurent series, and residues. Maximum and argument principles. Special topics.

MATH- 53100

Functions of a Complex Variable II

Credit Hrs:3

P: MATH 53000. 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, and Picard theorems.

MATH- 53200

Elements of Stochastic Processes STAT 53200

Credit Hrs:3

P: STAT 51900. See course listing for STAT 53200.

STAT- 53200

Elements of Stochastic Processes MATH 53200

Credit Hrs:3

P: STAT 51900. 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- 53300

Nonparametric Statistics

Credit Hrs:3

P: STAT 51600. 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, and Kruskal-Wallis test for one-way layout. Runs test and Kendall test for independence, one- and two-sample Kolmogorov-Smirnov tests, and nonparametric regression.

STAT- 53600

Introduction to Survival Analysis

Credit Hrs:3

P: STAT 51700. 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, and 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.

MATH- 53700

Applied Mathematics for Scientists and Engineers I

Credit Hrs:3

P: MATH 26100, 26600, 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.

MATH- 54400

Real Analysis and Measure Theory

Credit Hrs:3

P: MATH 44400. Algebras of sets, real number system, Lebesgue measure, measurable functions, Lebesgue integration, differentiation, absolute continuity, Banach spaces, metric spaces, general measure and integration theory, and Riesz representation theorem.

MATH- 54500

Principles of Analysis II

Credit Hrs:3

P: MATH 54400. Continues the study of measure theory begun in MATH 54400.

BIOS-S 546

Applied Logitudinal Data Analysis

Credit Hrs:3

Covers modern methods for analysis of repeated measures, correlated outcomes and longitudinal data. Topics: repeated measures ANOVA, random effects and growth curve models, generalized estimating equations (GEE) and generalized linear mixed models (GLMMs). Extensive use of statistical software, e.g. SAS, R.

MATH- 54600

Introduction to Functional Analysis

Credit Hrs:3

P: MATH 54500. Banach spaces, Hahn-Banach theorem, uniform boundedness principle, closed graph theorem, open mapping theorem, weak topology, and Hilbert spaces.

Offered in Summer of 2009

MATH- 54700

Analysis for Teachers I

Credit Hrs:3

P: MATH 26100. Set theory, logic, relations, functions, Cauchy's inequality, metric spaces, neighborhoods, and Cauchy sequence.

MATH- 54900

Applied Mathematics for Secondary School Teachers

Credit Hrs:3

P: MATH 26600 and 35100. 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.

MATH- 55200

Applied Computational Methods II

Credit Hrs:3

P: MATH 55900 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.

MATH- 55300

Introduction to Abstract Algebra

Credit Hrs:3

P: MATH 45300. Group theory: finite abelian groups, symmetric groups, Sylow theorems, solvable groups, Jordan-H-lder theorem. Ring theory: prime and maximal ideals, unique factorization rings, principal ideal domains, Euclidean rings, and factorization in polynomial and Euclidean rings. Field theory: finite fields, Galois theory, and solvability by radicals.

MATH- 55400

Linear Algebra

Credit Hrs:3

P: MATH 35100. Review of basics: vector spaces, dimension, linear maps, matrices, determinants, and linear equations. Bilinear forms, inner product spaces, spectral theory, and eigenvalues. Modules over principal ideal domain, finitely generated abelian groups, and Jordan and rational canonical forms for a linear transformation.

MATH- 55900

Applied Computational Methods I

Credit Hrs:3

P: MATH 26600 and MATH 35100 or 51100. 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.

MATH- 56100

Projective Geometry

Credit Hrs:3

P: MATH 35100. Projective invariants, Desargues' theorem, cross-ratio, axiomatic foundation, duality, consistency, independence, coordinates, and conics.

MATH- 56200

Introduction to Differential Geometry and Topology

Credit Hrs:3

P: MATH 35100 and 44500. 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, and Gauss-Bonnet and Poincare theorems on vector fields.

MATH- 56700

Dynamical Systems I

Credit Hrs:3

P: Math 54500, Math 57100. Covers the basic notions and theorems of the theory of dynamical systems and their connections with other branches of mathematics. Topics covered include fundamental concepts and examples, one-dimensional systems, symbolic dynamics, topological entropy, hyperbolicity, structural stability, bifurcations, invariant measures, and ergodicity. See Course Web Site for more information.

MATH- 57100

Elementary Topology

Credit Hrs:3

P: MATH 44400. Topological spaces, metric spaces, continuity, compactness, connectedness, separation axioms, nets, and function spaces.

MATH- 57200

Introduction to Algebraic Topology

Credit Hrs:3

P: MATH 57100. Singular homology theory, Ellenberg-Steenrod axioms, simplicial and cell complexes, elementary homotopy theory, and Lefschetz fixed point theorem.

MATH- 57400

Mathematical Physics I

Credit Hrs:3

P: Math 54500, 53000. Topics in special functions, representation theory, spectral theory, noncommutative geometry, mathematical foundations of statistical physics. The specific content of the course will vary from year to year, to be determined by the instructor.

MATH- 57800

Mathematical Modeling of Physical Systems I

Credit Hrs:3

P: MATH 26600, PHYS 15200, PHYS 25100, 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.

Offered in Summer of 2009

MATH- 58100

Introduction to Logic for Teachers

Credit Hrs:3

P: MATH 35100. Not open to students with credit in 38500. Logical connectives, rules of sentential inference, quantifiers, bound and free variables, rules of inference, interpretations and validity, theorems in group theory, and introduction to set theory.

MATH- 58300

History of Elementary Mathematics

Credit Hrs:3

P: MATH 26100. 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.

Offered in Summer of 2009 Offered in Spring of 2010

MATH- 58800

Mathematical Modeling of Physical Systems II

Credit Hrs:3

P: MATH 57800. 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.

BIOS-S 598

Topics in Biostatistical Methods

Credit Hrs:3

Directed study and reports for students who wish to undertake individual reading and study on approved topics.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 59800

Topics in Mathematics

Credit Hrs:1-5

By arrangement. Directed study and reports for students who wish to undertake individual reading and study on approved topics.

STAT- 59800

Topics in Statistical Methods

Credit Hrs:1-3

P: consent of instructor. Directed study and reports for students who wish to undertake individual reading and study on approved topics.

Offered in Summer of 2009 Offered in Fall of 2009 Offered in Spring of 2010

MATH- 61100

Methods of Applied Mathematics I

Credit Hrs:3

P: consent of instructor. Introduction to Banach and Hilbert spaces, linear integral equations with Hilbert-Schmidt kernels, eigenfunction expansions, and Fourier transforms.

MATH- 61200

Methods of Applied Mathematics II

Credit Hrs:3

P: MATH 61100. Continuation of theory of linear integral equations; Sturm-Liouville and Weyl theory for second-order differential operators, distributions in n dimensions, and Fourier transforms.

STAT- 61900

Probability Theory

Credit Hrs:3

P: STAT 51900. Probability Theory is the Foundation of statistical methodologies, which is fundamental in the practice of science. From this course students will get a precise mathematical understanding of probabilities and sigma-algebras, random weak convergence, characteristic functions, the central limit theorem, Lobesgue decomposition, conditioning and martingales.

BIOS-S 621

Advanced Statistical Computing

Credit Hrs:3

P: STAT 52100; experience with R/S plus programming. This course covers selected computational techniques useful in advanced statistical applications and statistical research, such as methods for solving linear equations, numerical optimization, numerical integration, Bayesion methods, bootstrap methods and stochastic search algorithms.

BIOS-S 627

Statistics in Pharmaceutical Research

Credit Hrs:3

An overview of the drug development process, including the various phases of development from pre-clinical to post-marketing. Topics: statistical issues in design, study monitoring, analysis and reporting. Additional topics may include regulatory and statistical aspects of population pharmacokinetics and real world applications.l

MATH- 62700

Mathematical Formulation of Physical Problems II

Credit Hrs:3

P: 62600. Continuation of 62600.

MATH- 64600

Functional Analysis

Credit Hrs:3

P: MATH 54600. Advanced topics in functional analysis, varying from year to year at the discretion of the instructor.

MATH- 66700

Dynamical Systems II

Credit Hrs:3

P: MATH 56700 Topics in dynamics. Continuation of Math 56700.

MATH- 67200

Algebraic Topology I

Credit Hrs:3

P: MATH 57200. Continuation of MATH 57200; cohomology, homotopy groups, fibrations, and further topics.

MATH- 67300

Algebraic Topology II

Credit Hrs:3

P: 67200. continuation of 67200, covering further advanced topics in algebraic and differential topology such as K-theory and characteristic classes.

MATH- 67400

Mathematical Physics II

Credit Hrs:3

P: MATH 57400. Topics in inverse spectrum and scattering problems and their applications to the theory of solitons, spectral theory of difference equations and orthogonal polynomials, geometric quantization, and rigorous results in statistical physics, quantum field theory and random processes. The specific content of the course varies from year to year, to be determined by the instructor.

MATH- 69200

Topics in Applied Mathematics

Credit Hrs:1-3