Course Catalog

Mathematics Courses (Math)

Prerequisite override applies to all graduate students for prerequisites at level 4000 and lower.

5110. Differential Geometry.
Introduction to geometry of curves and surfaces in three dimensions, using graphic and symbolic software. Prerequisites: C- or better in Math 2210, 2250; or Math 2210, 2270, 2280. (3 cr) (F)

5210. Introduction to Analysis I.
One and several variable calculus from an advanced point of view. Proofs of all main theorems in calculus. Prerequisite: C- or better in Math 4200 or 5510. (3 cr) (F)

5220. Introduction to Analysis II.
Continuation of Math 5210. Rigorous development of multivariable advanced calculus. Prerequisite: C- or better in Math 5210. (3 cr) (Sp)

5270. Complex Variables.
Basic theory and applications of complex variables for mathematics, physics, and engineering students. Topics include analytic functions, contour integration, and residue theorem conformal mappings. Prerequisites: C- or better in Math 2210, 2250; or C- or better in Math 2210, 2270, 2280. (3 cr) (Sp)

5310. Introduction to Modern Algebra.
Continuation of Math 4310. Topics include: Sylow theory for finite groups, factorization theory for commutative rings, and Galois theory. Prerequisite: C- or better in Math 4310. (3 cr) (Sp)

5340. Theory of Linear Algebra.
Vector space theory, linear transformations and matrices, eigenvalues and eigenvectors, inner product spaces, orthogonality, canonical forms, and Hermitian matrices. Prerequisite: C- or better in Math 2270; or C- or better in Math 4310, or consent or instructor. (3 cr) (F)

5410. Methods of Applied Mathematics.
Basic modeling and qualitative understanding, including dimensional analysis (Buckingham Pi theoram). Asymptotic solutions, perturbation approaches, boundary layers in differential equations, variational calculas, Hamilton's principle, and conservation of energy. Emphasizes practical approaches to science and engineering problems. Prerequisites: C- or better in Math 2210, 2250; or C- or better in Math 2210, 2270, 2280. (3cr)(F)

5420. Partial Differential Equations.
Modeling with partial differential equations, diffusion, and wave equations. Classical solution techniques including; maximum principles, separation of variables (eigenfunctions), method of characteristics, Fourier and Laplace transforms, and singularity methods (Green's Functions). Emphasizes understanding and solving physical equations. Prerequisite: C- or better in Math 2250 or 2280. (3 cr) (Sp)

5460. Introduction to the Theory and Application of Nonlinear Dynamical Systems.
Qualitative behavior of nonlinear maps and ordinary differential equations. Stability of solutions, bifurcation theory, chaos, and applications. Prerequisite: C- or better in Math 2250 or 2280. (3 cr) (Sp)

5510. Introduction to Topology.
Elementary point-set topology, topological spaces, separation axioms, metric spaces, compactness, connectedness, order topology, countability axioms, continuity, and homeomorphisms. Prerequisite: C- or better in Math 2210 or 4200. (3 cr) (F)

5570. Actuarial Math I.
Introduction to theory of risk and its application to construction and analysis of models for insurance systems. Prerequisites: C- or better in Math 5710, Stat 3000, and permission of instructor. (3 cr) (F)

5580. Actuarial Math II.
Continuation of Math 5570. Prerequisite: C- or better in Math 5570. (3 cr) (Sp)

5610. Computational Linear Algebra and Solution of Systems of Equations.
Numerical solutions of systems of linear and nonlinear equations, methods for eigensystems, least squares problems, finding roots of functions and nonlinear systems, constrained and unconstrained optimization. Prerequisites: C- or better in Math 2210, 2250 or 2270, and a high-level programming language. (3 cr) (F)

5620. Numerical Solutions of Differential Equations.
Numerical solution of differential equations, initial and boundary value problems, finite difference, finite element, and spectral methods (FFT) applied to ODEs and PDEs. Prerequisite: C- or better in Math 2210, 2250, 2270, or 2280; and a high-level programming language. (3 cr) (Sp)

5640. Optimization.
One-semester introductory survey of optimization, including both continuous and cominatorial problems. Topics include: linear programming, constrained and uncontrained optimization, network models, dynamic programming, and integer programming. Prerequisite: C- or better in Math 2210; C- or better in Math 2250 or 2270; and a high level programming language. (3 cr) (Sp)

5710. Introduction to Probability.
Discrete and continuous probability, random variables, distribution and density functions, joint distributions, Conditional probabilities and expectations, Bayes’ theorem, moments, moment generating functions, inequalities, convergence in probability and distribution, and central limit theorem. Prerequisites: C- or better in Math 2210, and C- or better in Math 2250 or 2270. (3 cr) (F,Sp)

5720. Introduction to Mathematical Statistics.
Basic theory of point and interval estimation and hypothesis testing. Topics include: sufficiency and completeness; method-of-moments, best unbiased, maximum likelihood, Bayes’, and empirical Bayes’ estimators; Neyman-Pearson lemma; and likelihood ratio tests. Prerequisite: C- or better in Math 5710. (3 cr) (Sp)

5740. Actuarial Financial Mathematics.
Introduces fundamental concepts of financial mathematics focusing on applications to non-life insurance. Topics include interest theory, cash flows, yield rates, annuities, portfolio insurance and derivatives. Prerequisites: Math 1220 and Stat 3000. (3 cr) (Sp)

5760. Stochastic Processes.
Application of stochastic processes to engineering and science. Topics include Markov chains, Poisson processes, renewal theory, and Brownian motion. Prerequisite: C- or better in Math 5710. (3 cr) (F)

5810, 5820. Topics in Mathematics.
Prerequisite: Permission of instructor. (1-3 cr) (F,Sp,Su) ®

5910. Directed Reading and Conference.
Prerequisite: Prior arrangement with a specific instructor. (1-3 cr) (F,Sp,Su) ®

5950. Honors Senior Project. A senior project required for completion of the departmental honors program. Prerequisite: Permission of instructor. (1-4 cr) (F,Sp,Su)

6110, 6120. Differential Geometry.
Topics include manifolds, calculus on manifolds, tensor calculus and differential forms, Lie groups, Riemannian geometry, deRham’s Theorem, and Hodge theory. Prerequisite: C- or better in Math 5110 or 5220; Math 6110 must be completed prior to Math 6120. (3 cr)(F) (3 cr)(Sp)

6210, 6220. Real Analysis.
Measure theory, abstract integration, differentiation, introduction to functional analysis, Hilbert and Banach spaces. Prerequisite: C- or better in Math 5210; Math 6210 must be completed prior to 6220. (3 cr)(F) (3 cr)(Sp)

6250. Graduate Internship/Cooperative Studies.
Graduate internship/cooperative work experience. (1-6) (F,Sp,Su) ®

6270. Complex Variables.
Analytic functions, singular points, conformal maps, harmonic functions, analytic continuation, Residue theory. Prerequisite: C- or better in Math 5210 or 5270. (3 cr)(Sp)

6310, 6320. Modern Algebra.
Algebraic structures, including vector spaces, groups, rings, algebras, and modules. Topics include: catagory theory, elementary commutative ring theory, and algebraic geometry. Prerequisite: C- or better in Math 5310; Math 6310 must be completed prior to 6320. (3 cr)(F) (3 cr)(Sp)

6340, 6350. Multilinear Algebra and Matrix Theory.
Permutation groups and representations, tensor spaces, symmetry classes of tensors, generalized matrix functions, matrices and graphs, and combinatorial matrix algebra. Prerequisite: C- or better in Math 5340; Math 6340 must be completed prior to 6350. (3 cr)(F) (3 cr)(Sp)

6410. Ordinary Differential Equations I.
Existence-uniqueness theory, linear equations and systems, nonlinear equations, and stability. Prerequisite: C- or better in Math 5210. (3 cr) (F)

6420. Partial Differential Equations I.
Introduction to the theory of partial differential equations, including existence and uniqueness. Prerequisite: C- or better in Math 5220 or 6410.
(3 cr) (Sp)

6440. Ordinary Differential Equations II.
Asymptotic behavior, periodicity, boundary value problems, and perturbation methods. Prerequisite: C- or better in Math 6410. (3 cr) (Sp)

6450. Partial Differential Equations II.
Advanced existence and uniqueness theorems, behavior of solutions, Sobolev spaces. Prerequisites: C- or better in Math 6210; and C- or better in Math 5420 or 6420. (3 cr) (Sp)

6470. Advanced Asymptotic Methods.
Theory of asymptotics and perturbations. Boundary layers for ordinary and partial differential equations. Free boundary problems, shocks, multiple-scale methods, and WKB methods. Prerequisite: C- or better in Math 5420. (3 cr)(Sp)

6500. Methods of Secondary School Mathematics Teaching.
A teaching methods course required of all prospective secondary school
mathematics teachers. To receive graduate credit, students must complete an extra project. Students having a Methods of Secondary Math Teaching Methods course on their transcripts will not be allowed to apply credit for this course toward a master’s degree. Prerequisites: Matriculation into the Master’s of Education Plan C program, the Master’s of Mathematics program, or the USOE Alternative Route to Licensure Program. (3 cr)(F,Sp)

6510, 6520. Topology.
Homotopy theory, fundamental groups, covering spaces, singular homology with applications to spheres and Euclidean spaces, CW complexes, cohomology ring, and Poincare duality. Prerequisites: C- or better in Math 4310, 5510; and C- or better in Math 5310 or consent of instructor; Math 6510 must be taken prior to 6520. (3 cr) (F,Sp)

6610. Matrix Computations.
Computational aspects of matrix theory, focusing on numerical methods for
solving linear systems, least squares problems, and eigenvalue problems. Prerequisites: C- or better in MATH 5210 or 5610, and experience with a highlevel programming language. (3 cr) (F)

6620. Numerical Analysis.
Numerical solution of ordinary and partial differential equations. Prerequisite: C- or better in Math 6610 or consent of instructor. (3 cr) (Sp)

6640. Optimization.
Unconstrained problems, smooth function methods, linearly constrained problems, linear and quadratic programming, nonlinearly constrained methods, and practicalities. Prerequisite: C- or better in Math 5220 or consent of instructor. (3 cr) (Sp)

6750, 6760. Probability Theory.
Probability spaces, random variables, distribution functions, expectations, independence, modes of convergence, limit theorems, and applications. Prerequisite: C- or better in Math 5210; Math 6750 must be taken prior to 6760. (3 cr)(F,Sp)

6810, 6820. Topics in Mathematics (Topic).
Prerequisite: Consent of instructor. (3 cr)(F) (3 cr)(Sp) ®

6910. Directed Reading and Conference.
Prerequisite: Prior arrangement with specific instructor. (1-3 cr) (F,Sp,Su) ®

6970. Thesis.
(1-9 cr) (F,Sp,Su) ®

6990. Continuing Graduate Advisement.
(1-2 cr) (F,Sp,Su) ®

7110, 7120. Geometry (Topic).
(3 cr) (F) (3 cr) (Sp) ®

7210, 7220. Analysis (Topic).
(3 cr) (F) (3 cr)(Sp) ®

7310, 7320. Algebra (Topic).
(3 cr)(F) (3 cr)(Sp) ®

7410, 7420. Differential Equations (Topic).
(3 cr) (F) (3 cr)(Sp) ®

7510, 7520. Topology (Topic).
(3 cr)(F) (3 cr)(Sp) ®

7610, 7620. Numerical Analysis (Topic).
(3 cr)(F) (3 cr)(Sp) ®

7750, 7760. Probability (Topic).
(3 cr)(F) (3 cr)(Sp) ®

7810, 7820. Topics in Mathematics (Topic).
(3 cr)(F) (3 cr)(Sp) ®

7910. College Teaching Internship.
(3 cr)(F,Sp,Su) ®

7970. Dissertation Research.
(1-15 cr) (F,Sp,Su) ®

7990. Continuing Graduate Advisement.
(1-9 cr) (F,Sp,Su) ®

Statistics Courses (Stat)

Prerequisite override applies to all graduate students for prerequisites at level 4000 and lower.

5100. Linear Regression and Time Series (CI/QI).
Methods for prediction and hypothesis testing in multiple linear regression models, including analysis of variance and covariance, logistic regression, introduction to time series, and signal processing. Prerequisite: C- or better in Stat 2000 or 3000. (3 cr) (F)

5120. Categorical Data Analysis.
Analysis of categorical data, contingency tables, goodness of fit, random sampling, log-linear and logistic regression models, sampling for proportions, as well as stratified and cluster sampling. Prerequisite: C- or better in Stat 5100. (3 cr) (F)

5200. Design of Experiments.
Design, analysis, and interpretation of experiments, split plots, incomplete blocks, confounding, fractional factorials, nested designs, two-and three-way analysis of variance, covariance, and multiple regression. Prerequisite: C- or better in Stat 2000 or 3000. (3 cr) (Sp)

5410/6410. Applied Spatial Stat.
Explores spatial point patterns, spatially continuous data, area (grid) data,
nearest neighbor distances, K function, complete spatial randomness, variogram, kriging, correlogram, and Moran’s I. For graduate (6000-level credit), a major project is required. Prerequisite: C- or better in STAT 3000. Knowledge of a statistical package (e.g., S-Plus, R, SAS, etc.) or any programming language (e.g., C/C++, FORTRAN, etc.) is strongly recommended. (3 cr) (F)

5570/6570. Stat Bioinformatics.
Introduction to current statistical issues in bioinformatics, primarily gene
expression and sequence analysis, using bioconductor tools. Topics include
data normalization and visualization, differential expression, annotation, scoring alignments, HMMs, and phylogenetic trees. For graduate (6000-level) credit, major project required. Prerequisite: C- or better in STAT 5100 or 5200. (3 cr) (Sp)

5600. Applied Multivariate Statistics (CI).
Introduction to multivariate statistical procedures for data analysis. Topics include MANOVA, principal component analysis, factor analysis, clustering, and classification. Prerequisite: C- or better in Stat 5100. (3 cr) (Sp)

5810, 5820. Topics in Statistics.
Prerequisite: Consent of instructor. (1-3 cr) (F) (1-3 cr) (Sp) ®

5890. Problem Solving in Statistics (CI).
Capstone course for Statistics majors, applying course material covered in the undergraduate major. Prerequisite: Permission of instructor. (3 cr) (Sp)

5940. Directed Reading and Conference.
Prerequisite: Prior arrangement with specific instructor. (1-3 cr) (F,Sp,Su) ®

5950. Senior Honors Project.
A senior project, required for completion of the departmental honors program and developed under the direction of a departmental faculty member. Prerequisite: Permission of instructor. (1-4 cr) (F,Sp,Su)

5970. Seminar.
Review of current literature and developments in the field of statistics. (1-3 cr) (F,Sp) ®

6100. Advanced Regression.
Explores the following topics in the theory of linear models: least squares
estimation, the general linear hypothesis, regression diagnostics for
multicollinearity, outliers, and influential points. Also includes discussion of robust regression, nonlinear regression, generalized linear models, ACE, generalized additive models, and regression models for survival data. Prerequisites: C- or better in MATH 5720 and STAT 5100. (3 cr) (F)

6180. Time Series.
Time and frequency domain time series analysis, including Box-Jenkins methods, spectral analysis and filtering, introduction to state space methodology. Prerequisite: C- or better in Math 5720 and Stat 5100. (3 cr) (Sp)

6190. Wavelet Methods for Time Series.
Explores time series models, time and frequency domain analysis, discrete wavelet transform, wavelet ANOVA, applications in physics and finance. Prerequisite: C- or better in Math 5720 and Stat 5100. (3 cr) (Sp)

6200. Messy Data Analysis.
Examines means and effects models, estimability, and type I-IV hypotheses.
Contrasts and sums of squares. Generalized linear models for experimental data. Linear mixed models. Generalized linear mixed models. Analysis of complex experimental designs. Nonreplicated experiments. Tests for additivity. Halfnormal plots. Prerequisite: C- or better in STAT 5200.(3 cr) (Sp)

6250. Graduate Internship/Co-op.
Educational work experience at the graduate level. Prerequisite: Permission of instructor. (1-8 cr) ®

6410/5410. Applied Spatial Statistics.
Explores spatial point patterns, spatially continuous data, area (grid) data,
nearest neighbor distances, K function, complete spatial randomness, variogram, kriging, correlogram, and Moran’s I. For graduate (6000-level credit), a major project is required. Prerequisite: C- or better in STAT 3000. Knowledge of a statistical package (e.g., S-Plus, R, SAS, etc.) or any programming language (e.g., C/C++, FORTRAN, etc.) is strongly recommended. (3cr) (F)

6530. Modern Nonparametric Statistics.
Examines topics in resampling methods including: the jackknife and the
bootstrap, bias, variance, and confidence intervals. Also explores the following topics in smoothing methods: histograms, kernel density estimates, and local polynomial regression. Includes testing procedures using ranks and empirical cumulative distribution functions. Prerequisites: C- or better in MATH 5710 and STAT 3000. (3 cr) (Sp)

6550. Statistical Computing.
Survey of algorithms and tools for modern statistical computing. Topics include simulation design and implementation, algorithms for linear regression and subset selection, smoothing algorithms, fast fourier transform, EM algorithm, numerical methods for maximum likelihood estimation, and neural networks. Prerequisites: C- or better in Stat 5110, Math 5720, and knowledge of a programming language. (3 cr) (Sp)

6560. Graphical Methods.
Statistical graphics and scientific visualization of one, two, and higher dimensional data. Well-chosen and designed graphics are vital in exploratory data analysis, model diagnostics, and data presentation. Includes specific methods and general principles, such as effective use of color and motion. Prerequisites: C- or better in Stat 3000, and programming experience. (3 cr) (F)

6570/5570. Statistical Bioinformatics.
Introduction to current statistical issues in bioinformatics, primarily gene
expression and sequence analysis, using bioconductor tools. Topics include
data normalization and visualization, differential expression, annotation, scoring alignments, HMMs, and phylogenetic trees. For graduate (6000-level) credit, major project required. Prerequisite: C- or better in STAT 5100 or 5200. (3 cr) (Sp)

6650. Statistical Learning: Multivariate Statistical Analysis for Bioinformatics, Data Mining, and Machine Learning.
Explores supervised learning, linear methods for regression and classification, model assessment and selection, model inference and averaging, additive models, boosting, neural networks, support vector machines, and unsupervised learning. Prerequisites: C- or better in MATH 5720 and STAT 5100. Programming experience in R or a related language is strongly recommended. (3 cr) (F)

6710. Mathematical Statistics I.
Modes of convergence of random variables, laws of large numbers, characteristic functions, and the central limit theorem. Prerequisite: C- or better in Math 5720. (3 cr) (F)

6720. Mathematical Statistics II.
Consistency, loss functions, risk, and notions of optimality of estimations. Hypothesis testing and confidence regions. Large sample theory, notions of robustness. Prerequisite: C- or better in Stat 6710. (3 cr) (Sp)

6740. Bayesian Statistics.
Conditional probability, Bayes’ theorem, conjugate and objective priors, Bayesian inference and decision theory, model averaging, multi-parameter and hierarchical models, sampling and numerical integration methods, linear models, generalized linear models, and models for correlated data. Prerequisites: MATH 5720 and STAT 5100. (3 cr) (Sp)

6810, 6820 Topics in Statistics (Topic).
Prerequisite: Permission of instructor. (3 cr) (F,Sp) ®

6890. Practical Statistical Consulting.
Introduction to statistical consulting for graduate students, for faculty in other research departments, and for business, industry, and government. Prerequisite: Permission of instructor. (1-3 cr) (F,Sp,Su) ®

6910. Seminar in Statistics.
Review of current literature and developments in statistics. Prerequisite: Permission of instructor. (1-3 cr) (F,Sp) ®

6950. Directed Reading and Conference.
Prerequisite: Prior arrangement with specific instructor. (1-4 cr) (F,Sp,Su) ®

6970. Thesis and Research.
Outlining and conducting research in statistics. Thesis preparation. (1-6 cr) (F,Sp,Su) ®

6990. Continuing Graduate Advisement.
(1-9 cr) (F,Sp,Su) ®

7110, 7120. Linear Models (Topic).
(3 cr) (F) (3 cr) (Sp) ®

7180, 7190. Time Series Analysis (Topic).
(3 cr)(F,Sp) ®

7210, 7220. Experimental Design (Topic).
(3cr) (F) (3cr) (Sp) ®

7310, 7320. Business and Industrial Statistics (Topic).
(3cr) (F) (3cr) (Sp) ®

7510, 7520. Nonparametric Statistics (Topic).
(3cr)(F) (3cr)(Sp) ®

7550, 7560. Computational and Graphical Statistics (Topic).
(3cr)(F) (3cr)(Sp) ®

7610, 7620. Multivariate Statistics (Topic).
(3cr)(F) (3cr)(Sp) ®

7710, 7720. Mathematical Statistics (Topic).
(3cr)(F) (3cr)(Sp) ®

7730, 7740. Bayesian Statistics and Decision Theory (Topic).
(3cr)(F) (3cr)(Sp) ®

7810, 7820. Topics in Statistics (Topic).
(1-3 cr)(F) (1-3 cr)(Sp) ®

7970. Dissertation Research.
(1-15 cr)(F,Sp,Su) ®

7990. Continuing Graduate Advisement.
(1-9cr)(F,Sp,Su) ®

® Repeatable for credit. Check with major department for limitations on number of credits that can be counted for graduation.