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Mathematical Sciences
Courses
MAT 651 - Foundations of Mathematics I
Credits 3Introduction to logic, set algebra and Boolean algebra, with applications to the theory of computing machines. Crosslisted with MAT 451. Credit at the 600-level requires additional work.
Prerequisites
Graduate standing.
MAT 652 - Foundations of Mathematics II
Credits 3This course is crosslisted with MAT 452. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Formalization, proofs, and models of quantificational logic; axiomatics; application to mathematical theories, including set theory.
Prerequisites
Graduate standing.
MAT 653 - Abstract Algebra I
Credits 3This course is crosslisted with MATH 453. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Sets, functions, groups, quotient groups, hom*omorphism theorems, Abelian groups, rings, polynomial rings, division rings, Euclidean domains, fields and vector spaces.
Prerequisites
Graduate standing.
MAT 654 - Abstract Algebra II
Credits 3This course is crosslisted with MATH 454. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Sets, functions, groups, quotient groups, hom*omorphism theorems, Abelian groups, rings, polynomial rings, division rings, Euclidean domains, fields and vector spaces.
Prerequisites
Graduate standing.
MAT 655 - Elementary Theory of Numbers I
Credits 3This course is crosslisted with MATH 455. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Topics include divisibility, arithmetic functions, congruences, quadratic residues, primitive roots, Diophantine equations, continued fractions, algebraic numbers, and partitions.
MAT 656 - Elementary Theory of Numbers II
Credits 3This course is crosslisted with MATH 456. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Topics include divisibility, arithmetic functions, congruences, quadratic residues, primitive roots, Diophantine equations, continued fractions, algebraic numbers, and partitions.
Prerequisites
Graduate standing.
MAT 657 - Introduction to Real Analysis I
Credits 3This course is crosslisted with MATH 457. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Topics include finite and infinite sets, axiomatic study of real numbers, topology of Cartesian spaces, sequences of functions, continuous functions, differentiation of functions of one variable.
Prerequisites
Graduate standing.
MAT 658 - Introduction to Real Analysis II
Credits 3This course is crosslisted with MATH 458. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Topics include uniform continuity and fixed point theorems, sequences of continuous functions, approximation theorems, Riemann-Stieltjes integral, uniform convergence and infinite integrals, series of functions, differentiation in Rn.
Prerequisites
Graduate standing.
MAT 659 - Elementary Complex Analysis
Credits 3This course is crosslisted with MAT 459. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Complex numbers, analytic functions, contour integration, conformal mapping, applications.
Prerequisites
Graduate standing.
MAT 661 - Probability Theory
Credits 3This course is crosslisted with MATH 461. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Fundamental concepts of probability; random variables, binomial, Poisson, normal, chi-square, T, F and other distributions; transformations of random variables; conditional and marginal distributions; central limit theorem and concepts associated with the field of statistics.
Prerequisites
Graduate standing.
MAT 663 - Advanced Matrix Theory and Applications
Credits 3This course is crosslisted with MATH 463. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Rigorous mathematical treatment of orthogonal matrices, Gram-Schmidt method, Q-R factorization, least-squares fits, eigenvalues and eigenvectors, linear difference equations, systems of linear differential equations, unitary similarities, Schur’s theorem, discrete Markov processes, power method, quadratic forms, singular value decompositions, pseudo-inverse, systems of linear inequalities, and simplex method.
Prerequisites
Graduate standing.
MAT 665 - Numerical Methods I
Credits 3The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program. This course is crosslisted with MATH 466. Credit at the 600-level requires additional work.Introduction to numerical mathematics and scientific computing. Topics include methods of error estimation, interpolation theory, numerical integration, and solutions of linear and non-linear equations. Emphasizes hands-on computer work based on these techniques.
Prerequisites
Graduate standing.
MAT 666 - Numerical Methods II
Credits 3The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program. This course is crosslisted with MATH 467. Credit at the 600-level requires additional work.Intermediate treatment of methods in computational linear algebra, numerical solutions of ordinary and partial differential equations, algorithmic design and analysis, and topics selected by the instructor.
Prerequisites
Graduate standing.
MAT 669 - Combinatorics I
Credits 3This course is crosslisted with MATH 469. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Graph models, covering circuits, graph colorings, trees and searching, general counting methods for arrangements and selections, generating functions, recurrence relations, and inclusion-exclusion.
Prerequisites
Graduate standing.
MAT 670 - Combinatorics II
Credits 3This course is crosslisted with MATH 470. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Advanced topics in combinatorics. Topics to be selected by the instructor.
Prerequisites
Graduate standing.
MAT 680 - College Geometry
Credits 3This course is crosslisted with MATH 480. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Study of advanced geometrical topics using the methods of proof of elementary geometry.
Prerequisites
Graduate standing.
MAT 683 - General Topology I
Credits 3This course is crosslisted with MATH 483. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Topological spaces, nets and filters, compactness, continuous functions, product and quotient spaces, introduction to algebraic topology.
Prerequisites
Graduate standing.
MAT 684 - General Topology II
Credits 3This course is crosslisted with MATH 484. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Topological spaces, nets and filters, compactness, continuous functions, product and quotient spaces, introduction to algebraic topology.
Prerequisites
Graduate standing.
MAT 688 - Partial Differential Equations
Credits 3The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.Method of separation of variables, Fourier series, divergence theorem and Green’s identities, equations of mathematical physics, initial and initial boundary value problems, well-posedness, heat conduction in a thin rod, vibrations of a string, Laplace’s equation, solution of the Dirichlet problem for a disc and for a rectangle. This course is crosslisted with MATH 488. Coursework at the 600-level requires additional work.
Prerequisites
Graduate standing.
MAT 690 - Independent Study
Credits 3This course is crosslisted with MAT 499. Credit at the 600-level requires additional work.
The 600-level MAT and STA courses that are normally available for graduate credit are those numbered 650 or higher; the exceptions are MAT 680, which may be counted for graduate credit in an education degree program, and STA 691, STA 693, and STA 695, which may be counted for graduate credit in a biological sciences program.
Library research and reports on topics of mathematical interest.
Prerequisites
Graduate standing.
MAT 701 - Foundations of Mathematics III
Credits 3Selection from the following topics: model theory, recursive function theory, set theory, mathematics of metamathematics.
Prerequisites
MAT 652
MAT 702 - Foundations of Mathematics IV
Credits 3Selection from the following topics: model theory, recursive function theory, set theory, mathematics of metamathematics.
Prerequisites
MAT 652
MAT 703 - Abstract Algebra III
Credits 3Detailed study of the following algebraic structures: groups, rings and ideals, fields, modules, and Galois theory.
Prerequisites
A year of undergraduate abstract algebra or consent of instructor.
MAT 704 - Abstract Algebra IV
Credits 3Detailed study of the following algebraic structures: groups, rings and ideals, fields, modules, and Galois theory.
Prerequisites
A year of undergraduate abstract algebra or consent of instructor.
MAT 707 - Real Analysis I
Credits 3Theory of measure, integration and differentiation: Banach spaces; Hilbert spaces; spaces of continuous functions.
Prerequisites
MAT 658
MAT 708 - Real Analysis II
Credits 3Theory of measure, integration and differentiation: Banach spaces; Hilbert spaces; spaces of continuous functions.
Prerequisites
MAT 658
MAT 709 - Complex Function Theory I
Credits 3Analytic functions, conformal mappings, Cauchy’s theorem, power series, Laurent series, the Riemann mapping theorem, harmonic functions, subharmonic functions, canonical mappings of multiply connected regions, analytic continuation.
Prerequisites
MAT 657 or MAT 659 or equivalent.
MAT 710 - Complex Function Theory II
Credits 3Analytic functions, conformal mappings, Cauchy’s theorem, power series, Laurent series, the Riemann mapping theorem, harmonic functions, subharmonic functions, canonical mappings of multiply connected regions, analytic continuation.
Prerequisites
MAT 657 or MAT 659 or equivalent.
MAT 711 - Survey of Mathematical Problems I
Credits 3Selected topics from logical reasoning, probability, combinatorics, graph theory, codes, number theory, constructibility, game theory, limits, functions, set theory and foundations, and plane geometry. Problem solving and techniques of proof emphasized throughout. Connections made between the mathematics of this course and secondary education mathematics.
Prerequisites
Graduate standing and consent of instructor.
MAT 712 - Survey of Mathematical Problems II
Credits 3Continuation of topics listed for MAT 711 with emphasis on problem solving and techniques of proof. Again, connections made between the mathematical content of this course and mathematical content for secondary education.
Prerequisites
MAT 711 or consent of instructor.
MAT 714 - History of Mathematics
Credits 3Historical development of mathematics from primitive origins to the present time. Lives of many mathematicians and their contributions to the development of mathematics.
Prerequisites
Graduate standing and consent of instructor.
MAT 716 - Integrative Mathematical Topics
Credits 3Survey of mathematical topics in an integrative manner. The topics may cover theory and applications in long stretches including probability and statistics; combinatorics, number theory and algebra; geometry and topology; ODE and PDE; computation and numerical analysis; Real and complex analysis.
Prerequisites
At least nine credits at 600-level as required in Requirement #1.
MAT 717 - Analytical Solution Methods for Partial Differential Equations, I
Credits 3Covers the basic theory and methods for solving linear partial differential equations. Emphasis on introducing various techniques to obtain analytical solutions of linear partial differential equations. Techniques include: Method of separation of variables; Fourier transform method; Laplace transform method; Green’s function method, etc.
Prerequisites
MAT 487/687, or MAT 458/658, or consent of instructor.
MAT 718 - Analytical Solution Methods for Partial Differential Equations, II
Credits 3Covers the basic theory and methods for solving nonlinear partial differential equations. Emphasise on introducing various techniques to obtain analytical solutions. Techniques include: Generalized method of characteristics, method of shock wave solution, method of travelling wave solution, perturbation method, method of similarity solution, etc.
Prerequisites
MAT 487/687, or MAT 717, or consent of instructor.
MAT 719 - Graph Theory I
Credits 3Advanced graduate level study of the topics: adjacency and incidence matrices, nonseparable graphs, trees, connectivity, edge-connectivity, Eulerian graphs, Hamiltonian graphs, line graphs, strong digraphs, groups and graphs, Cayley color graph, Reconstruction Problem, planar graphs, graph embeddings, crossing number, genus, and maximum genus.
Prerequisites
MAT 670or consent of instructor.
MAT 720 - Graph Theory II
Credits 3Advanced graduate level study of the topics: graph and map colorings, chromatic polynomials, matchings and independence in graphs, factorizations and decomposition, domination, extremal graph theory, and Ramsey theory.
Prerequisites
MAT 719
MAT 723 - Advanced Ordinary Differential Equations I
Credits 3Functional analysis; Frechet calculus; existence and uniqueness theorems for initial and boundary value problems; qualitative properties of solutions, particularly of linear equations.
Prerequisites
MAT 671-672 or MAT 673-674
MAT 724 - Advanced Ordinary Differential Equations II
Credits 3Topics to be selected from the following: Sturm-Liouville theory, stability theory, perturbation theory, numerical methods, the theory of invariant imbedding and functional differential equations.
Prerequisites
MAT 723
MAT 729 - Partial Differential Equations I
Credits 3Linear and nonlinear first order PDEs. Heat, wave and Laplace equations. Classical representation formulas in one and more dimensions. Properties of solutions: maximum principles, energy methods, uniqueness and regularity considerations.
Prerequisites
MAT 687 or MAT 717
MAT 730 - Partial Differential Equations II
Credits 3Develops a functional analytical framework which will give students a deeper understanding of the subject matter. Topics include Sobolev and Holder spaces, embedding inequalities, weak solutions, regularity and maximum principles.
Prerequisites
MAT 708 and MAT 729, or consent of instructor.
MAT 731 - Mathematical Modeling
Credits 3Process and techniques of mathematical modeling with an emphasis on differential equations based models, though other models may also be considered. Applications selected from physical, biological and social sciences. Modeling projects based on student interests. Symbolic computation software.
Prerequisites
MAT 687 or MAT 717 or consent of instructor.
MAT 733 - Topology
Credits 3Selected topics from algebraic and point-set topology with emphasis on algebraic topology.
Prerequisites
MAT 684 or consent of instructor.
MAT 734 - Topology
Credits 3Selected topics from algebraic and point-set topology with emphasis on algebraic topology.
Prerequisites
MAT 684 or consent of instructor.
MAT 736 - Lightning Radiative Transfer I
Credits 3The analysis of lightning events: cloud-to-ground and intra-cloud discharges, ground and space detection of lightning.
Prerequisites
MAT 729or consent of instructor.
MAT 737 - Lightning Radiative Transfer II
Credits 3Diffusion propagation of Lightning, transport phenomena, and applications of advanced Twersky scattering through clouds.
MAT 751 - Topics in Foundations of Mathematics
Credits 3Topics selected by the instructor.
Prerequisites
MAT 701,MAT 702
MAT 753 - hom*ological Algebra
Credits 3Modules, categories and factors, tensors, Hom, Tor, Ext, the dimensions of rings and modules, derived factors, cohom*ology of groups and algebras.
Prerequisites
MAT 703-704 or consent of instructor.
MAT 754 - hom*ological Algebra
Credits 3Modules, categories and factors, tensors, Hom, Tor, Ext, the dimensions of rings and modules, derived factors, cohom*ology of groups and algebras.
Prerequisites
MAT 703-704 or consent of instructor.
MAT 755 - Topics in Algebra
Credits 3Topics selected by the instructor.
Prerequisites
MAT 703, MAT 704or consent of instructor.
MAT 756 - Arithmetic on Elliptic Curves
Credits 3The group structure of elliptic curves over the reals, complex numbers, the rationals, number fields, and finite fields; Bezout’s theorem and its applications; projective geometry; genus; Mordell’s theorem; points of finite order; and heights. Additional topics may include complex multiplication; modular forms; and factoring using elliptic curves.
Prerequisites
MAT 653 and 654, or equivalent.
MAT 757 - Topics in Analysis
Credits 3Topics selected by the instructor.
Prerequisites
MAT 707, MAT 708or consent of instructor.
MAT 760 - Mathematical Scattering Theory and Applications I
Credits 3Scalar, vector, and tensor scattering with diverse techniques applied to earth system and space science. General Reciprocity Relations Corresponding to Different Directions of Incidence, Dyadic Scattering Theory, Two-Space Scattering Formalism of Victor Twersky, and Applications to Earth and Space Related Problems.
Prerequisites
MAT 717 or MAT 729 or consent of instructor.
MAT 761 - Mathematical Scattering Theory and Applications II
Credits 3Advanced statistical mechanics and spatial statistics in relation to Twersky scattering with applications from earth system and space science. Calculation of bulk propagation parameters using both configurational and ensemble average in addition to spatial average. Application of Twersky multiple two-Space Scattering formalism to space and earth related problems.
Prerequisites
MAT 760 or consent of instructor.
MAT 765 - Advanced Numerical Analysis
Credits 3Topics selected by instructor.Three hours lecture, two hours laboratory.Numerical solution of ordinary and partial differential equations; advanced programming techniques; experiments with the computer.
Prerequisites
MAT 666
MAT 766 - Advanced Numerical Analysis
Credits 3Topics selected by instructor. Three hours lecture, two hours laboratory.Numerical solution of ordinary and partial differential equations; advanced programming techniques; experiments with the computer.
Prerequisites
MAT 666
MAT 767 - Topics in Numerical Analysis
Credits 3Topics selected by the instructor.
Prerequisites
MAT 765-766
MAT 771 - Applied Analysis I
Credits 3Functional analysis in Banach spaces and Hilbert spaces, with emphasis on computational applications. Theoretical topics to be selected from: linear functionals and operators, fixed point theorems, iterative methods, elementary spectral theory. Applications to be selected from: finite element methods, finite difference methods, approximation and interpolation, optimization algorithms.
Prerequisites
MAT 658or consent of instructor
MAT 772 - Applied Analysis II
Credits 3Functional analysis in Banach spaces and Hilbert spaces, with emphasis on computational applications. Theoretical topics to be selected from: linear functionals and operators, fixed point theorems, iterative methods, elementary spectral theory. Applications to be selected from: finite element methods, finite difference methods, approximation and interpolation, optimization algorithms.
Prerequisites
MAT 771or consent of instructor.
MAT 775 - Calculus of Variations
Credits 3Variation of functionals, Euler-Lagrange equation, general variations, broken extremals, Weierstrass-Erdmann conditions, canonical forms, Noether’s theorem, Hamilton- Jacobi equations, Legendre’s condition, conjugate points, fields, E-function, sufficient conditions for extrema, Pontryagin’s principle, introduction to linear and non-linear optimal control theory.
Prerequisites
MATH 428 or 658 or consent of instructor.
MAT 776 - Topics in Applied Mathematics
Credits 3Students are presented with very advanced and important topics of applied mathematics that are not given in other graduate courses. The topics would depend on the particular instructor and the particular graduate students.
Prerequisites
MAT 659or MAT 688or consent of instructor.
MAT 781 - Advanced Graduate Workshop in Foundations
Credits 3Students are assigned advanced material to read, lecture on, and present to the class. Two years of 700-level mathematics in Foundations are required. The workshop is very time intensive, with additional weekly meetings required. Students will present polished lectures, based on their workshop presentations, at the Department’s Set Theory Seminar.
Prerequisites
MAT 751
MAT 789 - Topics in Advanced Mathematics
Credits 3Graduate-level course in some field of mathematics, at advanced level, depending upon the current interest of the staff and the students.
Prerequisites
Graduate standing.
MAT 790 - Independent Study
Credits 1 – 3Library work and reports on topics of mathematical interest.
Prerequisites
Graduate standing.
MAT 791 - Thesis
Credits 1 – 6Research, analysis, and writing towards completion of thesis and subsequent defense.
Prerequisites
Graduate standing.
MAT 793 - Teaching Concentration Professional Paper Research
Credits 1 – 3Individual research towards an applied professional paper under the direction of a faculty member.
Prerequisites
Consent of instructor.
MAT 799 - Dissertation
Credits 3-6Research analysis and writing toward completion of dissertation and subsequent defense.
Prerequisites
Successful completion of qualifying examination and approval by department.
STA 663 - Applied Statistics for Engineers
Credits 3Elementary probability, commonly used discrete and continuous probability distributions, estimation and hypothesis testing, categorical data testing, regression, model building, analysis of variance, product and system reliability and engineering applications, and quality control. Crosslisted with STAT 463. Credit at the 600-level requires additional work.
Prerequisites
Graduate standing.
STA 667 - Introduction to Mathematical Statistics I
Credits 3Introduction to probability theory, random variables and their probability distributions, common discrete probability models, common continuous probability models, multivariate probability distributions, functions of random variables, methods of transformations, limiting distributions, and limit theorems. Crosslisted with STAT 467. Credit at the 600-level requires additional work.
Prerequisites
Graduate standing.
STA 668 - Introduction to Mathematical Statistics II
Credits 3Sample and sampling distributions, estimation theory, evaluation of estimation, unbiased estimation, sufficiency, information inequality, methods of estimation, method of moments, maximum likelihood estimation, Bayesian estimation, confidence intervals, hypotheses testing, uniformly most powerful tests, likelihood ratio tests and related procedures, linear models, and non-parametric models.
Prerequisites
STA 667or consent of instructor.
STA 669 - Environmental Statistics I: Univariate Methods
Credits 3Principles of environmental sampling, testing for outliers, tests for normality, transformations for normality, sample size determinations, analysis of censored data, estimation of background contaminations, tolerance and confidence limits, calibration problem, quality control charts for data quality assessment of environmental data, statistical issues in environmental remediation, and probability of hot spot detection. Usage of statistical software packages. Crosslisted with STAT 469. Credit at the 600-level requires additional work.
Prerequisites
Graduate standing.
STA 690 - Independent Study
Credits 1-3This course, when taught by a member of the graduate faculty, may be applied to a graduate program. For listings and a course description of this 600-level course, please consult the current Undergraduate Catalog under the corresponding 400 number.
Prerequisites
Graduate standing.
STA 691 - Statistics for Scientists I
Credits 3Frequency distributions, descriptive statistics, elementary probability; Bernoulli, binomial, and normal distributions; statistical sampling, estimation, and hypothesis testing. Crosslisted with STAT 491. Credit at the 600-level requires additional work.
Prerequisites
Graduate standing.
STA 692 - Statistics for Scientists II
Credits 3Chi-square tests for goodness-of-fit and independence, simple and multiple linear regression, designing an experiment (analysis of variance), multiple comparisons. Crosslisted with STAT 492. Credit at the 600-level requires additional work.
Prerequisites
Graduate standing.
STA 693 - Applied Regression Analysis
Credits 3Line fitting; multiple linear and curvilinear regression models; variable selection techniques and examination of residuals, estimation, testing, and prediction; simple, multiple, and partial correlation. Crosslisted with STAT 493. Credit at the 600-level requires additional work.
Prerequisites
Graduate standing.
STA 695 - Nonparametic Statistics
Credits 3Survey of nonparametric procedures with emphasis on application; binomial, Mann-Whitney, Wilcoxon, Kruskal-Wallis, Friedman, Kolmogorov-Smironov, and chi-square tests; measures of association; regression. Comparisons with parametric techniques. Crosslisted with STAT 495. Credit at the 600-level requires additional work.
Prerequisites
Graduate standing.
STA 713 - Experimental Design
Credits 3Fundamental principles of analysis of variance; one-way, two-way, and higher order designs; nested designs; randomized blocks; split plot designs; Latin squares; multiple comparisons; analysis of covariance.
Prerequisites
MATH 181 and one of the following: STAT 411,
STA 663
STA 693
STA 715 - Multivariate Statistical Methods
Credits 3Multivariate techniques with emphasis on application. Topics include multivariate analysis of variance, discriminant analysis, canonical correlation and independence, principal component analysis, factor analysis, cluster analysis and analysis of repeated measurements.
Prerequisites
MATH 181, MATH 463 and one of the following: STAT 411,
STA 663
STA 691
STA 731 - Probability Theory and Its Applications
Credits 3Topics include: set theory, limits of sets, probability space, random variables, measurability, independence, expectation, probability inequalities, convergence, laws of large numbers, central limit theorem, moment generating functions, characteristic functions, large deviation theory, martingale theory, random walk.
Prerequisites
MAT 657
STA 750 - Time Series Analysis
Credits 3Topics include ARMA and ARIMA processes; autocorrelation and partial autocorrelation functions; spectral density and periodogram; Yule-Walker equations; model fitting, forecasting and diagnostics; state-space models and the Kalman filter; multivariate time series; use of statistical software.
Prerequisites
STA 667
STA 751 - Spatial Statistics
Credits 3Stochastic process, first and second order stationarity, intrinsic hypothesis, models of spatial dependence, different forms of Kriging — Ordinary Kriging, Universal Kriging, Probability Kriging, bicubic splines, conditional simulation.
Prerequisites
STA 667
STA 753 - Bayesian Data Analysis
Credits 3This course will present methods for statistical modeling and data analysis from a Bayesian perspective. Topics include: Bayes’ Theorem, prior and posterior distributions, computational algorithms for posterior simulation, statistical software and programming, as well as model formulation and diagnostics for linear, generalized linear, and hierarchical models.
Prerequisites
STA 667
STA 755 - Stochastic Modeling I
Credits 3Probability theory, Markov chains in discrete and continuous time, the Poisson process, renewal theory, queueing theory, reliability theory, martingales, stationary processes, statistical inference for stochastic processes, and simulation techniques.
Prerequisites
STA 667
STA 756 - Stochastic Modeling II
Credits 3Probability theory, Markov chains in discrete and continuous time, the Poisson process, renewal theory, queueing theory, reliability theory, martingales, stationary processes, statistical inference for stochastic process, and simulation techniques.
Prerequisites
STA 755
STA 761 - Regression Analysis I
Credits 3Fitting a straight line, matrix theory, examining residuals, selecting the “best” fit, multiple regression, non-linear regressions, multivariate normal, estimation, classification, principal components, canonical correlation, distribution of characteristic roots.
Prerequisites
STA 667
MAT 663
STA 762 - Regression Analysis II
Credits 3Fitting a straight line, matrix theory, examining residuals, selecting the “best” fit, multiple regression, non-linear regressions, multivariate normal, estimation, classification, variance-covariance matrix, testing sets of variates, principal components, canonical correlation, distribution of characteristic roots.
Prerequisites
STA 667
MAT 663
STA 763 - Analysis of Variance I
Credits 3Special topics in matrix theory; noncentral chi-square, F, and t; the multivariate normal distribution; Cochran’s theorem; point and interval estimation; one-, two-, three-, higher-way layouts; Latin squares, incomplete blocks and nested designs, analysis of covariance; random effects models; mixed models; randomization models.
Prerequisites
STA 667
MAT 663
STA 764 - Analysis of Variance II
Credits 3Special topics in matrix theory; noncentral chi-square, F, and t; the multivariate normal distribution; Cochran’s theorem; point and interval estimation; one-, two-, three-, higher-way layouts; Latin squares, incomplete blocks and nested designs, analysis of covariance; random effects models; mixed models; randomization models.
Prerequisites
STA 667
MAT 663
STA 765 - Statistical Decision Theory
Credits 3Introduction to decision theory, decision rules, loss functions, risk functions, decision principles, utility theory, prior information and subjective probability, noninformative priors, the posterior distribution, conjugate families, predictive distribution, Bayesian estimators, generalized Bayes estimators, credible regions, hypothesis testing, admissibility of Bayes rules, robustness of Bayes rules, minimax analysis, invariance, Bayesian sequential analysis.
Prerequisites
STA 667
STA 767 - Mathematical Statistics I
Credits 3Basic probability theory, conditional probability, independence, random variables, probability distribution functions, distribution functions, transformations, function of random variables, expectations, moment generating functions, discrete and continuous distributions, exponential family, joint distribution, marginal distribution, modes of convergence, limiting distribution, random sample, sampling distribution, principle of data reduction.
Prerequisites
STA 667
STA 768 - Mathematical Statistics II
Credits 3Random sample, sampling theory, point estimation, sufficiency, likelihood, method of moment, maximum likelihood estimator, Bayes estimator, unbiasedness, optimality, decision theory, hypothesis testing, likelihood ratio tests, Bayes test, most powerful test, set estimation, evaluating interval estimators, sequential estimation, asymptotics, robustness, linear models.
Prerequisites
STA 767
STA 777 - Survival Analysis
Credits 3Statistical methods for modeling and analysis of time to event data. Topics include survival function and hazard function; Kaplan-Meier estimator; Greenwood’s formula; log-rank and weighted log-rank tests; regression modeling of survival data including proportional hazards model and accelerated failure time model; competing risks.
Prerequisites
STA 768
STA 789 - Topics in Advanced Statistics
Credits 3Graduate-level course in some field of statistics, depending upon the current interest of the faculty and the students.
Prerequisites
Graduate standing.
STA 790 - Independent Study
Credits 1 – 3Library research and reports on topics of statistical interest.
Prerequisites
Graduate standing.
STA 791 - Thesis
Credits 3 – 6Research, analysis, and writing towards completion of thesis and subsequent defense.
Prerequisites
Graduate standing.
STA 793 - Techniques of Statistical Consulting
Credits 1 – 3Seminar series and practicum covering technical and nontechnical aspects of statistical consulting, including skills for effective communication with clients, report writing, issues in sampling and design of experiments, and other statistical tools commonly used in a consulting setting.
Prerequisites
Graduate standing.
STA 799 - Dissertation
Credits 3-6Research analysis and writing toward completion of dissertation and subsequent defense. A minimum of 24 dissertation credits is required for the degree program.
Prerequisites
Successful completion of qualifying examination and approval by department.
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