Mathematics, Pure & Applied Mathematics Concentration (M.S.) - Graduate - 2011 University Catalog

You are viewing the 2011 University Catalog. Please see the newest version of the University Catalog for the most current version of this program's requirements.

The Department of Mathematical Sciences offers an MS in Mathematics with four different concentrations and an MS in Statistics. The Statistics degree will be discussed under Statistics. In addition, the department contributes to the Ed.D. in Pedagogy by offering the specialization in Mathematics Education. The Mathematics Education specialization is described under Pedagogy (Ed.D.).

The Master of Science degree in Mathematics is offered with concentrations in computer science, mathematics education, pure and applied mathematics, or statistics. Concentrations consist primarily of taking four to six courses in the area of the concentration. The master's degree in mathematics with a computer science concentration differs from the MS degrees in Computer Science, as does the master's degree with a statistics concentration differ from the MS in Statistics. The MS in Computer Science is discussed under Computer Science and the MS in Statistics is discussed under Statistics. The Mathematics degrees are discussed below. The MS degrees in Mathematics with concentrations in computer science, pure and applied mathematics, and statistics provide students with the advanced material needed for positions of leadership in business, industry and government as well as for teaching at the high school and community college level. The concentration in mathematics education will upgrade the skills of teachers and offers a special combination of courses in mathematics, mathematics education and the use of technology in mathematics education. This degree does not lead to certification. All the concentrations prepare students to pursue doctoral degrees.

At present, 19 full-time faculty members are teaching graduate courses in pure and applied mathematics, mathematics education or statistics. Our curriculum in mathematics has extensively integrated modern methods of computing. The special interests of the faculty include algebra, analysis, applied statistics, chaos theory, combinatorics, dynamical systems, game theory, graph theory, logic, mathematical modeling, mathematics/computer science education, methods and techniques of teaching mathematics, modeling in the biological, chemical and physical sciences, operations research, problem solving, representation theory, statistical computing and graphics, voting theory, and the use of technology in education. Our faculty in mathematics education are known throughout the United States.

Computer facilities comprise access to a VAX cluster, several stand-alone VAX microcomputers and a Sun Local Area Network. The Sun Local Area Network of workstations and servers consists of an Enterprise 450, SparcServer 1000, Ultra 30, Ultra 10's, Sparc 20's, and Sparc 5's. The VAX cluster which consists of DEC VAX 7620, 6610, 7620, 6310, 3500, 4000, 3500 microVAX II with four LSI/11 micros connected to it, and two ALPHA 2100. These VAX's may be accessed from the VAX laboratory that contains a variety of DEC terminals or via the MSUnet from numerous remote sites. Outside dial-ups to MSUnet are available. Software packages available through the VAX system include: ADA, Basic, C, C++, COBOL, FORTRAN, GPSS, Ingress, Lisp, Macro, MAPLE, Minitab, Pascal, Pl/1, Prolog, SAS, SAS graphics, SPSSX, and SPSS graphics. The network of SUN Microsystems' file servers, computer servers and individual workstations operates under UNIX. Software packages and programming languages available on the SUN network include Maple, MATLAB, Iris Explorer, Rational Rose, SAS, S plus, Ingres, mSQL, JavaStudio and Java Workshop. Programming languages available include: C, C++, Java, gcc, Ada FORTRAN, Pascal, Lisp, Prolog, Perl, LaTEX, and smalltalk. The Sun network is also connected to MSUnet. Laboratories of Power Macintoshes and Dell Pentium PC's are available throughout the campus for student use and make a wide variety of software such as JMP, MacSpin, Data Desk, Solo, Statisix and Office available for student use.


MATHEMATICS w/CONC:Pure&ApplMath

Complete 33 semester hours including the following 4 requirement(s):

  1. PURE MATHEMATICS

    Complete 4 courses for 12 semester hours: .

    MATH 521 Real Variables I 3
    MATH 525 Complex Variables I 3
    MATH 531 Abstract Algebra I 3
    MATH 535 Linear Algebra I 3
  2. APPLIED MATHEMATICS

    Complete 4 courses for 12 semester hours: .

    MATH 530 Mathematical Computing 3
    MATH 560 Numerical Analysis 3
    MATH 584 Operations Research 3
    MATH 591 Applied Industrial Mathematics 3
  3. ELECTIVES

    Complete 9 semester hours (or 6 semester hours if electing Thesis Option) from the following:

    1. If equivalent courses haven't been previously taken, take the following. Only 6 hours can be used for credit.

      MATH 515 Intermediate Analysis I 3
      MATH 516 Intermediate Analysis II 3
      MATH 518 Foundations of Abstract Algebra 3
    2. Complete 3 semester hours-9 semester hours from the following:

      CMPT 574 Pixel and Image Processing 3
      CMPT 575 Introduction to Computer Graphics 3
      CMPT 576 Object-Oriented Software Development 3
      CMPT 578 Introduction to Artificial Intelligence 3
      CMPT 580 Machine Organization and Architecture 3
      CMPT 581 Systems Software Design 3
      CMPT 582 Theory of Automata and Formal Languages 3
      CMPT 583 Computer Algorithms 3
      CMPT 584 Operating System Design 3
      CMPT 585 Topics in Computer Science 3
      CMPT 586 File Structures and Databases 3
      CMPT 587 Microcomputers and Computer Interfaces 3
      CMPT 588 Fundamentals of Programming Languages 3
      CMPT 589 Computer Simulation of Discrete Systems 3
      CMPT 590 Computer Simulation of Continuous Systems 3
      CMPT 591 Compiler Theory and Construction 3
      CMPT 592 Data Base Design and Implementation 3
      CMPT 593 Structured System Design and Analysis 3
      CMPT 594 Software Engineering and Reliability 3
      CMPT 596 Principles of Data Communication 3
      CMPT 678 Neurocomputing 3
      CMPT 680 Parallel Architectures and Algorithms 3
      CMPT 683 Advanced Computer Algorithms 3
      CMPT 690 Independent Study in Computer Science 3
      MATH 520 Set Theory 3
      MATH 521 Real Variables I 3
      MATH 522 Real Variables II 3
      MATH 525 Complex Variables I 3
      MATH 526 Complex Variables II 3
      MATH 530 Mathematical Computing 3
      MATH 531 Abstract Algebra I 3
      MATH 532 Abstract Algebra II 3
      MATH 535 Linear Algebra I 3
      MATH 536 Linear Algebra II 3
      MATH 537 Mathematical Logic 3
      MATH 540 Probability 3
      MATH 551 Topology 3
      MATH 554 Projective Geometry 3
      MATH 555 Differential Geometry 3
      MATH 560 Numerical Analysis 3
      MATH 564 Ordinary Differential Equation 3
      MATH 566 Partial Differential Equations 3
      MATH 568 Applied Mathematics: Continuous 3
      MATH 569 Applied Mathematics: Discrete 3
      MATH 580 Combinatorial Mathematics 3
      MATH 581 Graph Theory 3
      MATH 584 Operations Research 3
      MATH 590 Advanced Topics 3
      MATH 591 Applied Industrial Mathematics 3
      MATH 595 Seminar 1-4
      MATH 690 Independent Study in Mathematics 3
      MATH 698 Master's Thesis 3
      STAT 541 Applied Statistics 3
      STAT 542 Statistical Theory I 3
      STAT 543 Statistical Theory II 3
      STAT 544 Statistical Computing 3
      STAT 545 Practicum in Statistics I 3
      STAT 546 Non-Parametric Statistics 3
      STAT 547 Design and Analysis of Experiments 3
      STAT 548 Applied Regression Analysis 3
      STAT 549 Sampling Techniques 3
      STAT 595 Topics in Statistics 3
      STAT 597 Research Methods in Statistical Science 3
      STAT 640 Biostatistics I 3
      STAT 641 Biostatistics II 3
      STAT 642 Introduction to Stochastic Processes 3
      STAT 645 Advanced Topics in Statistics 3
      STAT 646 Multivariate Analysis 3
      STAT 647 Practicum in Statistics II 3
      STAT 648 Advanced Statistical Methods 3
      STAT 649 Independent Study in Statistics 3
  4. CULMINATING EXPERIENCE

    Complete 1 of the following options:

    1. Successfully complete the Comprehensive Examination.

    2. THESIS OPTION

      1. Complete for 3 semester hours.

        MATH 698 Master's Thesis 3
      2. Submit the completed Thesis original and one copy to the Graduate Office. See Thesis Guidelines for details.


Course Descriptions:

CMPT574: Pixel and Image Processing

This course provides an introductory and comprehensive treatment of pixel and image processing with applications to fine arts, face recognition, etc. Topics include sampling and quantization, convolution, equalization, filtering, image segmentation, image operations, morphological image processing. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580 and permission of graduate coordinator.

CMPT575: Introduction to Computer Graphics

An introduction to computer graphics, including the algorithms to generate two-dimensional and three-dimensional graphical pictures. An overview of ray tracing, shading and color theory. Interactive graphics. Graphics devices. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580 and permission of graduate coordinator.

CMPT576: Object-Oriented Software Development

Introduction to the major features of the object-oriented paradigm and their realization in an object-oriented programming language. Introduction to major methods and tools used in object-oriented analysis and design. Implementation and testing issues. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 581, CMPT 583 and permission of graduate coordinator.

CMPT578: Introduction to Artificial Intelligence

An introduction to artificial intelligence including representations of knowledge, problem solving, games, heuristics and backtracking, expert systems, theorem proving, the language LISP and PROLOG. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 583 and permission of graduate coordinator.

CMPT580: Machine Organization and Architecture

Basic computer organization and design, digital functions, data representation, microprogramming, CPU organization, the assembler language, and addressing techniques. Required of majors. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate coordinator.

CMPT581: Systems Software Design

Assemblers, macroprocessors, linkers and loaders, introduction to compilers and run facilities. Required of majors. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580, and permission of graduate coordinator.

CMPT582: Theory of Automata and Formal Languages

Languages and grammars, finite automata and regular grammars, context free grammars, push-down automata, Turing machines, computability, deterministic languages, linear bounded automata and stack automata. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate coordinator.

CMPT583: Computer Algorithms

Algorithms: definition, design and analysis; sorting and searching techniques and introductory dynamic programming studied as algorithms with complexity theory and optimization techniques applied. Required of majors. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate coordinator.

CMPT584: Operating System Design

Design and implementation of operating systems, multiprogramming, multiprocessor, device management, scheduling, virtual memory, case studies. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 581, and permission of graduate coordinator.

CMPT585: Topics in Computer Science

Recent developments in the field. Topics such as Monte Carlo methods, graphics, expert systems, security, networks and special areas of applications. May be repeated twice for a maximum of 9.0 credits as long as the topic is different. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580 and permission of graduate coordinator.

CMPT586: File Structures and Databases

Secondary storage devises. Data transfer. Primary and secondary access methods. Sequential and random access methods. File design. File organizations and corresponding processing. File maintenance. Sorting large files. Databases concepts. Required of majors. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate coordinator.

CMPT587: Microcomputers and Computer Interfaces

Introduction to geneology, manufacture and hardware design of microprocessors, microcomputer architecture, instruction sets and programming, microcomputer peripherals and interfaces. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580, and permission of graduate coordinator.

CMPT588: Fundamentals of Programming Languages

A comparative approach to modern programming languages with emphasis on non-imperative languages, and an introduction to parallel languages. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate coordinator.

CMPT589: Computer Simulation of Discrete Systems

Introduction to simulation and discrete simulation models. Queuing theory and stochastic processes. Simulation methodology including generation of random numbers and variates, design of simulation experiments, analysis of data generated by simulation experiments and validation of models. Survey of current simulation languages and selected applications. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580, permission of graduate coordinator.

CMPT590: Computer Simulation of Continuous Systems

Computer simulation of continuous systems with emphasis on conservation principles and governing equations, numerical treatment of systems of algebraic and differential equations, the use of software packages and simulation languages, verification and validation techniques, and interpretation and presentation of results. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580, permission of graduate coordinator.

CMPT591: Compiler Theory and Construction

Introduction to the formal description of programming languages, the theory of parsing, and the concepts and techniques used in the construction of compilers. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 581, permission of graduate coordinator.

CMPT592: Data Base Design and Implementation

To develop in-depth understanding of data base concepts and issues. The major emphasis of the course is on the conceptual (logical) organization, retrieval, and manipulation of data. Required of majors. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 586, permission of graduate coordinator.

CMPT593: Structured System Design and Analysis

A study of the design of large scale computer systems relative to the constraints imposed by hardware, software and particular types of applications. Recent work in automated system design will be discussed. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 586, and permission of graduate coordinator.

CMPT594: Software Engineering and Reliability

Principles and methods for the analysis, design, implementation, testing, and verification of software systems. Topics include requirements analysis, domain analysis, implementation, testing, verification, and software management. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate coordinator.

CMPT596: Principles of Data Communication

Physical and logical aspects of data communications: analog-digital, broadband-baseband, TDM-FDM, protocols, modulation techniques, hardware for communication. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580, and permission of graduate coordinator.

CMPT678: Neurocomputing

Basic neural network concepts, definitions, and building blocks; learning laws; simple implementations; associative networks; mapping networks; survey of applications. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 583, and permission of graduate coordinator.

CMPT680: Parallel Architectures and Algorithms

This course provides a study of the state-of-art of parallel processing algorithms and architectures. Parallel processing uses multiple processors working together in a synchronized fashion to solve large problems fast. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 580 and CMPT 583, and permission of graduate coordinator.

CMPT683: Advanced Computer Algorithms

Dynamic programming, game trees and backtracking techniques, branch and bound, polynomial evaluation and fast Fourier transform algorithms; complexity and analysis, and optimization techniques will be applied. NP-hard problems and NP-completeness. (3 hours lecture.) 3 sh.

Prerequisites: CMPT 583, and permission of graduate coordinator.

CMPT690: Independent Study in Computer Science

Independent study under the direction of a faculty member, offering the opportunity to pursue topics in computer science which may be outside the scope of regular curricular offerings or may be an extension of an existing course or courses. Approval must be obtained from the graduate coordinator or and faculty advisor. May be repeated once for a maximum of 6.0 credits. () 3 sh.

Prerequisites: Permission of graduate coordinator.

MATH515: Intermediate Analysis I

Properties of the real number system, limits, continuous functions, intermediate value theorem, derivative, mean value theorem, Riemann integral. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH516: Intermediate Analysis II

This course is a continuation of MATH 515. Topics include functions of several variables, partial derivatives, Green's theorem, Stoke's theorem, divergence theorem, implicit function theorem, inverse function theorem, infinite series, uniform convergence. (3 hours lecture.) 3 sh.

Prerequisites: MATH 515 or MATH 425 or equivalent, permission of graduate program coordinator.

MATH518: Foundations of Abstract Algebra

Fundamental concepts of algebra including groups, rings, integral domains and fields, with important examples. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH520: Set Theory

Historical development, paradoxes, ordered sets, Schroder-Bernstein theorem, axiom of choice, transfinite induction, cardinal and ordinal numbers. (3 hours lecture.) 3 sh.

Prerequisites: MATH 222 and permission of graduate program coordinator.

MATH521: Real Variables I

Real number system, Lebesgue measure and integration, differentiation, Fourier series, LP, metric, normed vector, Banach and Hilbert spaces. (3 hours lecture.) 3 sh.

Prerequisites: MATH 426 and permission of graduate program coordinator.

MATH522: Real Variables II

Real number system, Lebesgue measure and integration, differentiation, Fourier series, LP, metric, normed vector, Banach and Hilbert spaces. (3 hours lecture.) 3 sh.

Prerequisites: MATH 521, permission of graduate program coordinator.

MATH525: Complex Variables I

Integration and differentiation in the complex domain, Cauchy's theorem, Cauchy's integral formula, Laurent expansion, residues, elements of conformal mapping, series and product representations. (3 hours lecture.) 3 sh.

Prerequisites: MATH 426 and permission of graduate program coordinator.

MATH526: Complex Variables II

Integration and differentiation in the complex domain, Cauchy's theorem, Cauchy's integral formula, Laurent expansion, residues, elements of conformal mapping, series and product representations. (3 hours lecture.) 3 sh.

Prerequisites: MATH 525, permission of graduate program coordinator.

MATH530: Mathematical Computing

Introduction to mathematical computing techniques using a computer algebra system and algorithmic approach to solving mathematical problems. Mathematical applications taken from various areas of mathematics, the sciences, engineering, and business. (3 hours lecture.) 3 sh.

Prerequisites: Permission of the graduate program coordinator or consent of the instructor.

MATH531: Abstract Algebra I

Basic algebraic structures including groups, rings, fields, modules and lattices. (3 hours lecture.) 3 sh.

Prerequisites: MATH 431 and permission of graduate program coordinator.

MATH532: Abstract Algebra II

Basic algebraic structures including groups, rings, fields, modules and lattices. (3 hours lecture.) 3 sh.

Prerequisites: MATH 531, permission of graduate program coordinator.

MATH535: Linear Algebra I

Vector spaces and linear transformations, including inner product, matrix representations, binary and quadratic forms, eigenvectors, canonical forms, and functions of matrices. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335 and permission of graduate program coordinator.

MATH536: Linear Algebra II

Vector spaces and linear transformations, including inner product, matrix representations, binary and quadratic forms, eigenvectors, canonical forms, and functions of matrices. (3 hours lecture.) 3 sh.

Prerequisites: MATH 535, permission of graduate program coordinator.

MATH537: Mathematical Logic

Propositional and predicate calculus, model theory, Godel's completeness theorems and decidability. (3 hours lecture.) 3 sh.

Prerequisites: MATH 425 and permission of graduate program coordinator.

MATH540: Probability

Sample spaces and events, combinatorial analysis, conditional probability and stochastic independence, random variables and probability distributions, expected value and variance, probability generating functions, continuous random variables. (3 hours lecture.) 3 sh.

Prerequisites: MATH 340 and permission of graduate program coordinator.

MATH551: Topology

Basic point-set topology, topological spaces, homeomorphisms, compactness, connectedness, separation properties, uniformities, metrizability, introductory algebraic topology, homology groups and homotopy. (3 hours lecture.) 3 sh.

Prerequisites: MATH 425, and permission of graduate program coordinator.

MATH554: Projective Geometry

Projective planes and spaces are studied by synthetic and analytic approaches. Topics covered include the theorems of Desargues and Pappus, harmonic sequences, projectivities, coordinatization, finite planes, and conics. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335 and permission of graduate program coordinator.

MATH555: Differential Geometry

Application of vectors to the study of classical three-dimensional geometry. Topics include: plane and space curves, first and second fundamental forms, lines of curvature, asymptotic lines, geodesics. (3 hours lecture.) 3 sh.

Prerequisites: MATH 222 and permission of graduate program coordinator.

MATH560: Numerical Analysis

Error analysis, interpolation and approximation theory, numerical solution of linear and nonlinear equations, numerical differentiation and integration, numerical solution of differential equations. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335, and permission of graduate program coordinator.

MATH564: Ordinary Differential Equation

Linear and nonlinear equations, Green's functions, power series solutions, autonomous systems, existence and uniqueness, singularities, Sturm-Liouville systems. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335, and 420, and permission of graduate program coordinator.

MATH566: Partial Differential Equations

First order equations, separation of variables, series solutions, hyperbolic, parabolic and elliptic equations, characteristics, transform methods. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335, and 420, and permission of graduate program coordinator.

MATH568: Applied Mathematics: Continuous

Formulation, manipulation and evaluation of mathematical models of continuous systems. Topics selected from: conservation principles and the classical equations of mathematical physics, applications of the qualitative and quantitative theory of ordinary and partial differential equations, optimization, calculus of variations, stability theory, stochastic models. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335, and 340, and 420, and 425, and permission of graduate program coordinator.

MATH569: Applied Mathematics: Discrete

Introduction to the basic ideas of discrete mathematics and its applications. Counting principles, permutations, combinations, algorithms, complexity, graphs, trees, searching and sorting, recurrence relations, generating functions, inclusion-exclusion, the pigeonhole principle, chromatic number, eulerian chains and paths, hamiltonian chains and paths, flows in networks, finite Markov chains. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335, and 340, and 425, and permission of graduate program coordinator.

MATH580: Combinatorial Mathematics

Arrangements and selections, binomial coefficients, Stirling numbers, generating functions, recurrence relations, inclusion-exclusion, Polya enumeration formula, combinatorial graph theory, combinatorial geometries. (3 hours lecture.) 3 sh.

Prerequisites: MATH 222 and graduate program coordinator's permission.

MATH581: Graph Theory

Graphs, digraphs, and trees. Connectivity, separability, planarity, and colorability. Cliques, independent sets, matchings, flows and tours. Graphs as mathematical models; graph algorithms. (3 hours lecture.) 3 sh.

Prerequisites: MATH 222, and 335, and graduate program coordinator's permission.

MATH584: Operations Research

An in-depth study of one or at most two topics in operations research, selected from linear programming and game theory, linear and nonlinear programming, queuing theory, inventory theory, simulation models. (3 hours lecture.) 3 sh.

Prerequisites: MATH 425 and STAT 440 and permission of graduate program coordinator.

MATH590: Advanced Topics

An in-depth study of a topic or topics selected from areas such as algebra, analysis, geometry, probability and statistics, and applied mathematics, with special emphasis upon recent developments in the field. May be repeated once for a maximum of 6.0 credits as long as the topic is different. (3 hours lecture.) 3 sh.

Prerequisites: Graduate program coordinator's permission.

MATH591: Applied Industrial Mathematics

Formulation, modeling, and solution of mathematical problems from engineering, science and business. Topics include statistical distributions, Monte Carlo method, function fitting, transforms optimization, regression analysis, cost-benefit analysis, ordinary differential equations, partial differential equations, numerical methods, divided differences, splines, Galerkin's method, and finite elements. (3 hours lecture.) 3 sh.

Prerequisites: MATH 335, MATH 425, MATH 530, STAT 440 or permission of graduate program coordinator.

MATH595: Seminar

Guided study of selected topics in major field of interest. May be repeated once for a maximum of 6.0 credits as long as the topic is different. (1-4 hours seminar.) 1 - 4 sh.

Prerequisites: Graduate program coordinator's permission.

MATH690: Independent Study in Mathematics

Independent study under the direction of a faculty member, offering the opportunity to pursue topics in mathematics which may be outside the scope of regular curricular offerings or may be an extension of an existing course or courses. Approval must be obtained from the graduate coordinator and faculty advisor. May be repeated once for a maximum of 6.0 credits during the graduate program. () 3 sh.

Prerequisites: Permission of graduate program coordinator. Departmental approval.

MATH698: Master's Thesis

Independent research project done under faculty advisement. Students must follow the MSU Thesis Guidelines, which may be obtained from the Graduate School. Students should take MATH 699 if they don't complete MATH 698 within the semester. () 3 sh.

Prerequisites: Permission of graduate program coordinator.

STAT541: Applied Statistics

Review of estimation and hypothesis testing for one sample and two sample problems; introduction to non-parametric statistics and linear regression; fundamental principles of design, completely randomized design, randomized block design, latin square, and 2 factor design. (3 hours lecture.) 3 sh.

Prerequisites: STAT 330 or STAT 443 and permission of graduate program coordinator.

STAT542: Statistical Theory I

Discrete and continuous probability distributions, multivariate distributions, sampling theory, transformations, Chi-squared, 'F' and 't' distributions. Point estimation, properties of estimators, sufficiency, exponential families, interval estimation, hypothesis testing, power, Neyman-Pearson Lemma, likelihood ratio tests. The impact of the above theory on areas such as regression analysis, analysis of variance and analysis of discrete data. (3 hours lecture.) 3 sh.

Prerequisites: STAT 541 and permission of graduate program coordinator.

STAT543: Statistical Theory II

Discrete and continuous probability distributions, multivariate distributions, sampling theory, transformations, Chi-squared, 'F' and 't' distributions. Point estimation, properties of estimators, sufficiency, exponential families, interval estimation, hypothesis testing, power, Neyman-Pearson Lemma, likelihood ratio tests. The impact of the above theory on areas such as regression analysis, analysis of variance and analysis of discrete data. (3 hours lecture.) 3 sh.

Prerequisites: STAT 542 and permission of graduate program coordinator.

STAT544: Statistical Computing

Computer systems for data analysis and data graphics, and intermediate level statistical methodology are investigated. Several statistical computing packages are utilized and evaluated. (3 hours lecture.) 3 sh.

Prerequisites: STAT 541 or STAT 548, and CMPT 183, and permission of graduate program coordinator.

STAT545: Practicum in Statistics I

An applied experience in which students work with practitioners in industry, government or research organizations utilizing statistical techniques in a research setting. Students will work with statisticians on projects involving experimental design and data collection as well as the analysis and interpretation of the data. May be repeated once. () 3 sh.

Prerequisites: STAT 541, STAT 544, and STAT 547 or STAT 548, and permission of graduate program coordinator.

STAT546: Non-Parametric Statistics

Selected distribution-free tests and estimation techniques including sign, Kolmogorov-Smirnov, Wilcoxon signed rank, Mann-Whitney, Chi-square, rank correlation, Kendall's Tau, Kruskal-Wallace, Friedman, McNemar, and others. (3 hours lecture.) 3 sh.

Prerequisites: STAT 330 and permission of graduate program coordinator.

STAT547: Design and Analysis of Experiments

Fundamental principles of design; fixed, random and mixed models; factorial designs; designs with restricted randomization; split-plot design; confounding; fractional replication; experimental and sampling errors. (3 hours lecture.) 3 sh.

Prerequisites: STAT 541 or STAT 548, and permission of graduate program coordinator.

STAT548: Applied Regression Analysis

Fitting equations to data; matrices, linear regression; correlation; analysis of residuals; multiple regression; polynomial regression; partial correlation; stepwise regression; regression and model building; regression applied to analysis of variance problems; introduction to nonlinear regression. (3 hours lecture.) 3 sh.

Prerequisites: STAT 330 or STAT 443, and permission of graduate program coordinator.

STAT549: Sampling Techniques

Sampling and survey methodology; basic sampling theory; simple, stratified, random, cluster, systematic and area sampling. Sampling errors and estimation procedures. (3 hours lecture.) 3 sh.

Prerequisites: STAT 330 or STAT 443, and permission of graduate program coordinator.

STAT595: Topics in Statistics

Topics such as exploratory data analysis, statistical graphics, statistical quality control and statistical quality assurance, Bayesian methods and Markov chain monte carlo studies. May be repeated twice for a total of 9.0 credits. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate program coordinator.

STAT597: Research Methods in Statistical Science

Preparation for research in statistical science. Application of mathematics and computing science to the development, modeling, validation and evaluation of statistical research methods. Identification of statistical issues in real world problems and novel applications of statistical methods to these problems. Development of research proposals in statistical science. (3 hours lecture.) 3 sh.

Prerequisites: STST 552 or equivalent and departmental approval.

STAT640: Biostatistics I

Fundamental statistical concepts and methods used by statistical scientists in the health, biological, medical and pharmaceutical industries. Categorical data analysis, logistic regression, generalized linear models, nonparametric regression techniques. (3 hours lecture.) 3 sh.

Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.

STAT641: Biostatistics II

Fundamental statistical concepts and methods used by statistical scientists in the health, biological, medical and pharmaceutical industries. Survival analysis and designs for clinical trials. (3 hours lecture.) 3 sh.

Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.

STAT642: Introduction to Stochastic Processes

Generating functions, convolutions, recurrent events, random walk models, gambler's ruin problems, Markov chains and processes, time dependent stochastic processes, queuing theory and epidemic models. (3 hours lecture.) 3 sh.

Prerequisites: MATH 540 and permission of graduate program coordinator.

STAT645: Advanced Topics in Statistics

Recent developments in statistical science. Topics such as data mining, statistical genomics, computationally intensive data-analytic methods, statistical consulting, dynamic statistical graphics and visualization, applied time series analysis. May be repeated with no limit as long as the topic is different. (3 hours lecture.) 3 sh.

Prerequisites: Permission of graduate program coordinator.

STAT646: Multivariate Analysis

Analysis of multiple response variables simultaneously; covariance and the multivariate normal distribution; manova, discriminant functions; principle components and canonical correlations. (3 hours lecture.) 3 sh.

Prerequisites: STAT 541, STAT 548 and permission of graduate program coordinator.

STAT647: Practicum in Statistics II

An applied experience in which students work with practitioners in industry, government or research organizations utilizing advanced statistical techniques in a research setting. Students will be expected to exhibit the ability to work independently on projects involving advanced techniques in experimental design, analysis and interpretation of data. May be repeated once. () 3 sh.

Prerequisites: STAT 542, STAT 545, at least one 600-level course, and permission of graduate program coordinator.

STAT648: Advanced Statistical Methods

Advanced statistical concepts and methods used by statistical scientists in the analysis of designed experiments and observational studies. Response surface methodology, analysis of covariance, the general linear model, the cell means model and the analysis of variance of unbalanced or messy data. (3 hours lecture.) 3 sh.

Prerequisites: STAT 544, STAT 547, STAT 548, and permission of graduate program coordinator.

STAT649: Independent Study in Statistics

Independent study under the direction of a faculty member, offering the opportunity to pursue topics in statistics which may be outside the scope of regular curricular offerings or may be an extension of an existing course or courses. Approval must be obtained from the graduate coordinator and faculty advisor. May be repeated once for a maximum of 6.0 credits during the graduate program. () 3 sh.

Prerequisites: Permission of graduate program coordinator and departmental approval.