Mathematics, Mathematics Education Concentration (M.S.) - Graduate - 2012 University Catalog

You are viewing the 2012 University Catalog. Please see the newest version of the University Catalog for the most current version of this program's requirements.

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:Math Education

Complete 33 semester hours including the following 3 requirement(s):

  1. MATHEMATICS EDUCATION

    Complete the following 4 requirement(s):

    1. Complete 1 course for 3 semester hours from the following list.

      MATH 570 Administration and Supervision of Mathematics (3 hours lecture) 3
      MATH 571 Curriculum Construction in Mathematics (3 hours lecture) 3
      MATH 572 Contemporary Teaching of Mathematics (3 hours lecture) 3
      MATH 573 Mathematics Materials for Teachers of Mathematics (3 hours lecture) 3
    2. Complete 1 course for 3 semester hours from the following list.

      MATH 574 Problem Analysis in Secondary Mathematics (3 hours lecture) 3
      MATH 575 Selected Topics in Mathematics Education (3 hours lecture) 3
      MATH 579 Approaching School Mathematics Through Applications (3 hours lecture) 3
    3. Complete for 3 semester hours.

      MATH 513 Computer Science Concepts for High School Teachers (3 hours lecture) 3
    4. Complete an additional 1 course from the following list.

      MATH 570 Administration and Supervision of Mathematics (3 hours lecture) 3
      MATH 571 Curriculum Construction in Mathematics (3 hours lecture) 3
      MATH 572 Contemporary Teaching of Mathematics (3 hours lecture) 3
      MATH 573 Mathematics Materials for Teachers of Mathematics (3 hours lecture) 3
      MATH 574 Problem Analysis in Secondary Mathematics (3 hours lecture) 3
      MATH 575 Selected Topics in Mathematics Education (3 hours lecture) 3
      MATH 579 Approaching School Mathematics Through Applications (3 hours lecture) 3
  2. ELECTIVES

    Complete the following 2 requirements:

    1. MAJOR ELECTIVES

      Complete 15 semester hours from at least 3 of the following:

      1. ALGEBRA

        .

        MATH 518 Foundations of Abstract Algebra (3 hours lecture) 3
        MATH 531 Abstract Algebra I (3 hours lecture) 3
        MATH 532 Abstract Algebra II (3 hours lecture) 3
        MATH 535 Linear Algebra I (3 hours lecture) 3
        MATH 536 Linear Algebra II (3 hours lecture) 3
      2. ANALYSIS

        .

        MATH 515 Intermediate Analysis I (3 hours lecture) 3
        MATH 516 Intermediate Analysis II (3 hours lecture) 3
        MATH 521 Real Variables I (3 hours lecture) 3
        MATH 522 Real Variables II (3 hours lecture) 3
        MATH 525 Complex Variables I (3 hours lecture) 3
        MATH 526 Complex Variables II (3 hours lecture) 3
      3. APPLIED MATHEMATICS - Continuous

        MATH 560 Numerical Analysis (3 hours lecture) 3
        MATH 564 Ordinary Differential Equation (3 hours lecture) 3
        MATH 566 Partial Differential Equations (3 hours lecture) 3
        MATH 568 Applied Mathematics: Continuous (3 hours lecture) 3
      4. APPLIED MATHEMATICS - Discrete

        .

        MATH 569 Applied Mathematics: Discrete (3 hours lecture) 3
        MATH 580 Combinatorial Mathematics (3 hours lecture) 3
        MATH 581 Graph Theory (3 hours lecture) 3
        MATH 584 Operations Research (3 hours lecture) 3
      5. STATISTICS

        MATH 540 Probability (3 hours lecture) 3
        STAT 541 Applied Statistics (3 hours lecture) 3
        STAT 542 Statistical Theory I (3 hours lecture) 3
        STAT 543 Statistical Theory II (3 hours lecture) 3
        STAT 544 Statistical Computing (3 hours lecture) 3
        STAT 545 Practicum in Statistics I 3
        STAT 546 Non-Parametric Statistics (3 hours lecture) 3
        STAT 547 Design and Analysis of Experiments (3 hours lecture) 3
        STAT 548 Applied Regression Analysis (3 hours lecture) 3
        STAT 549 Sampling Techniques (3 hours lecture) 3
        STAT 640 Biostatistics I (3 hours lecture) 3
        STAT 641 Biostatistics II (3 hours lecture) 3
        STAT 642 Introduction to Stochastic Processes (3 hours lecture) 3
        STAT 645 Advanced Topics in Statistics (3 hours lecture) 3
        STAT 646 Multivariate Analysis (3 hours lecture) 3
        STAT 647 Practicum in Statistics II 3
        STAT 648 Advanced Statistical Methods (3 hours lecture) 3
        STAT 649 Independent Study in Statistics 3
      6. GEOMETRY

        .

        MATH 551 Topology (3 hours lecture) 3
        MATH 554 Projective Geometry (3 hours lecture) 3
        MATH 555 Differential Geometry (3 hours lecture) 3
      7. COMPUTER SCIENCE

        .

        CMPT 574 Pixel and Image Processing (3 hours lecture) 3
        CMPT 575 Introduction to Computer Graphics (3 hours lecture) 3
        CMPT 576 Object-Oriented Software Development (3 hours lecture) 3
        CMPT 578 Introduction to Artificial Intelligence (3 hours lecture) 3
        CMPT 580 Machine Organization and Architecture (3 hours lecture) 3
        CMPT 581 Systems Software Design (3 hours lecture) 3
        CMPT 582 Theory of Automata and Formal Languages (3 hours lecture) 3
        CMPT 583 Computer Algorithms (3 hours lecture) 3
        CMPT 584 Operating System Design (3 hours lecture) 3
        CMPT 585 Topics in Computer Science (3 hours lecture) 3
        CMPT 586 File Structures and Databases (3 hours lecture) 3
        CMPT 587 Microcomputers and Computer Interfaces (3 hours lecture) 3
        CMPT 588 Fundamentals of Programming Languages (3 hours lecture) 3
        CMPT 589 Computer Simulation of Discrete Systems (3 hours lecture) 3
        CMPT 590 Computer Simulation of Continuous Systems (3 hours lecture) 3
        CMPT 591 Compiler Theory and Construction (3 hours lecture) 3
        CMPT 592 Data Base Design and Implementation (3 hours lecture) 3
        CMPT 593 Structured System Design and Analysis (3 hours lecture) 3
        CMPT 594 Software Engineering and Reliability (3 hours lecture) 3
        CMPT 596 Principles of Data Communication (3 hours lecture) 3
        CMPT 678 Neurocomputing (3 hours lecture) 3
        CMPT 680 Parallel Architectures and Algorithms (3 hours lecture) 3
        CMPT 683 Advanced Computer Algorithms (3 hours lecture) 3
        CMPT 690 Independent Study in Computer Science 3
        CMPT 694 Software Quality Assurance (3 hours lecture) 3
        CMPT 695 Seminars in Computer Science (1-4 hours seminar) 1-4
        CMPT 696 Local Area Networks (3 hours lecture) 3
        CMPT 697 Master's Project in Computer Science (3 hours lecture) 3
    2. ADDITIONAL ELECTIVES

      Complete 2 courses for 6 semester hours from the following list.

      CMPT 574 Pixel and Image Processing (3 hours lecture) 3
      CMPT 575 Introduction to Computer Graphics (3 hours lecture) 3
      CMPT 576 Object-Oriented Software Development (3 hours lecture) 3
      CMPT 578 Introduction to Artificial Intelligence (3 hours lecture) 3
      CMPT 580 Machine Organization and Architecture (3 hours lecture) 3
      CMPT 581 Systems Software Design (3 hours lecture) 3
      CMPT 582 Theory of Automata and Formal Languages (3 hours lecture) 3
      CMPT 583 Computer Algorithms (3 hours lecture) 3
      CMPT 584 Operating System Design (3 hours lecture) 3
      CMPT 585 Topics in Computer Science (3 hours lecture) 3
      CMPT 586 File Structures and Databases (3 hours lecture) 3
      CMPT 587 Microcomputers and Computer Interfaces (3 hours lecture) 3
      CMPT 588 Fundamentals of Programming Languages (3 hours lecture) 3
      CMPT 589 Computer Simulation of Discrete Systems (3 hours lecture) 3
      MATH 520 Set Theory (3 hours lecture) 3
      MATH 521 Real Variables I (3 hours lecture) 3
      MATH 522 Real Variables II (3 hours lecture) 3
      MATH 525 Complex Variables I (3 hours lecture) 3
      MATH 526 Complex Variables II (3 hours lecture) 3
      MATH 530 Mathematical Computing (3 hours lecture) 3
      MATH 531 Abstract Algebra I (3 hours lecture) 3
      MATH 532 Abstract Algebra II (3 hours lecture) 3
      MATH 535 Linear Algebra I (3 hours lecture) 3
      MATH 536 Linear Algebra II (3 hours lecture) 3
      MATH 537 Mathematical Logic (3 hours lecture) 3
      MATH 540 Probability (3 hours lecture) 3
      MATH 551 Topology (3 hours lecture) 3
      MATH 554 Projective Geometry (3 hours lecture) 3
      MATH 555 Differential Geometry (3 hours lecture) 3
      MATH 560 Numerical Analysis (3 hours lecture) 3
      MATH 564 Ordinary Differential Equation (3 hours lecture) 3
      MATH 566 Partial Differential Equations (3 hours lecture) 3
      MATH 568 Applied Mathematics: Continuous (3 hours lecture) 3
      MATH 569 Applied Mathematics: Discrete (3 hours lecture) 3
      MATH 570 Administration and Supervision of Mathematics (3 hours lecture) 3
      MATH 571 Curriculum Construction in Mathematics (3 hours lecture) 3
      MATH 572 Contemporary Teaching of Mathematics (3 hours lecture) 3
      MATH 573 Mathematics Materials for Teachers of Mathematics (3 hours lecture) 3
      MATH 574 Problem Analysis in Secondary Mathematics (3 hours lecture) 3
      MATH 575 Selected Topics in Mathematics Education (3 hours lecture) 3
      MATH 576 Research Seminar in Mathematics Education (3 hours seminar) 3
      MATH 577 Mathematics Education in the Elementary School (3 hours lecture) 3
      MATH 578 Special Topics in Mathematics Education (3 hours lecture) 3
      MATH 579 Approaching School Mathematics Through Applications (3 hours lecture) 3
      MATH 580 Combinatorial Mathematics (3 hours lecture) 3
      MATH 581 Graph Theory (3 hours lecture) 3
      MATH 584 Operations Research (3 hours lecture) 3
      MATH 590 Advanced Topics (3 hours lecture) 3
      MATH 591 Applied Industrial Mathematics (3 hours lecture) 3
      MATH 595 Seminar (1-4 hours seminar) 1-4
      STAT 541 Applied Statistics (3 hours lecture) 3
      STAT 542 Statistical Theory I (3 hours lecture) 3
      STAT 543 Statistical Theory II (3 hours lecture) 3
      STAT 544 Statistical Computing (3 hours lecture) 3
      STAT 545 Practicum in Statistics I 3
      STAT 546 Non-Parametric Statistics (3 hours lecture) 3
      STAT 547 Design and Analysis of Experiments (3 hours lecture) 3
      STAT 548 Applied Regression Analysis (3 hours lecture) 3
      STAT 549 Sampling Techniques (3 hours lecture) 3
  3. CULMINATING EXPERIENCE

    Successfully complete the Comprehensive Examination.


Course Descriptions:

CMPT574: Pixel and Image Processing (3 hours lecture)

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 sh.

Prerequisites: CMPT 580 and permission of graduate coordinator.

CMPT575: Introduction to Computer Graphics (3 hours lecture)

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 sh.

Prerequisites: CMPT 580 and permission of graduate coordinator.

CMPT576: Object-Oriented Software Development (3 hours lecture)

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 sh.

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

CMPT578: Introduction to Artificial Intelligence (3 hours lecture)

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 sh.

Prerequisites: CMPT 583 and permission of graduate coordinator.

CMPT580: Machine Organization and Architecture (3 hours lecture)

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

Prerequisites: Permission of graduate coordinator.

CMPT581: Systems Software Design (3 hours lecture)

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

Prerequisites: CMPT 580, and permission of graduate coordinator.

CMPT582: Theory of Automata and Formal Languages (3 hours lecture)

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 sh.

Prerequisites: Permission of graduate coordinator.

CMPT583: Computer Algorithms (3 hours lecture)

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 sh.

Prerequisites: Permission of graduate coordinator.

CMPT584: Operating System Design (3 hours lecture)

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

Prerequisites: CMPT 581, and permission of graduate coordinator.

CMPT585: Topics in Computer Science (3 hours lecture)

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 sh.

Prerequisites: CMPT 580 and permission of graduate coordinator.

CMPT586: File Structures and Databases (3 hours lecture)

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 sh.

Prerequisites: Permission of graduate coordinator.

CMPT587: Microcomputers and Computer Interfaces (3 hours lecture)

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

Prerequisites: CMPT 580, and permission of graduate coordinator.

CMPT588: Fundamentals of Programming Languages (3 hours lecture)

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

Prerequisites: Permission of graduate coordinator.

CMPT589: Computer Simulation of Discrete Systems (3 hours lecture)

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 sh.

Prerequisites: CMPT 580, permission of graduate coordinator.

CMPT590: Computer Simulation of Continuous Systems (3 hours lecture)

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 sh.

Prerequisites: CMPT 580, permission of graduate coordinator.

CMPT591: Compiler Theory and Construction (3 hours lecture)

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

Prerequisites: CMPT 581, permission of graduate coordinator.

CMPT592: Data Base Design and Implementation (3 hours lecture)

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 sh.

Prerequisites: CMPT 586, permission of graduate coordinator.

CMPT593: Structured System Design and Analysis (3 hours lecture)

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 sh.

Prerequisites: CMPT 586, and permission of graduate coordinator.

CMPT594: Software Engineering and Reliability (3 hours lecture)

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 sh.

Prerequisites: Permission of graduate coordinator.

CMPT596: Principles of Data Communication (3 hours lecture)

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

Prerequisites: CMPT 580, and permission of graduate coordinator.

CMPT678: Neurocomputing (3 hours lecture)

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

Prerequisites: CMPT 583, and permission of graduate coordinator.

CMPT680: Parallel Architectures and Algorithms (3 hours lecture)

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 sh.

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

CMPT683: Advanced Computer Algorithms (3 hours lecture)

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 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.

CMPT694: Software Quality Assurance (3 hours lecture)

This course examines (i) planned and systematic patterns of all actions necessary to provide adequate confidence that a product conforms to established requirements, and (ii) a set of activities designed to evaluate the process by which high-quality complex software products are developed. 3 sh.

Prerequisites: CMPT 594 or permission of graduate advisor.

CMPT695: Seminars in Computer Science (1-4 hours seminar)

Guided study of selected topics in major field of interest. 1 - 4 sh.

Prerequisites: CMPT 581, 583, and 586 and permission of graduate coordinator.

CMPT696: Local Area Networks (3 hours lecture)

Fundamental issues and concepts underlying Local Area Network (LAN) development via microcomputers: topology, transmission media and technology, error control, protocols. 3 sh.

Prerequisites: CMPT 596, and permission of graduate coordinator.

CMPT697: Master's Project in Computer Science (3 hours lecture)

Analysis of a significant problem related to computing and design of a solution. Where appropriate, implementation and testing as well as documentation of the solution. 3 sh.

Prerequisites: Completion of the computer science required core courses and permission of graduate coordinator.

MATH513: Computer Science Concepts for High School Teachers (3 hours lecture)

This course is specifically designed to help high school mathematics teachers prepare to use the microcomputer as a tool in their classrooms. Topics include an introduction to computer literacy, elements of BASIC programming, the evaluation of commercial software, the appropriate use of the software and a survey of relevant professional literature. Minimal prior knowledge of BASIC is assumed. May not be used for credit by Computer Science majors. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH515: Intermediate Analysis I (3 hours lecture)

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

Prerequisites: Permission of graduate program coordinator.

MATH516: Intermediate Analysis II (3 hours lecture)

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 sh.

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

MATH518: Foundations of Abstract Algebra (3 hours lecture)

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

Prerequisites: Permission of graduate program coordinator.

MATH520: Set Theory (3 hours lecture)

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

Prerequisites: MATH 222 and permission of graduate program coordinator.

MATH521: Real Variables I (3 hours lecture)

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

Prerequisites: MATH 426 and permission of graduate program coordinator.

MATH522: Real Variables II (3 hours lecture)

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

Prerequisites: MATH 521, permission of graduate program coordinator.

MATH525: Complex Variables I (3 hours lecture)

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 sh.

Prerequisites: MATH 426 and permission of graduate program coordinator.

MATH526: Complex Variables II (3 hours lecture)

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 sh.

Prerequisites: MATH 525, permission of graduate program coordinator.

MATH530: Mathematical Computing (3 hours lecture)

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 sh.

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

MATH531: Abstract Algebra I (3 hours lecture)

Basic algebraic structures including groups, rings, fields, modules and lattices. 3 sh.

Prerequisites: MATH 431 and permission of graduate program coordinator.

MATH532: Abstract Algebra II (3 hours lecture)

Basic algebraic structures including groups, rings, fields, modules and lattices. 3 sh.

Prerequisites: MATH 531, permission of graduate program coordinator.

MATH535: Linear Algebra I (3 hours lecture)

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

Prerequisites: MATH 335 and permission of graduate program coordinator.

MATH536: Linear Algebra II (3 hours lecture)

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

Prerequisites: MATH 535, permission of graduate program coordinator.

MATH537: Mathematical Logic (3 hours lecture)

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

Prerequisites: MATH 425 and permission of graduate program coordinator.

MATH540: Probability (3 hours lecture)

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 sh.

Prerequisites: MATH 340 and permission of graduate program coordinator.

MATH551: Topology (3 hours lecture)

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

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

MATH554: Projective Geometry (3 hours lecture)

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 sh.

Prerequisites: MATH 335 and permission of graduate program coordinator.

MATH555: Differential Geometry (3 hours lecture)

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 sh.

Prerequisites: MATH 222 and permission of graduate program coordinator.

MATH560: Numerical Analysis (3 hours lecture)

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

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

MATH564: Ordinary Differential Equation (3 hours lecture)

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

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

MATH566: Partial Differential Equations (3 hours lecture)

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

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

MATH568: Applied Mathematics: Continuous (3 hours lecture)

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 sh.

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

MATH569: Applied Mathematics: Discrete (3 hours lecture)

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 sh.

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

MATH570: Administration and Supervision of Mathematics (3 hours lecture)

Problems of organization, administration and supervision in the mathematics program of the school. Functions, duties and qualifications of the supervisor investigated. Current problems and research findings. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH571: Curriculum Construction in Mathematics (3 hours lecture)

Contemporary proposals for the mathematics of grades K through 12. Consideration is given to the problem of implementation of current recommendations. Examination is made of mathematical concepts underlying various programs. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH572: Contemporary Teaching of Mathematics (3 hours lecture)

Pedagogy, resources, and research related to the teaching of standards-based mathematics in grades 6-12. Emphasis is on creating student-centered learning environments, resources and materials for contemporary mathematics classrooms, models of effective teaching and learning, alternative assessment, appropriate uses of technology and multicultural aspects of mathematics. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH573: Mathematics Materials for Teachers of Mathematics (3 hours lecture)

The construction, adaptation and effective use of classroom materials and activities designed to enhance and expand the teaching of mathematics and mathematical thinking in the middle and high school grades with special attention given to basic commercial and simple teacher- and student-made manipulatives and models with broad use from the development of concepts and skills to their maintenance, review, and extension plus applications to problem solving. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH574: Problem Analysis in Secondary Mathematics (3 hours lecture)

Psychology and techniques of problem-solving. Discovery and heuristic methods. Intuitive and inductive reasoning in the solution of nonroutine problems from high school mathematics. Problem formation and solution. 3 sh.

Prerequisites: MATH 222 and permission of graduate program coordinator.

MATH575: Selected Topics in Mathematics Education (3 hours lecture)

Selection of topics associated with secondary and early college years of mathematics investigated from an advanced point of view. Topics selected to give the teacher a professionalized subject matter viewpoint of such areas as algebra, geometry, number theory, real and complex analysis, probability and history of mathematics. 3 sh.

Prerequisites: MATH 222 and permission of graduate program coordinator.

MATH576: Research Seminar in Mathematics Education (3 hours seminar)

Designed for matriculated graduate students in the mathematics education program. Students survey and analyze recent research projects. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH577: Mathematics Education in the Elementary School (3 hours lecture)

The contemporary mathematics curriculum of the elementary and middle school. The role of behavioral objectives and learning theory in curriculum development/teacher training. Related research findings. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH578: Special Topics in Mathematics Education (3 hours lecture)

Topics may be selected from areas such as assessment, cooperative learning, elementary education, fractals, graphing calculators, NCTM Standards, and other special areas of interest to mathematics educators. May be repeated once for a maximum of 6.0 credits as long as the topic is different. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH579: Approaching School Mathematics Through Applications (3 hours lecture)

Topics in middle grade and secondary mathematics are explored with an emphasis on their application to both traditional and more recently developed areas. Applied problems are used to motivate mathematical topics, and mathematical knowledge is used to explore solutions to applied problems. 3 sh.

Prerequisites: Permission of graduate program coordinator.

MATH580: Combinatorial Mathematics (3 hours lecture)

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

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

MATH581: Graph Theory (3 hours lecture)

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

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

MATH584: Operations Research (3 hours lecture)

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 sh.

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

MATH590: Advanced Topics (3 hours lecture)

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 sh.

Prerequisites: Graduate program coordinator's permission.

MATH591: Applied Industrial Mathematics (3 hours lecture)

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 sh.

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

MATH595: Seminar (1-4 hours 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 sh.

Prerequisites: Graduate program coordinator's permission.

STAT541: Applied Statistics (3 hours lecture)

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 sh.

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

STAT542: Statistical Theory I (3 hours lecture)

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 sh.

Prerequisites: STAT 541 and permission of graduate program coordinator.

STAT543: Statistical Theory II (3 hours lecture)

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 sh.

Prerequisites: STAT 542 and permission of graduate program coordinator.

STAT544: Statistical Computing (3 hours lecture)

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

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 sh.

Prerequisites: STAT 330 and permission of graduate program coordinator.

STAT547: Design and Analysis of Experiments (3 hours lecture)

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 sh.

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

STAT548: Applied Regression Analysis (3 hours lecture)

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 sh.

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

STAT549: Sampling Techniques (3 hours lecture)

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

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

STAT640: Biostatistics I (3 hours lecture)

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 sh.

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

STAT641: Biostatistics II (3 hours lecture)

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 sh.

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

STAT642: Introduction to Stochastic Processes (3 hours lecture)

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 sh.

Prerequisites: MATH 540 and permission of graduate program coordinator.

STAT645: Advanced Topics in Statistics (3 hours lecture)

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 sh.

Prerequisites: Permission of graduate program coordinator.

STAT646: Multivariate Analysis (3 hours lecture)

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

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 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.