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| MATH 601-602 Abstract Algebra I, II |
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Prerequisite: MATH 501.
Continuous course; 3 lecture hours. 3-3 credits.
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A study of algebraic structures (including groups, rings, and fields), Galois theory,
homomorphisms, subalgebras, direct products, direct decompositions, subdirect decompositions,
free algebras, varieties of algebras.
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| MATH 603-604 Advanced Probability Theory |
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Prerequisites: MATH 508 and STAT 503 or STAT 513.
Continuous course; 3 lecture hours. 3-3 credits.
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A measure-theoretic approach to the theory of probability. Borel sets, probability measures,
and random variables. Special topics include characteristic functions, modes of
convergence, and elements of stochastic processes.
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| MATH 607-608 Real Analysis I, II |
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Prerequisite: MATH 508.
Continuous course; 3 lecture hours. 3-3 credits.
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The real number system, Lebesgue measure, functions of bounded variation, differentiation
and integration, the LP spaces, introduction to Banach and Hilbert spaces, general measure
theory, and the Lebesgue-Stieltjes integral.
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| MATH 611-612 Complex Analysis I, II |
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Prerequisite: MATH 508.
Continuous course; 3 lecture hours. 3-3 credits.
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Elementary functions, analyticity, Cauchy's theorem and integral formula, Taylor and
Laurent series, poles, residues, analytic continuation, Riemann surfaces, periodic functions,
conformal mapping, and applications.
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| MATH 615 Topics in Numerical Analysis |
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May be taken twice for credit.
Prerequisites: MATH 515-516 and permission of instructor.
Semester course; 3 lecture hours. 3 credits.
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Special topics in
computer methods for numerical analysis selected from such subjects as analysis of numerical
methods for solving ordinary differential equations; elliptic, hyperbolic, and parabolic partial
differential equations; solutions of large linear systems by iterative methods.
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| MATH 617-618 Applied Mathematics I, II |
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Prerequisites: MATH 517 and 518.
Continuous course; 3 lecture hours. 3-3 credits.
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Partial differential equations; equations of Helmholtz, Laplace,
and Poisson; the diffusion equation, integral transforms, Green's function methods, calculus of
variation, eigenvalues and eigenfunctions by variational methods, integral equations, Fredholm
and Volterra equations, and Fredholm and Hilbert-Schmidt theories.
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| MATH 619 Operational Methods |
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Prerequisite: MATH 508.
Semester course; 3 lecture hours. 3 credits.
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Transform methods applied to existence theory, explicit solutions to problems of mathematical
physics, distributions of Schwartz and Gelfand-Silov, kernel theorems of Schwartz,
mathematical framework of quantum field theory.
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| MATH 620 Theory of Partial Differential Equations |
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Prerequisites: MATH 301 and 508.
Semester course; 3 lecture hours. 3 credits.
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Classification of partial differential equations; elliptic,
hyperbolic, and parabolic equation; potential theory, techniques of solving various partial
differential equations; application to electromagnetism and solid mechanics.
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| MATH 621 Boundary-Value Problems |
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Prerequisites: MATH 517-518.
Semester course; 3 lecture hours. 3 credits.
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Survey of boundary-value problems, approximate analytic solutions such as Galerkin's
method and the Ritz method; application to heat transfer, fluid mechanics, and potential theory.
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| MATH 639 Studies in Operations Research |
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Prerequisites: at least one graduate-level course in mathematical sciences pertaining to the study area and
permission of instructor.
Semester course; 3 lecture hours. 3 credits.
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Selected areas in operations research will be studied, such as integer
programming, nonlinear programming, large scale systems, stochastic models.
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| MATH 641 Mathematical Programming |
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Prerequisite: MATH 527.
Semester course; 3 lecture hours. 3 credits.
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Necessary and sufficient conditions for optimal solutions. Duality theory. Theoretical and
practical development of solution techniques for operations research problems. Some current
algorithms will be discussed.
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| MATH 645 Queueing Theory |
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Prerequisite: STAT 503.
Semester course; 3 lecture hours. 3 credits.
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This operations research course provides a development of some basic queueing systems. Such
systems will include birth-death queues, as well as the M/G/1 and GI/M/S queueing systems.
Other topics may include the GI/G/1 queues, overflow queues, and some basic queueing
networks.
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| MATH 649 Practical Optimization |
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Prerequisites: MATH 527 and CMSC 255.
Semester course; 3 lecture hours. 3 credits.
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The application of optimization theory toward the solution of practical problems
in operations research. The use and analysis of computer programs available to solve such
problems. The algorithms used in these programs will be discussed from a practical and
theoretical point of view.
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| MATH 661 Number and Operations |
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| Semester course; 3 lecture hours. 3 credits.
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Ways of representing numbers, relationships between numbers, number systems, the meanings of operations and how they relate to one another, and computation within the number system as a foundation for algebra; episodes in history and development of the number system; and examination of the developmental sequence and learning trajectory as children learn number concepts. A core course for preparation as a K-8 mathematics specialist. Not applicable to M.S. in Mathematical Sciences.
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| MATH 662 Geometry and Measurements |
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| Semester course; 3 lecture hours. 3 credits.
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Explorations of the foundations of informal measurement and geometry in one, two and three dimensions. The van Hiele model for geometric learning is used as a framework for how children build their understanding of length, area, volume, angles and geometric relationships. Visualization, spatial reasoning and geometric modeling are stressed. As appropriate, transofrmational geometry, congruence, similarity and geometric constructions will be discussed. A core course of preparation as a K-8 mathematics specialist. Not applicable to M.S. in Mathematical Sciences.
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| MATH 663 Functions and Algebra |
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| Semester course; 3 lecture hours. 3 credits.
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Examination of representation and analysis of mathematical situations and structures using generalization and algebraic symbols and reasoning. Attention will be given to the transition from arithmetic to algebra, working with quantitative change, and the description of and prediction of change. A core course for preparation as a K-8 mathematics specialist. Not applicable to M.S. in Mathematical Sciences.
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| MATH 664 Statistics and Probability |
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| Semester course; 3 lecture hours. 3 credits.
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An introduction to probability, descriptive statistics and data analysis; exploration of randomness, data representation and modeling. Descriptive statistics will include measures of central tendency, dispersion, distributions and regression. Analysis of experiments requiring hypothesizing, experimental design and data gathering. A core course for preparation as a K-8 mathematics specialist. Not applicable to M.S. in Mathematical Sciences.
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| MATH 665 Rational Numbers and Proportional Reasoning |
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| Semester course; 3 lecture hours. 3 credits.
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Basic number strands in fractions and rational numbers, decimals and percents; ratios and proportions in the school curriculum. Interpretations, computations and estimation with a corrdinated program of activities that develop both rational number concepts and skills and proportional reasoning. A core course for preparation as a K-8 mathematics specialist. Not applicable to M.S. in Mathematical Sciences.
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| MATH 690 Research Seminar |
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Prerequisite: graduate standing.
Semester course; 1 credit.
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Discussion of topics in the mathematical sciences as stimulated by independent reading in selected areas and at
least one oral presentation by each student. May be taken more than once for credit.
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| MATH 691 Special Topics in Mathematics |
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Prerequisite: Permission of instructor.
Semester course; 1-3 lecture hours. 1-3 credits.
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A detailed study of selected topics in mathematics. Possible topics
include commutative rings and algebras, topological groups, special functions, Fourier analysis,
abstract harmonic analysis, operator theory, functional analysis, differential geometry, Banach
algebras and control theory. May be taken more than once for credit.
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| MATH 697 Directed Research |
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Prerequisite: graduate standing.
Semester course; variable credit, 1-3 credits per semester.
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Supervised individual research and study in an area not covered in the present
curriculum or in one which significantly extends present coverage. Research culminates with an
oral presentation and submission of a written version of this presentation to the supervising
faculty member. May be taken more than once for credit.
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| MATH 698 Thesis |
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Prerequisite: graduate standing.
1-3 credits per course. A total of 3 or 6 credits may be applied to the MS degree in
Applied Mathematics/Mathematical Sciences or to the MS degree in Mathematics/Mathematical
Sciences. (A total of 3 credits for an expository thesis or a total of 6 credits for a research thesis).
Hours to be arranged.
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Independent research culminating in the writing of the required thesis as described in this Bulletin.
A grade of S (satisfactory), U (unsatisfactory) or F (failure) may be assigned in this course.
May be taken more than once for credit.
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Department of Mathematics
Virginia Commonwealth University
1001 West Main Street, Richmond, VA 23284-2014
Phone: (804) 828-1301; Fax: (804) 828-8785; E-mail: Mathematics
  
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