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Graduate Catalog 2013-2014

CatalogGraduateCollege of Arts and SciencesMATHCourse Descriptions

Mathematics Course Descriptions

All course descriptions carry behind the name and number a parenthesis ( ) indicating the credit hours, lecture hours, and the lab hours per week. For example: NSCI 110 (4-3-2). The first number in the parenthesis indicates the credit value of the course (4); the second number indicates the number of lecture hours (3) per week; and the third number indicates the number of lab hours per week (2).

CSC 501  (3-3-0)  Special Topics in Computer Science: In-depth studies of selected topics in areas of computer science not covered in other computer courses, such as software, hardware utilization, programming languages, numerical methods, syntactic descriptions, symbolic functions, and manipulations, with course requirements including one or more of the following: readings in the literature and research on computer science, introductory research projects, major computer programming projects, seminars, or new course development.
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MATH 501  (3-3-0)  Teaching Mathematics Using Computers: A study of the use of computers in mathematics teaching and research, incorporating evaluations of instructional software and examining integrative techniques for applications of microcomputers in middle grades math, consumer math, general math, geometry, advanced mathematics, trigonometry, and calculus.
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MATH 502  (3-3-0)  Topics in Mathematics for Teachers: An intensive study of current topics in mathematics of interest to public school teachers including but not limited to such topics as algebra, geometry, trigonometry, functions, statistics, probability, and use of technology.
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MATH 504  (3-3-0)  Current Trends in Mathematics Education: The primary purpose of this course is to explore mathematics education from methodological and research perspectives. This will be accomplished by developing teaching, research, writing, presentation, and discussion skills.
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MATH 506  (3-3-0)  Analysis for Teachers II: A continuation of MATH 505, emphasizing proofs and covering such topics as the integral, applications of the integral, L'Hospital's Rule, infinite series, and multiple integrals.
Prerequisite: MATH 502
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MATH 507  (3-3-0)  Linear Algebra I: The first course in a two-semester sequence in linear algebra, including such topics as systems of linear equations, matrices, vector spaces, linear transformations, determinants, canonical forms of matrices, and inner product spaces.
Prerequisite: MATH 251 or consent of the department.
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MATH 508  (3-3-0)  Numerical Analysis: A practical survey of numerical analysis, with topics included from iterative methods of nonlinear equations, the approximation theory, numerical solutions of ordinary and partial differential equations, and numerical linear algebra.
Prerequisite: MATH 251 And MATH 331 And MATH 507
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MATH 509  (3-3-0)  Linear Programming and Applications: An applications-oriented course developing some of the theories and computational techniques of linear programming - the simplex method, the concept of duality, and the Duality Theorem, matrix representation of the Simplex Algorithm, sensitivity analysis, integer programming - and applying them to transportation problems.
Prerequisite: MATH 372
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MATH 511  (3-3-0)  Abstract Algebra I: The first course of a two-semester sequence in abstract algebra, including such topics as groups, normal subgroups, quotient groups, homomorphisms, Cayley's Theorem, Cauchy's Theorem, permutation groups, Sylow's Theorem, direct products, finite abelian groups, rings, ring homomorphisms, ideals, quotient rings, Euclidean rings, and polynomial rings.
Prerequisite: MATH 361 or consent of department
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MATH 521  (3-3-0)  Real Analysis I: The first course of a three-semester sequence in real analysis, including such topics as real number systems, elements of point-set topology and metric spaces, sequences and series of real numbers, continuity, differentiation, integration, the Reimann-Stieltjes Integral, sequences, and series of functions, point wise and uniform convergence, functions of several variables, implicit function, and inverse function theorems.
Prerequisite: MATH 412 or consent of department
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MATH 531  (3-3-0)  Topology I: The first course in a three-semester sequence in topology, presenting an axiomatic development of topological spaces and including such topics as continuity, compactness, connectedness, separation axioms, metric spaces, and convergence.
Prerequisite: MATH 412 or consent of department
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MATH 533  (3-3-0)  Advanced Studies in Teaching Mathematics: An in-depth investigation of a variety of techniques and topics pertaining to curriculum, methodology, technology and research in teaching mathematics in grades 6-9, including an exploration of problem analysis, descriptive statistics and elementary probability. Statistical software such as Excel and SPSS will be used to reinforce concepts.
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MATH 541  (3-3-0)  Complex Analysis I: The first course of a three-semester sequence in complex variables, including such topics as complex numbers and their geometrical representation, point sets, sequences and mappings in the complex plane, single-valued analytic functions of a complex variable, elementary functions, and integration.
Prerequisite: MATH 412 or consent of department
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MATH 571  (3-3-0)  Ordinary Differential Equation: A course including such topics as existence and uniqueness theorems, linear systems, autonomous systems, periodicity, boundedness and stability of solutions, nonlinear equations, perturbation theory, Sturm-Liouville systems, etc.
Prerequisite: MATH 331 or consent of department
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MATH 581  (3-3-0)  Operational Mathematics: A study of the theories of Laplace and Fourier transforms and their applications both to ordinary and partial differential equations (including integral equations) and to problems in engineering and the physical sciences.
Prerequisite: MATH 331
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MATH 607  (3-3-0)  Vector Space Methods in System Optimization: An introduction to algebraic and functional analysis concepts used in systems modeling and optimization: vector spaces, linear mappings, spectral decompositions, adjoins, orthogonal projections, duality, fixed points and differentials, with additional emphasis on least squares estimations, minimum norm problems in Banach spaces, linearization in Hilbert space, iterative solutions of systems of equations, and optimization problems.
Prerequisite: MATH 241 And MATH 521
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MATH 611  (3-3-0)  Linear Algebra II: The second course of a two-semester sequence, including such topics as vector spaces, linear independence and bases, dual spaces, inner product spaces, modules, extension fields, roots of polynomials, elements of Galois theory, solvability by radicals, Galois groups over the rationals, algebra of linear transformations, matrices, canonical forms; triangular form, Nilpotent transformation, Jordan form, rational canonical form, Hermitian, unitary, and Normal transformations real quadratic forms.
Prerequisite: MATH 507
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MATH 612  (3-3-0)  Abstract Algebra II: A presentation of advanced topics in abstract algebra, including categories and functions, direct sums and free abelian groups, finitely generated abelian groups, commutative rings, localization, principal rings, direct products and sums of modules, homology sequence, Euler characteristic, Jordan-Holder Theorem, free algebras, tensor products, Noetherian rings and modules, extensions of rings, extension of homomorphisms, transcendental extension of homorphisms, Hilbert's Nullstellensatz, algebraic sets, representations of finite groups, and semi-simplicity of group algebra.
Prerequisite: MATH 511
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MATH 621  (3-3-0)  Real Analysis II: A study of such topics as the Lebesgue measure, the Lebesgue integral, differentiation and integration theory, the classical Banach spaces, metric spaces, elements of topological spaces, compact spaces, abstract measure and integration theory, the Danielle integral, mappings of measure spaces, and elements of functional analysis.
Prerequisite: MATH 521
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MATH 622  (3-3-0)  Real Analysis III: A continuation of MATH 621, including such topics as extension of a linear function, construction of measure, the space of Lp (X), (1 p 4), integration on a product space, complex measures, the Haar integral, bounded functions, and almost periodic functions.
Prerequisite: MATH 621
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MATH 631  (3-3-0)  Topology II: A continuation of MATH 531, including the following additional topics: embedding and metrication, function and quotient spaces, and complete metric spaces.
Prerequisite: MATH 531
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MATH 632  (3-3-0)  Topology III: A study of advanced topics such as homotopy and the fundamental group, homology theory, exactness, the excision theorem, Mayer-Vietoris sequences, the Eilenberg-Steenrod axioms, cohomology and duality, and higher homotopy groups.
Prerequisite: MATH 631
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MATH 641  (3-3-0)  Complex Analysis II: The second course of a two-semester sequence in complex analysis, including metric spaces and the topology in C, elementary properties and examples of analytic functions, complex integration, singularities, the maximum modulus theorem, compactness and convergence in the space of analytic functions.
Prerequisite: MATH 541
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MATH 642  (3-3-0)  Complex Analysis III: A continuation of MATH 641, including such advanced topics as Runge’s Theorem, analytic continuity and Reimann surfaces, harmonic functions, entire functions, and the range of an analytic function.
Prerequisite: MATH 641
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MATH 651  (3-3-0)  Functional Analysis I: The first course of a two-semester sequence, including such topics as normed spaces, Banach spaces, the dual space, continuous linear mappings (spaces), topological vector spaces, the open mapping and closed graph theorems, equicontinuous mappings, and theorems of Banach and Banach-Steinhaus, convex sets, separation of convex sets, and the Hahn-Banach Theorem.
Prerequisite: MATH 621
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MATH 652  (3-3-0)  Functional Analysis II: The second course of a two-semester sequence, including such topics as locally convex spaces, metrizable locally convex spaces, the determination of various dual spaces and their topologies, compact convex sets, weakly compact sets, semireflexivity, reflexivity, extreme points, Krien Milman Theorem, Eberlein-Smulian Theorem, and metric properties of normed spaces.
Prerequisite: MATH 651
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MATH 671  (3-3-0)  Partial Differential Equations: A study of topics such as Cauchy-Kowalewski theorem, existence and regularity of the solutions, Dirichlet problem for linear elliptic equations, Cauchy problems, hyperbolic equations, and fundamental solutions of linear equations with constant coefficients.
Prerequisite: MATH 331 And MATH 571
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MATH 681  (3-3-0)  Tensor Analysis: A study of such topics as tensor algebra, covariant and contravariant components, christoffel symbols, and applications of tensor analysis.
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MATH 699  (6-6-0)  Thesis Research: An extensive research experience in an approved topic of choice.
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MATH 710  (3-3-0)  Topics in Abstract Algebra: Discussions of special and advanced topics, forming an axiomatic and rigorous study of algebra within the scope of research interests of the instructor.
Prerequisite: MATH 612
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MATH 720  (3-3-0)  Topics in Real Analysis: Discussions of special and advanced topics, forming an axiomatic and rigorous study of real analysis within the scope of research interests of the instructor.
Prerequisite: MATH 632
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MATH 730  (3-3-0)  Topics in Topology: Discussions of special and advanced topics, forming an axiomatic and rigorous study of topology within the scope of research interests of the instructor.
Prerequisite: MATH 632
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MATH 740  (3-3-0)  Topics in Complex Analysis: Discussions of special and advanced topics, forming an axiomatic and rigorous study of complex analysis within the scope of research interests of the instructor.
Prerequisite: MATH 642
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MATH 899  (0-0-0)  Thesis Non-Credit: This course is required for students that have completed their course work and the number of thesis hours for credit required in their graduate degree program. Students who will continue to use University resources in completing their thesis must enroll in this course.
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STAT 561  (3-3-0)  Probability Theory: A course including such topics as probability distributions, limit theorems, special functions, and probability models.
Prerequisite: STAT 301 or consent of department.
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STAT 562  (3-3-0)  Applied Regression Analysis: A course including such topics as matrix theory, correlation analysis, least squares, curve fitting, simple and multiple regression, response surfaces, and the applications of statistical software packages.
Prerequisite: MATH 251
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STAT 563  (3-3-0)  Design and Analysis of Experiment: The applications of statistics in the design and analysis of experiments. Topics will include: Principles of Design of Experiments, One-way Analysis of Variance, Factorial Designs, Hierarchical or Nested Designs, Linear and Multiple Regression Analysis, Two way Analysis of Variance, and other related topics.
Prerequisite: STAT 561
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STAT 564  (3-3-0)  Mathematical Statistics: Theories of distributions and statistical inference, Point and Interval Estimation, Tests of Hypotheses, Sufficiency, Completeness, and Unbiased Minimum Variance Unbiased Estimation (UMVUE'S) Interval Estimation.
Prerequisite: STAT 561
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STAT 571  (3-3-0)  Statistical Computing: A survey of some of the standard statistical software packages, like EXCEL, SAS, and SPSS.. These packages will be used to solve statistical problems.
Prerequisite: MATH 561
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STAT 572  (3-3-0)  Time Series Analysis: A discussion of the theoretical and applied aspects of Time Series. Topics include: Introduction to forecasting, Non-Seasonal Box-Jenkins Models and their tentative identification, Seasonal Box-Jenkins Models and their tentative identification, Estimation and diagnostic checking for Box-Jenkins models, Time Series Regression, Exponential Smoothing, Transfer Function Models, Classical Regression Analysis.
Prerequisite: STAT 561
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STAT 661  (3-3-0)  Advanced Probability Theory: A course including such topics as probability distributions, characteristic and generating functions, convergence and approximations, asymptotic sampling theory and decision functions.
Prerequisite: STAT 561
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STAT 662  (3-3-0)  Advanced Mathematical Statistics: Topics include parametric estimation, tests of hypotheses, linear models and nonparametric estimation, sufficiency, unbiased estimation, Bayes estimators, and the multivariate normal theory.
Prerequisite: STAT 661
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STAT 750  (3-3-0)  Topics in Statistics: A study of special and advanced topics in statistics within the scope of research interests of the instructor.
Prerequisite: STAT 662
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