MTHSC 600 Theory of Probability 3(3,0) Principle topics include combinatorial theory, probability axioms, random variables, expected values, special discrete and continuous distributions, jointly distributed random variables, correlation, conditional expectation, law of large numbers, central limit theorem. Preq: MTHSC 206 or consent of instructor.
MTHSC 603 Introduction to Statistical Theory 3(3,0) Principle topics include sampling distributions, point and interval estimation, maximum likelihood estimators, method of moments, least squares estimators, tests of hypotheses, likelihood ratio methods, regression and correlation analysis, introduction to analysis of variance. Preq: MTHSC 400 or equivalent.
MTHSC 605 Statistical Theory and Methods II 3(3,0) Principle topics include simple linear regression, multiple regression and correlation analysis, one-way analysis of variance, multiple comparison, multifactor analysis of variance, experimental design. Computation and interpretation of results are facilitated through use of statistical computer packages. Preq: MTHSC 301.
MTHSC 606 Sampling Theory and Methods 3(3,0) Probability-based treatment of sampling methodology. Theory and application of estimation techniques are treated using simple and stratified random sampling, cluster sampling, and systematic sampling. Preq: MTHSC 302 and 400, or consent of instructor.
MTHSC 607 Regression and Time Series Analysis 3(3,0) Theory and application of the regression and time series. Approaches to empirical model building and data analysis are treated. Computation and interpretation of results are facilitated through the use of interactive statistical packages. Preq: MTHSC 302, 311, 400; or consent of instructor.
MTHSC 608 Topics in Geometry 3(3,0) Introduction to topics in special geometries which include non-Euclidean space concepts such as projective geometry, finite geometries, and intuitive elementary topology. Brief introduction to vector geometry. Preq: MTHSC 206.
MTHSC 612 Introduction to Modern Algebra 3(3,0) Introduction to the concepts of algebra. Topics include the number system and the elementary theory of groups, rings, and fields. Preq: MTHSC 311.
MTHSC 619 Discrete Mathematical Structures I 3(3,0) Applies theoretical concepts of sets, functions, binary relations, graphs, Boolean algebras, propositional logic, semigroups, groups, homomorphisms, and permutation groups to computer characteristics and design, words over a finite alphabet and concatenation, binary group codes, and other communication or computer problems. Preq: MTHSC 311.
MTHSC 634 Advanced Engineering Mathematics 3(3,0) Fourier series, Laplace and Fourier transform, and numerical methods for solving initial value and boundary-value problems in partial differential equations are developed. Applications to diffusion wave and Dirichlet problems are given. Matrix methods and special functions are utilized. Preq: MTHSC 208.
MTHSC 635 Complex Variables 3(3,0) Elementary functions; differentiation and integration of analytic functions; Taylor and Laurent series; contour integration and residue theory; conformal mapping; Schwarz-Christoffel transformation. Preq: MTHSC 206.
MTHSC 640 Linear Programming 3(3,0) Introduction to linear programming covering the simplex algorithm, duality, sensitivity analysis, network models, formulation of models, and the use of simplex codes to solve, interpret, and analyze problems. Preq: MTHSC 206, 311, or consent of instructor.
MTHSC 641 Introduction to Stochastic Models 3(3,0) Introductory treatment of stochastic processes, finite-state Markov chains, queueing, dynamic programming, Markov decision processes, reliability, decision analysis, and simulation. Both theory and applications are stressed. Preq: MTHSC 400.
MTHSC 653 Advanced Calculus I 3(3,0) Limits, continuity, and differentiation of functions of one and several variables, the Riemann integral, and vector analysis. Preq: MTHSC 206.
MTHSC 654 Advanced Calculus II 3(3,0) Continuation of MTHSC 653. Transformations, multiple integrals, line and surface integrals, infinite sequences and series, and improper integrals. Preq: MTHSC 453.
MTHSC 660 Introduction to Numerical Analysis I 3(3,0) Introduction to the problems of numerical analysis emphasizing computational procedures and application. Topics include sources of error and conditioning, matrix methods, systems of linear equations, nonlinear equations, interpolation and approximation by splines, poly-nominals and trigonometric functions. Preq: MTHSC 206 or 207 and 360 or equivalent.
MTHSC 663 Mathematical Analysis I 3(3,0) Basic properties of the real number system, sequences and limits; continuous functions, uniform continuity and convergence; integration, differentiation, functions of several real variables, implicit function theory. Preq: MTHSC 206.
MTHSC 709 Geometry for the Middle Grades 3(3,0) Hands-on approach to constructions with straight-edge and compass; polygons including tessellations and polyhedra; symmetry and transformational geometry; coordinate geometry measurement with dimensional analysis; perspective drawing and related topics; history of geometry; reasoning and informal proof with congruence; and computer software, calculator use, and Internet.
MTHSC 715 Quantitative Literacy I 3(3,0) Data analysis and gathering data from surveys including box-and-whisker plots, bar charts, circle graphs, and stem-and-leaf plots. Construction of surveys to gather data to test a hypothesis. All material are presented by student activities using cooperative learning and manipulatives.
MTHSC 716 Quantitative Literacy II 3(3,0) Probability and simulation; application of these concepts to simulate various processes such as traffic control. All material are presented by student activities using cooperative learning and manipu-latives.
MTHSC 719 Discrete Mathematics 3(3,0) Discrete mathematics emphasizing applications to computer science; propositions and logic; Boolean Algebra and switching circuits; recursion and induction; relations and partially ordered sets, graphs, and trees.
MTHSC 721 Matrix Algebra 3(3,0) Matrices and systems of equations; determinants; vector spaces and linear transformations; eigenvalues. Restricted to graduate students in Secondary Education.
MTHSC 723 Applications of Linear and Modern Algebra 3(3,0) Various applied problems whose solutions rely on techniques and results of linear and modern algebra. Problems are selected from such areas as economics, forest management, genetics, population growth, transportation networks, cryptography, satellite communications, electronic switching circuits, chemistry, physics, sociology, and others. Preq: MTHSC 721 or equivalent or consent of instructor.
MTHSC 725 Combinatorial Mathematics for Teachers 3(3,0) Permutations; combinations; generating functions; recurrence relations; principle of inclusion-exclusion; partitions; Latin squares; block designs; finite geometries; graphs; codes; Polya's theorem; recreational mathematics. Restricted to graduate students in Secondary Education.
MTHSC 727 Analysis Concepts for Teachers 3(3,0) Elementary functions, differential calculus and integral calculus; enrichment material and a theoretical perspective of calculus. Restricted to teachers who hold a current teaching certificate in secondary mathematics. Completion of this course satisfies the special certification requirements for AB-calculus teachers in South Carolina.
MTHSC 730 Modern Geometry for Teachers 3(3,0) Concepts of Euclidean geometry reviewed and extended by means of coordinates, vectors, matrices; conic sections. Restricted to graduate students in Secondary Education.
MTHSC 741 Introduction to Linear Programming with Applications 3(3,0) Development of mathematical theory of simplex algorithm; survey of mathematical background; matrix algebra, systems of linear equations and vector spaces; problem formulation is emphasized. Restricted to graduate students in Secondary Education.
MTHSC 761 Probability and Statistics for Teachers 3(3,0) Probability, conditional probability, descriptive statistics, random variables, probability functions, binomial distribution, normal distribution, sampling, estimation, decision making. Restricted to graduate students in Secondary Education.
MTHSC 783 Theory of Numbers 3(3,0) Properties of integers, divisors, and prime numbers; fundamental properties of congruence; polynomials and primitive roots; quadratic residues. Restricted to graduate students in Secondary Education.
MTHSC 791 Selected Topics in Mathematics Education 1-3(1-3,0) Mathematical problems in elementary or secondary school curricula. Restricted to graduate students in Elementary or Secondary education. May be repeated for credit, but only if different topics are covered.
MTHSC 800 Probability 3(3,0)F Basic probability theory with emphasis on results and techniques useful in operations research and statistics. Topics include axiomatic probability, advanced combinatorial probability, conditional informative expectation, functions of random variables, moment generating functions, distribution theory, and limit theorems. Preq: MTHSC 206.
MTHSC 801 General Linear Hypothesis I 3(3,0)F Least-square estimates; Gauss-Markov theorem; confidence ellipsoids, and confidence intervals for estimable functions; tests of hypotheses; one-, two-, and higher-way layouts; analysis of variance for other models. Preq: MTHSC 403, 311.
MTHSC 802 General Linear Hypothesis II 3(3,0)S Continuation of MTHSC 801.
MTHSC 803 Stochastic Processes 3(3,0)S,SS Theory and analysis of time series, recurrent events, Markov chains, random walks, renewal theory, application to communication theory and operations research. Preq: MTHSC 400 or 800.
MTHSC 804 Statistical Inference 3(3,0) Sampling distributions; maximum likelihood estimation and likelihood ratio tests; asymptotic confidence intervals for Binomial, Poisson, and Exponential parameters; two-sample methods; nonparametric tests; ANOVA; regression; model building. Preq: MTHSC 400 or equivalent or consent of instructor.
MTHSC 805 Data Analysis 3(3,0) Methodology in analysis of statistical data emphasizing applications to real problems using computer-oriented techniques: computer plots, transformations, criteria for selecting variables, error analysis, multiple and stepwise regression, analysis of residuals, model building in time series and ANOVA problems, jackknife and random subsampling, multidimensional scaling, clustering. Preq: MTHSC 301 and 400, or MTHSC 401 and 800.
MTHSC 806 Nonparametric Statistics 3(3,0)F Order statistics; tolerance limits; rank-order statistics; Kolmogorov-Smirnov one-sample statistics; Chi-square goodness-of-fit test; two-sample problem; linear rank statistics; asymptotic relative efficiency. Preq: MTHSC 600 or 800.
MTHSC 807 Applied Multivariate Analysis 3(3,0)F Applied multivariate analysis: computer plots of multivariate observations; multidimensional scaling; multivariate tests of means, covariances, and equality of distributions; univariate and multivariate regressions and their comparisons; MANOVA; principal components analysis; factor analysis; analytic rotations; canonical correlations. Preq: MTHSC 403 and 805 or consent of instructor.
MTHSC 808 Reliability and Life Testing 3(3,0)S Probability models and statistical methods relevant to parametric and nonparametric analysis of reliability and life testing data. Preq: MTHSC 400 and 401 or equivalent.
MTHSC 809 Time Series Analysis, Forecasting, and Control 3(3,0)F Modeling and forecasting random processes; autocorrelation functions and spectral densities; model identification, estimation and diagnostic checking; transfer function models; feedforward and feedback control schemes. Preq: MTHSC 600 and 605, or MTHSC 800 and 605, or equivalent.
MTHSC 810 Mathematical Programming 3(3,0) Formulation and solution of linear programming models; mathematical development of the simplex method; revised simplex method; duality; sensitivity analysis; parametric programming, implementation and software packages. Preq: MTHSC 311.
MTHSC 811 Nonlinear Programming 3(3,0)S Theoretical development of nonlinear optimization with applications, classical optimization, convex and concave functions, separable programming, quadratic programming, and gradient methods. Preq: MTHSC 440, 454.
MTHSC 812 Discrete Optimization 3(3,0)F Principal methods used in integer programming and discrete optimization; branch and bound, implicit enumeration, cutting planes, group knapsack, Lagrangian relaxation, surrogate constraints, heuristics (performance analysis), separation/branching strategies, and polynomial time algorithms for specific problems on special structures. Preq: MTHSC 810 or equivalent.
MTHSC 813 Advanced Linear Programming 3(3,0)S Development of linear programming theory using inequality systems, convex cones, polyhedra and duality; solution algorithms, and computational considerations for large scale and special structured problems using techniques of upper bounded variables, decomposition, partitioning and column generation; game theory; nonlinear representations and other methods such as ellipsoid and Karmarkar. Preq: MTHSC 440, 810 or equivalent.
MTHSC 814 Network Flow Programming 3(3,0)F Max-flow/min-cut theorem, combinatorial applications, minimum cost flow problems (transportation, shortest path, transshipment), solution algorithms (including the out-of-kilter), and implementation and computational considerations. Preq: MTHSC 440, 810 or equivalent.
MTHSC 816 Network Algorithms and Data Structures 3(3,0)F Design, analysis, and implementation of algorithms and data structures associated with the solution of problems formulated as networks and graphs; applications to graph theory, combinatorial optimization, and network programming. Coreq: MTHSC 640, 810, 854, 863 or consent of instructor.
MTHSC 817 Stochastic Models in Operations Research I 3(3,0)F Stochastic control; structure of sequential decision processes; stochastic inventory models; recursive computation of optimal policies; discrete parameter finite Markov decision processes; various optimality criteria; computation by policy improvement and other methods; existence of optimal stationary policies; stopping-rule problems; examples from financial management, maintenance and reliability, search, queuing, and shortest path. Preq: MTHSC 803.
MTHSC 818 Stochastic Models in Operations Research II 3(3,0)S Introduction to queuing theory: Markovian queues, repairman problems, queues with an embedded Markov structure, the queue GI/G/1, queues with a large number of servers, decision making in queues; introduction to reliability theory; failure distributions; stochastic models for complex systems; maintenance and replacement policies; reliability properties of multicomponent structures. Preq: MTHSC 817.
MTHSC 819 Multicriteria Optimization 3(3,0)S Theory and methodology of optimization problems with vector-valued objective functions; preference orders and domination structures; generating efficient solutions; solving multicriteria decision-making problems; noninteractive and interactive methods with applications. Preq: MTHSC 810 or equivalent.
MTHSC 820 Complementarity Models 3(3,0)S Theory, algorithms, and applications of linear and nonlinear complementarity; classes of matrices and functions and corresponding algorithms; applications to economics, mechanics, and networks; generalizations to fixed-point problems and nonlinear systems of equations. Preq: MTHSC 810.
MTHSC 821 Linear Analysis 3(3,0)S,SS Normed spaces; Hilbert spaces, Banach spaces, linear functionals, linear operators, orthogonal systems. Preq: MTHSC 454 or 453 and 853.
MTHSC 822 Measure and Integration 3(3,0)F Rings and algebras of sets, inner and outer measures; measurability and additivity, examples on the line and in space, Lebesgue integration, types of convergence, Lebesgue spaces; integration and differentiation, product measure, Fubini theorem. Preq: MTHSC 454.
MTHSC 823 Complex Analysis 3(3,0) Topological concepts; complex integration; local and global properties of analytic functions; power series; representation theorems; calculus of residues. Designed for nonengineering majors. Preq: MTHSC 464.
MTHSC 825 Introduction to Dynamical Systems Theory 3(3,0)F Techniques of analysis of dynamical systems; sensitivity analysis, linear systems, stability, and control; theory of differential and difference equations. Preq: MTHSC 454 and 311 or 453 and 853.
MTHSC 826 Partial Differential Equations 3(3,0)F First-order equations: elliptic, hyperbolic, and parabolic. Second-order equations: existence and uniqueness results, maximum principles, finite difference, and Hilbert Space methods. Preq: MTHSC 821 or consent of instructor.
MTHSC 827 Dynamical System Neural Networks 3(3,0) Modeling problems in the context of dynamical systems theory; useful methods from Lyapunov stability, local linearization, qualitative analysis using graph theory and numerical approximations; several dynamical systems neural networks including binary code recognizers and binary matrix choosers. Preq: MTHSC 206, 311.
MTHSC 831 Fourier Series 3(3,0)SS Fourier series with applications to solution of boundary value problems in partial differential equations of physics and engineering. Introduction to Bessel functions and Legendre polynominals. Preq: MTHSC 464.
MTHSC 837 Calculus of Variations and Optimal Control 3(3,0)SS Fundamental theory of the calculus of variations; variable end points; the parametric problem; the isoperimetric problem; constraint inequalities; introduction to the theory of optimal control; connections with the calculus of variations; geometric concepts. Preq: MTHSC 453 or 463.
MTHSC 841 Applied Mathematics I 3(3,0)F Derivation of equations from conservation laws, dimensional analysis, scaling and simplification; methods such as steepest descent, stationary phase, perturbation series, boundary layer theory, WKB theory, multiple-scale analysis, and ray theory applied to problems in diffusion processes, wave propagation, fluid dynamics, and mechanics. Preq: MTHSC 208 and 453 or 463.
MTHSC 842 Applied Mathematics II 3(3,0) Continuation of MTHSC 841.
MTHSC 851 Abstract Algebra I 3(3,0)S Basic algebraic structures: groups, rings, and fields; permutation groups, Sylow theorems, finite albelian groups, polynomial domains, factorization theory, and elementary field theory.
MTHSC 852 Abstract Algebra II 3(3,0)F Continuation of MTHSC 851 including selected topics from ring theory and field theory.
MTHSC 853 Matrix Analysis 3(3,0) Topics in matrix analysis that support an applied curriculum: similarity and eigenvalues; Hermitian and normal matrices; canonical forms; norms; eigenvalue localizations; singular value decompositions; definite matrices. Preq: MTHSC 311, 453 or 463.
MTHSC 854 Theory of Graphs 3(3,0)S Connectedness; path problems; trees; matching theorems; directed graphs; fundamental numbers of the theory of graphs; groups and graphs. Preq: Consent of instructor.
MTHSC 855 Combinatorial Analysis 3(3,0)F Combinations; permutations; permutations with restricted position; Polya's theorem; principle of inclusion and exclusion; partitions; recurrence relations; generating functions; Mobius inversion; enumeration techniques; Ramsey numbers; finite projective and affine geometries; Latin rectangles; orthogonal arrays; block designs; error detecting and error correcting codes. Preq: MTHSC 311.
MTHSC 856 Applicable Algebra 3(3,0)S Applied algebraic ideas in lattice theory and Boolean Algebra; finite-state sequential machines; group theory as applied to network complexity and combinatorial enumeration; algebraic coding theory. Topics vary with background and interests of students. Preq: MTHSC 851 and 853 or consent of instructor.
MTHSC 860 Introduction to Scientific Computing 3(3,0)S,SS Floating point models, conditioning and numerical stability, numerical linear algebra, integration, systems of ordinary differential equations and zero finding; emphasis is on the use of existing scientific software. Preq: CP SC 110, MTHSC 208, 311.
MTHSC 861 Advanced Numerical Analysis I 3(3,0)F Interpolation and approximation; numerical quadrature; numerical solution of functional differential equations; integral equations and overdetermined linear systems; eigenvalue problems; approximation using splines. Preq: MTHSC 453, 460.
MTHSC 863 Digital Models I 3(3,0)F Experimental mathematics; pseudo-stochastic processes; analytical and algebraic formulations of time-independent simulation; continuous-time simulation and discrete-time simulation; digital optimization; Fibonacci search; ravine search; gradient methods; current research in digital analysis. Preq: MTHSC 311, 453, digital computer experience.
MTHSC 865 Data Structures 3(3,0)F Representation and transformation of information; formal description of processes and data structures; tree and list structures; pushdown stacks; string and formula manipulation; hashing techniques; interrelation between data structure and program structure; storage allocation methods. Preq: Computational maturity, consent of instructor.
MTHSC 881 Mathematical Statistics 3(3,0)S Fundamental concepts of sufficiency, hypothesis testing and estimation; robust estimation; resam-pling (jackknife, bootstrap, etc.) methods; asymptotic theory; two-stage and sequential sampling problems; ranking and selection procedures. Preq: MTHSC 403 or equivalent.
MTHSC 884 Statistics for Experimenters 3(3,0) Statistical methods for students who are conducting experiments; introduction to descriptive statistics, estimation, and hypothesis testing as they relate to design of experiments; higher-order layouts, factorial and fractional factorial designs, and response surface models. Preq: MTHSC 206 or equivalent.
MTHSC 885 Advanced Data Analysis 3(3,0)F Continuation of MTHSC 805 covering alternatives to ordinary least squares, influence and diagnostic considerations, robustness, special statistical computation methods. Preq: MTHSC 603, 800, 805.
MTHSC 891 Master's Thesis Research 1-12
MTHSC 892 Master's Project Course 1(0,1) For students in the nonthesis option of the MS degree program in the Mathematical Sciences. Successful completion includes a presentation of the master's project to the student's advisory committee and acceptance of the paper by the committee.
MTHSC 900 Seminar in Preparing for College Teaching in the Mathematical Sciences 3(3,0)N Elements involved in being a college professor with emphasis on broadening the student's mathematical experiences within a framework of improving classroom performance. Preq: Completion of the departmental PhD qualifying examinations.
MTHSC 901 Probability Theory I 3(3,0)N Axiomatic theory of probability; distribution functions; expectation; Cartesian product of infinitely many probability spaces, and the Kolmogorov consistency theorem; models of convergence; weak and strong laws of large numbers. Preq: MTHSC 400 and 822, or MTHSC 800 and 822 or consent of instructor.
MTHSC 902 Probability Theory II 3(3,0)N Continuation of MTHSC 901; characteristic functions, infinitely divisible distributions, central limit theorems, laws of large numbers, conditioning, and limit properties of sums of dependent random variables, conditioning, martingales. Preq: MTHSC 901.
MTHSC 927 Functional Analysis 3(3,0)N Linear operators on specific spaces, spectral theory, semigroups of operators and the Hille-Yosida theorem, applications of linear spaces and operators, convexity. Preq: MTHSC 821.
MTHSC 954 Advanced Graph Theory 3(3,0)F Continuation of MTHSC 854 including the four-color theorem, domination numbers, Ramsey theory, graph isomorphism, embeddings, algebraic graph theory, and tournaments. Research papers are also examined. Preq: MTHSC 854 or consent of instructor.
MTHSC 970 Directed Studies in Mathematical Sciences 1-3(1-3,0) Directed individual studies on topics in the mathematical sciences supervised by faculty. May be repeated for a maximum of 18 credits. Preq: Consent of instructor.
MTHSC 974 Selected Topics in Mathematical Sciences 3(3,0) Advanced topics in the mathematical sciences from current areas of interest presented in lecture format. May be repeated for a maximum 24 credits, but only if different topics are covered. Preq: Consent of instructor.
MTHSC 981 Selected Topics in Mathematical Statistics and Probability 1-3(1-3,0) Advanced topics in mathematical statistics and probability of current interest. May be repeated for credit, but only if different topics are covered.
MTHSC 982 Selected Topics in Analysis 1-3(1-3,0) Advanced analysis topics from current problems of interest. May be repeated for credit, but only if different topics are covered.
MTHSC 983 Selected Topics in Computational Mathematics 1-3(1-3,0) Advanced topics in computational mathematics and numerical analysis from current problems of interest. May be repeated for credit, but only if different topics are covered.
MTHSC 985 Selected Topics in Algebra and Combinatorics 1-3(1-3,0) Advanced topics in algebra and combinatorics from current problems of interest. May be repeated for credit, but only if different topics are covered.
MTHSC 986 Selected Topics in Geometry 1-3(1-3,0) Advanced topics in geometry from current problems of interest. May be repeated for credit, but only if different topics are covered.
MTHSC 988 Selected Topics in Operations Research 1-3(1-3,0) Advanced topics in operations research from current problems of interest. May be repeated for credit, but only if different topics are covered.
MTHSC 989 Selected Topics in Mathematical Education 3(3,0) Advanced topics in the mathematical sciences from the area of mathematics education. May be repeated for credit, but only if different topics are covered. Preq: Consent of instructor.
MTHSC 991 Doctoral Dissertation Research 1-12