Mathematics Course Catalog
Also available: Department of Mathematics courses offered this semester and the
Schedule of Courses.
Schedules are also available showing when
upperdivision undergraduate
and graduate courses are planned for future semesters.
The authoritative source for course information is the Marshall University Catalog.
 MTH 098  Basic Skills in Mathematics I
 This course prepares students with low placement scores for the second level of the mathematics skills sequence. PR: ACT Math <17.
3 hours
 MTH 099  Basic Skills in Mathematics II
 The purpose of this course is to adequately prepare students with low placement test scores to take college level mathematics course required in their progam of study. PR: ACT Math 17 or ACT Math 18 or MTH098.
3 hours
 MTH 121  Concepts and Applications of Mathematics (CT)
 Critical thinking course for nonscience majors that develops quantitative reasoning skills. Topics include logical thinking, problemsolving, linear modeling, beginning statistics and probability, exponential and logarithmic models, formula use, and financial concepts. PR: ACT Math 19 or MTH099.
3 hours
 MTH 122  Plane Trigonometry
 A study of the trigonometric functions, graphs of the trigonometric functions, identities, equations, inverse trigonometric functions, vectors, complex numbers, and applications. PR: ACT Math 21 or MTH127 or MTH130.
3 hours
 MTH 125  Mathematical Thinking (CT)
 A critical thinking course for nonscience majors. Topics include number systems, sequences, modular arithmetic, deductive arguments, linear programming, techniques of problem solving, and history of mathematics. PR: ACT Math 19 or MTH099.
3 hours
 MTH 127  College Algebra  Expanded Version
 A brief but careful review of the main techniques of algebra. Polynomial, rational, exponential, and logarithmic functions. Graphs, equations and inequalities, sequences. PR: ACT Math 19 or ACT Math 20 or MTH099.
5 hours
 MTH 130  College Algebra
 Polynomial, rational, exponential, and logarithmic functions. Graphs, equations and inequalities, sequences. PR: ACT Math 21.
3 hours
 MTH 132  Precalculus with Science Applications
 Functions used in calculus including polynomial, rational, exponential, logarithmic, and trigonometric. Systems of equations and inequalities, conic sections, polar and parametric equations, sequences and series, Binomial Theorem. PR: ACT Math 24 or MTH127 or MTH130.
5 hours
 MTH 140  Applied Calculus
 A brief survey of calculus including both differentiation and
integration with applications. Not to be substituted for Mathematics
229. PR: ACT Math 24 or MTH127 or MTH130.
3 hours
 MTH 140H  Applied Calculus Honors
 A brief survey of
calculus including both differentiation and integration with
applications. This honors course will also introduce topics from
differential equations with applications.
PR: ACT Math 25 or MTH127 or MTH130.
3 hours
 MTH 160  Applied Mathematical Reasoning
 A critical thinking course in applied mathematical reasoning. Topics
include logic, problem solving, linear modeling, beginning statistics
and probability, exponential and logarithmic modeling, formula use.
PR: ACT Math 19 or MTH 099.
5 hours
 MTH 220  Discrete Structures
 Sets, relations, directed and undirected graphs, monoids, groups, lattices, Boolean algebra, and propositional logic.
PR: ACT Math 27 or MTH132 or MTH229 or IST131.
3 hours
 MTH 225  Introductory Statistics
 Basic probability, descriptive statistics, fundamental statistical inference procedures involving estimation and hypothesis testing for a variety of situations with wide applications. PR: ACT Math 21 or MTH121 or higher.
3 hours
 MTH 229  Calculus with Analytic Geometry I (CT)
 An introduction to calculus and analytic geometry, emphasizing critical thinking. Limits, derivatives, and integrals of the elementary functions of one variable, including transcendental functions. PR: ACT Math 27 or MTH 132.
5 hours
 MTH 229H  Calculus with Analytic Geometry I (Honors) (CT)

An introduction to calculus and analytic geometry for honors students, emphasizing critical thinking. Limits, derivatives, and integrals of the
elementary functions of one variable, including transcendental functions.
PR: ACT Math 27 or MTH 132.
5 hours
 MTH 230  Calculus with Analytic Geometry II
 Applications of the integral, techniques of integration, and infinite series. A study of conic sections, polar coordinates, and parametric equations. PR: MTH229 or IST230.
4 hours
 MTH 231  Calculus with Analytic Geometry III
 Vectors, curves, and surfaces in space. Derivatives and integrals of functions of more than one variable. A study of the calculus of vectorvalued functions. PR: MTH230.
4 hours
 MTH 280283  Special Topics
 Courses on special topics not listed among the current course offerings. PR: Permission of instructor.
1 to 4 hours
 MTH 300  Introduction to Higher Mathematics
 A transition between elementary calculus and higher mathematics with emphasis on techniques of proofs. PR: MTH230.
4 hours
 MTH 326  Applied Statistical Methods
 Use of statistical
packages; introduction to descriptive, probability and sampling
distributions; forecasting, inferences concerning one and two samples;
simple and multiple regression, analysis of variance and covariance.
PR: C or better in MTH 225.
3 hours
 MTH 329  Elementary Linear Algebra
 Systems of linear equations, matrices and determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and applications. PR: ACT Math 27 or MTH132 or MTH229 or IST131.
3 hours
 MTH 331  Linear Algebra
 Vector spaces, matrices and determinants, linear transformations,
eigenvalues and eigenvectors, and applications. PR or CR: MTH300.
4
hours
 MTH 335  Differential Equations
 First and secondorder ordinary differential equations. Applications include vibrations and electrical circuits. Laplace transform, approximate solutions, orthogonal functions, Fourier series; partial differential equations including heat, wave, and Laplace equations. PR: MTH231.
4 hours
 MTH 345  Applied Probability and Statistics
 Statistical methods in scientific/engineering research, with
emphasis on applications. Probability modeling, experimental
design/survey sampling, estimation/hypothesis testing procedures,
regression, ANOVA/factor analysis. Implementation using statistical
software such as Excel/SAS. PR: MTH230 or IST230.
3
hours
 MTH 360  Introduction to Complex Variables
 An introductory survey of complex numbers, analytic functions,
properties of elementary functions, integrals, series, residues and
poles, with a focus on practical applications. PR: MTH 231
3 hours
 MTH 361  Vector Calculus
 A course in ndimensional calculus: the derivative, the integral,
and applications. Coordinatefree methods are emphasized. PR: MTH 231.
3 hours
 MTH 400  Structure of Algebra
 Informal development of modern elementary algebra. Recommended for preservice middle school teachers and for elementary and secondary inservice teachers. May not be used for either a 512 mathematics specialization or for a degree offered by the Department of Mathematics. PR: MTH130.
3 hours
 MTH 401  Structure of Modern Geometry
 Informal development of geometry with an exploration of probability and statistics. Recommended for pre service middle school teachers and for elementary and secondary inservice teachers. May not be used for either a 512 mathematics specialization or for a degree offered by the Department of Mathematics. PR: MTH130 or MTH127.
3 hours
 MTH 404  Mathematics Methods and Materials
 Content and contentspecific pedagogy for secondary mathematics education majors. PR: CI470 and Admitted to Teacher ED 5.
3 hours
 MTH 405  History of Mathematics
 A study of the history of mathematics from the time of the ancient Greeks to the end of the nineteenth century. PR: MTH300.
3 hours
 MTH 411  Mathematical Modeling
 Students work in teams to
construct mathematical models of various realworld situations. Problems
to be modeled are drawn from diverse areas of application and use a wide
range of undergraduate mathematics. PR: MTH231.
3
hours
 MTH 412  Regression Analysis
 Topics in determining
regression models; deriving parameter estimates using calculus; detailed
coverage of tests of assumptions and remedial procedures
(transformations and weighted least squares); multiple and polynomial
regression; tests and corrections for autocorrelation. PR: One previous
course in statistics and some familiarity with calculus and linear
algebra, or permission of instructor.
3 hours
 MTH 413  Experimental Designs
 Principles of experimentation; analysis of variance and covariance; latin square and related designs; factorial designs, response surface; robustness;
nested and splitplot designs. PR: One previous course in statistics and some familiarity with calculus and linear algebra, or permission of instructor
3 hours
 MTH 415  Partial Differential Equations
 Elementary partial
differential equations. Heat Equation, Laplace's Equation, separation of
variables, Fourier series, vibrating strings, eigenvalue problems,
finite differences, Bessel functions, Legendre polynomials. PR: MTH331
and MTH335.
3 hours
 MTH 416  Advanced Differential Equations
 Differential equations are studied qualitatively. Topics include the existence and uniqueness of solutions and the behavior of solutions including stability of nonlinear systems, periodic solutions, and approximation using pertubation methods. PR: MTH300 and MTH335.
3 hours
 MTH 420  Nonparametric Methods
 Coverage of a variety of
nonparametric or distributionfree methods for practical statistical
inference problems in hypothesis testing and estimation, including
rank procedures and randomization procedures. PR: One previous course
in statistics and some familiarity with calculus and linear algebra, or
permission of instructor
3 hours
 MTH 422  Appl Time Series Analysis
 Finding statistical models to represent various time dependent phenomena and processes; coverage of a variety of forecasting techniques, with an emphasis on adaptive, regression, and BoxJenkins procedures. PR: MTH230.
3 hours
 MTH 425  Sampling Design and Estimation
 Coverage of the
theory and applications of a variety of sampling designs, sample size
determination; ration and regression estimated comparisons among the
designs. PR: MTH 326 or permission of instructor
3 hours
 MTH 427  Advanced Calculus I
 A rigorous study of the real number system, continuity and differentiability of functions of a single variable, integration of functions of a single variable, infinite series. PR: MTH231 and MTH300. CR: MTH331.
3 hours
 MTH 428  Advanced Calculus II
 A rigorous development of algebra and topology of Euclidean spaces, differentiability and integrability of functions of several variables. PR: MTH427.
3 hours
 MTH 430  Topology I
 First course in topology. Basics of pointset topology: metric and topological spaces, continuity, connectedness, compactness, products, quotients. Surfaces and simplicial complexes, Euler characteristics. PR: MTH300.
3 hours
 MTH 431  Topology II
 First course in algebraic topology. Homotopy, fundamental group, simplicial homology. PR: MTH430 and MTH450.
3 hours
 MTH 440  Graph Theory and Combinatorics
 This course is designed to introduce students in mathematical sciences to the theorems, techniques, and applications of graph theory and combinatorics. PR: MTH300.
3 hours
 MTH 442  Numerical Linear Algebra
 Direct and iterative methods for numerical solution of linear systems of equations. Eigenvalues and eigenvectors. Error Analysis and norms. Related topics and applications. PR: MTH331.
3 hours
 MTH 443  Numerical Analysis
 Computer arithmetic, roots of equations, interpolation, linear systems, and numerical differentiation and integration. Analysis of errors in and convergence properties of algorithms. Computer implementation of methods. PR: MTH331 and a programming language.
3 hours
 MTH 445  Probability & Statistics I
 Probability spaces, conditional probability, and applications. Random variables, distributions, expectation, and moments. PR: MTH231.
3 hours
 MTH 446  Probability & Statistics II
 Statistical inference: estimation of parameters, tests of hypotheses. Regression, analysis of variance. PR: MTH445.
3 hours
 MTH 448  Modern Geometries
 Finite geometrics, basic background material for the modern development of Euclidean Geometry, other geometries. PR: MTH300.
3 hours
 MTH 449  Projective Geometry
 Projective Geometry using both synthetic and algebraic methods. PR: MTH300.
3 hours
 MTH 450  Modern Algebra I
 Structure of the abstract mathematical systems; groups, rings, fields, with illustrations and applications from number theory. PR: MTH300 and MTH331.
3 hours
 MTH 452  Modern Algebra II
 Continuation of MTH 450. PR: MTH450.
3 hours
 MTH 455  Number Theory
 A survey of some basic properties of the integers: divisibility (prime numbers, factorization, perfect numbers), congruences (modular arithmetic, linear and quadratic congruences, the Chinese Remainder Theorem), and Diophantine equations. PR: MTH300.
3 hours
 MTH 460  Complex Variables I
 Complex numbers, analytic functions, properties of elementary functions, integrals, series, residues and poles, conformal mapping. PR: MTH231.
3 hours
 MTH 461  Complex Variables II
 Continuation of MTH 460. PR: MTH460.
3 hours
 MTH 464  Statistical Computing
 Introduction to the
commonly used statistical computing techniques, procedure and methods,
with extensive use of R language and environment, and SAS for
statistical computing and graphics. PR: MTH 445 or MTH 446
3
hours
 MTH 466  Stochastic Processes
 Review of probability theory.
Topics include stationary processes, discrete and continuous time Markov
chains, Markovian queueing systems, random walks, renewal processes,
Brownian motion and Markov Chain Monte Carlo. PR: MTH 231 and MTH 445
3 hours
 MTH 480483  Special Topics
 Courses on special topics not
listed among the current course offerings. PR: Permission of instructor.
1 to 4 hours
 MTH 485488  Independent Study
 An independent program of study of advanced topics not normally covered in other courses. The topics are chosen upon mutual agreement between the student and the instructor. PR: Permission of instructor.
1 to 4 hours
 MTH 491  Senior Seminar
 Capstone experience in reading, doing, writing and speaking mathematics. Students will explore topics related to a theme chosen by the instructor.
2 hours
 MTH 500  Structure of Algebra
 Informal development of modern elementary algebra. Recommended for preservice middle school teachers and for elementary and secondary inservice teachers. May not be used for a 5Adult (or 512) mathematics specialization. May not be used for any degree offered by the Department of Mathematics.
3 hours
 MTH 501  Structure Modern Geometry
 Informal development of geometry with an exploration of probability and statistics. Recommended for preservice middle school teachers and for elementary and secondary inservice teachers. May not be used for a 5Adult (or 512) mathematics specialization. May not be used for any degree offered by the Department of Mathematics.
3 hours
 MTH 512  Regression Analysis

Determining regression models; deriving parameter estimates using calculus; detailed coverage of tests of assumptions and remedial procedures
(transformations and weighted leastsquares); multiple and polynomial regression; tests and corrections for autocorrelation.
3 hours
 MTH 513  Experimental Designs


Analysis of variance and covariance models with derivations using calculus; detailed testing of model assumptions and remedial measures (as
transformations) to yield adequate models; use of various statistical designs.
3 hours
 MTH 518  Biostatistics
 Statistical skills for
biological/biomedical research, with emphasis on applications.
Experimental design/survey sampling, estimation/hypothesis testing
procedures, regression, ANOVA, multiple comparisons. Implementation
using statistical software such as SAS, BMDP.
3
hours
 MTH 520  Nonparametric Statistics
 Coverage of a variety
of nonparametric or distributionfree methods for practical statistical
inference problems in hypothesis testing and estimation, including rank
procedures and randomization procedures.
3 hours
 MTH 527  Advanced Calculus I
 A rigorous study of the real number system, continuity and differentiability of functions of a single variable, integration of functions of a single variable, infinite series.
3 hours
 MTH 528  Advanced Calculus II
 A rigorous development of algebra and topology of Euclidean spaces, differentiability and integrability of functions of several variables. PR: MTH527.
3 hours
 MTH 545  Probability and Statistics I
 Probability spaces, conditional probability, and applications. Random variables, distributions, expectation, and moments.
3 hours
 MTH 546  Probability and Statistics II
 Parametric statistics: sampling methods, estimation of parameters, tests of hypotheses. Regression, analysis of variance. PR: MTH545.
3 hours
 MTH 548  Modern Geometries
 Finite geometrics, basic background material for the modern development of Euclidean Geometry, other geometries.
3 hours
 MTH 549  Projective Geometry
 Projective geometry using both synthetic and algebraic methods.
3 hours
 MTH 550  Modern Algebra I
 Structure of the abstract mathematical systems; groups, rings, fields, with illustrations and applications from Number Theory.
3 hours
 MTH 552  Modern Algebra II
 Continuation of MTH550. PR: MTH550.
3 hours
 MTH 580583  Special Topics
 Courses on special topics not listed among the current course offerings. PR: Permission of instructor.
1 to 4 hours
 MTH 585588  Independent Study
 PR: Permission of instructor.
1 to 4 hours
 MTH 589  TA Seminar
 An introduction to techniques of teaching mathematics with emphasis on lower level mathematics courses. PR: Assignment to teach as a teaching assistant.
1 hour
 MTH 610  Advanced Modern Algebra
 Advanced topics in algebraic structures, applications, and related topics beyond a firstyear course in modern algebra. PR: MTH552.
3 hours
 MTH 613  Mathematical Modeling
 Students will work in teams to construct mathematical models of various realworld situations. Problems to be modeled will be drawn from diverse areas of application and will use a wide range of undergraduate mathematics.
3 hours
 MTH 615  Partial Differential Equations
 Elementary partial differential equations. Heat equation, Laplace's equation, separation of variables, Fourier series, vibrating strings, eigenvalue problems, finite differences, Bessel functions, Legendre polynomials.
3 hours
 MTH 616  Advanced Differential Equations
 Differential equations are studied qualitatively. Topics include the existence and uniqueness of solutions and the behavior of solutions including the stability of nonlinear systems, periodic solutions, and approximation using perturbation methods.
3 hours
 MTH 630  Topology I
 General topology including separation axioms, connectedness, compactness, convergence, continuity, metric spaces, product and quotient spaces.
3 hours
 MTH 631  Topology II
 First course in algebraic topology. Homotopy, fundamental group, simplicial homology. PR: MTH550 and MTH630.
3 hours
 MTH 632  Advanced Topology
 Advanced topics in topology, applications, and related topics beyond a first year course in topology. PR: MTH631.
3 hours
 MTH 635  Graph Theory and Combinatorics
 The course is designed to introduce students in mathematical sciences to the theorems, techniques and applications of graph theory and combinatorics.
3 hours
 MTH 640  Complex Variables I
 Complex numbers, analytic functions, properties of elementary functions, integrals, series, residues and poles, conformal mapping. PR: MTH527.
3 hours
 MTH 641  Complex Variables II
 Continuation of MTH640. PR: MTH640.
3 hours
 MTH 642  Numerical Linear Algebra
 Direct and iterative methods for numerical solution of linear systems of equations. Eigenvalues and eigenvectors. Error Analysis and norms. Related topics. PR: MTH643.
3 hours
 MTH 643  Numerical Analysis
 The theory and technique of numerical computation involving the difference calculus, the summation calculus, interpolation methods, solutions of equations, and methods of solution of ordinary differential equations.
3 hours
 MTH 650  Real Variables I
 A study of measure and integration and related topics. PR: MTH528.
3 hours
 MTH 651  Real Variables II
 Continuation of MTH650. PR: MTH650.
3 hours
 MTH 655  Number Theory
 A survey of some basic properties of the integers: divisibility (prime numbers, factorization,perfect numbers), congruences (modular arithmetic, linear and quadratic congruences, the Chinese Remainder Theorem), and Diophantine equations.
3 hours
 MTH 660  Stochastic Processes
 Theory and applications of Markov chains. PR: MTH545.
3 hours
 MTH 661  Advanced Mathematical Statistics
 Topics in mathematical statistics including distribution theory for functions of random variables, covergence concepts, sufficient statistics, finding optimal estimates for parameters, optimal tests of hypotheses. PR: MTH546.
3 hours
 MTH 662  Multivariate Mathematical Statistics
 Multivariate distribution theory and statistical inference including estimation and tests concerning mean vectors and covariance matrices (maximumliklihood and liklihoodratio techniques emphasized). PR: MTH545.
3 hours
 MTH 663  Time Series Forecasting
 Finding statistical models to represent various time dependent phenomena and processes; coverage of a variety of forecasting techniques, with an emphasis on adaptive, regression, and BoxJenkins procedures.
3 hours
 MTH 667  Numerical Partial Differential Equations
 Finite difference methods for elliptic, parabolic, and hyperbolic PDEs. Study of properties such as consistency, convergence, and stability. Computer implementation. PR: MTH527.
3 hours
 MTH 670  Independent Study
 An independent program of study of advanced topics not normally covered in other courses. The topics are chosen upon mutual agreement between the student and the instructor. PR: Permission of instructor.
1 to 4 hours
 MTH 681  Thesis
 Graduate students have the option of including a thesis in their program of study.
1 to 6 hours
 MTH 690693  Special Topics
 Courses on special topics not listed among the current course offerings. PR: Permission of instructor.
1 to 4 hours