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.
100level courses
 MTH 100  Preparation for College Mathematics A
 A masterybased course that will prepare students for quantitative
reasoning courses in their majors.
PR: Math ACT of 18 or below.
3 hours
General syllabus for MTH 100
 MTH 102  Preparation for College Mathematics B

A masterybased course that will prepare students for College Algebra.
PR: Math ACT of 18 or below.
4 hours
General syllabus for MTH 102
 MTH 102B  Abridged Preparaaton for College Mathematics B
 An abridged masterybased course that will prepare students for
College Algebra.
PR: MTH 100 or MTH 121 or MTH 121B; and permission of
the Math Department.
1 hour
General syllabus for MTH 102B
 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
General syllabus for MTH 121
 MTH 121B  Concepts and Applications of Mathematics with Algebra Review (CT)
 A quantitative reasoning skills course for nonscience majors. Topics
include logical thinking, problem solving strategies, beginning
statistics and probability, exponential and logarithms modeling, formula
use, with basic algebra review.
PR: ACT Math 1718 or MTH100.
4 hours
General syllabus for MTH 121B
 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
General syllabus for MTH 122
 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 or MTH100.
3 hours
General syllabus for MTH 125
 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 or MTH102.
5 hours
General syllabus for MTH 127
 MTH 130  College Algebra
 Polynomial, rational, exponential, and logarithmic functions. Graphs, equations and inequalities, sequences.
PR: ACT Math 21.
3 hours
General syllabus for MTH 130
 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
General syllabus for MTH 132
 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
General syllabus for MTH 140
 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
General syllabus for MTH 140H
 MTH 160  Applied Mathematical Reasoning (CT)
 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
General syllabus for MTH 160
200level courses
 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
General syllabus for MTH 220
 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
General syllabus for MTH 225
 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
General syllabus for MTH 229
 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 30
5 hours
General syllabus for MTH 229H
 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
General syllabus for MTH 230
 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
General syllabus for MTH 231
 MTH 280283  Special Topics
 Courses on special topics not listed among the current course offerings.
PR: Permission of instructor.
1 to 4
hours
300level courses
 MTH 300  Introduction to Higher Mathematics
 A transition between elementary calculus and higher mathematics with emphasis on techniques of proofs.
PR: MTH230.
4 hours
General syllabus for MTH 300
 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
General syllabus for MTH 326
 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
General syllabus for MTH 329
 MTH 331  Linear Algebra
 Vector spaces, matrices and determinants, linear transformations,
eigenvalues and eigenvectors, and applications.
PR or CR: MTH300.
4 hours
General syllabus for MTH 331
 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
General syllabus for MTH 335
 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
General syllabus for MTH 345
 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
General syllabus for MTH 360
 MTH 361  Vector Calculus
 A course in ndimensional calculus: the derivative, the integral,
and applications. Coordinatefree methods are emphasized.
PR: MTH 231.
3 hours
General syllabus for MTH 361
400level courses
 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
General syllabus for MTH 400
 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
General syllabus for MTH 401
 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
General syllabus for MTH 404
 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
General syllabus for MTH 405
 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
General syllabus for MTH 411
 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
General syllabus for MTH 412
 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
General syllabus for MTH 413
 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
General syllabus for MTH 415
 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
General syllabus for MTH 416
 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
General syllabus for MTH 420
 MTH 422  Applied 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 or permission.
3 hours
General syllabus for MTH 422
 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
General syllabus for MTH 425
 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
General syllabus for MTH 427
 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
General syllabus for MTH 428
 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
General syllabus for MTH 430
 MTH 431  Topology II
 First course in algebraic topology. Homotopy, fundamental group, simplicial homology.
PR: MTH430 and MTH450.
3 hours
General syllabus for MTH 431
 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
General syllabus for MTH 440
 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
General syllabus for MTH 442
 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
General syllabus for MTH 443
 MTH 445  Probability & Statistics I
 Probability spaces, conditional probability, and applications. Random variables, distributions, expectation, and moments.
PR: MTH231.
3 hours
General syllabus for MTH 445
 MTH 446  Probability & Statistics II
 Statistical inference: estimation of parameters, tests of hypotheses. Regression, analysis of variance.
PR: MTH445.
3 hours
General syllabus for MTH 446
 MTH 448  Modern Geometries
 Finite geometrics, basic background material for the modern development of Euclidean Geometry, other geometries.
PR: MTH300.
3 hours
General syllabus for MTH 448
 MTH 449  Projective Geometry
 Projective Geometry using both synthetic and algebraic methods.
PR: MTH300.
3 hours
General syllabus for MTH 449
 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
General syllabus for MTH 450
 MTH 452  Modern Algebra II
 Continuation of MTH 450.
PR: MTH450.
3 hours
General syllabus for MTH 452
 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
General syllabus for MTH 455
 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
General syllabus for MTH 464
 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
General syllabus for MTH 466
 MTH 470  Applied Survival Analysis

 Survival and hazard functions, parametric and nonparametric
methods, models and inferences for survival data, and regression
diagnosis.
PR: 445, or permission.
3 hours
General syllabus for MTH 470
 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 490  Internship

 A supervised internship in an area of mathematics, applied
mathematics, or statistics. By permission only.
PR: MTH 300 and permission
212 hours
General syllabus for MTH 490
 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
General syllabus for MTH 491
Graduate courses
 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
General syllabus for MTH 500
 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
General syllabus for MTH 501
 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
General syllabus for MTH 512
 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
General syllabus for MTH 513
 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. May not be used for
any degree offered by the Department of Mathematics.
3 hours
General syllabus for MTH 518
 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
General syllabus for MTH 520
 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
General syllabus for MTH 527
 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
General syllabus for MTH 528
 MTH 545  Probability and Statistics I
 Probability spaces, conditional probability, and applications. Random variables, distributions, expectation, and moments.
3 hours
General syllabus for MTH 545
 MTH 546  Probability and Statistics II
 Parametric statistics: sampling methods, estimation of parameters, tests of hypotheses. Regression, analysis of variance.
PR: MTH545.
3 hours
General syllabus for MTH 546
 MTH 548  Modern Geometries
 Finite geometrics, basic background material for the modern development of Euclidean Geometry, other geometries.
3 hours
General syllabus for MTH 548
 MTH 549  Projective Geometry
 Projective geometry using both synthetic and algebraic methods.
3 hours
General syllabus for MTH 549
 MTH 550  Modern Algebra I
 Structure of the abstract mathematical systems; groups, rings, fields, with illustrations and applications from Number Theory.
3 hours
General syllabus for MTH 550
 MTH 552  Modern Algebra II
 Continuation of MTH550.
PR: MTH550.
3 hours
General syllabus for MTH 552
 MTH 564  Statistical Computing
 Introduction to the commonly used statistical computing techniques, procedures and methods, with extensive use of R language and environment,
and SAS for statistical computing and graphics. (CR/PR: MTH 545 or MTH 546)
3 hours.
General syllabus for MTH 564
 MTH 570 Applied Survival Analysis
 Survival and hazard functions, parametric and nonparametric methods, models and inferences for survival data, proportional hazard, and regression
diagnosis.
3 hours.
PR: MTH 545, or permission
General syllabus for MTH 570
 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  Graduate Mathematics Seminar

A seminar on topics relevant to graduate students in mathematics, including collegelevel teaching, conducting research, professional ethics, and mathematics careers. This course does not satisfy any degree requirements.
1 hour
General syllabus for MTH 589
 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
General syllabus for MTH 610
 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
General syllabus for MTH 613
 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
General syllabus for MTH 615
 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
General syllabus for MTH 616
 MTH 630  Topology I
 General topology including separation axioms, connectedness, compactness, convergence, continuity, metric spaces, product and quotient spaces.
3 hours
General syllabus for MTH 630
 MTH 631  Topology II
 First course in algebraic topology. Homotopy, fundamental group, simplicial homology.
PR: MTH550 and MTH630.
3 hours
General syllabus for MTH 631
 MTH 632  Advanced Topology
 Advanced topics in topology, applications, and related topics beyond a first year course in topology.
PR: MTH631.
3 hours
General syllabus for MTH 632
 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
General syllabus for MTH 635
 MTH 640  Complex Variables I
 Complex numbers, analytic functions, properties of elementary functions, integrals, series, residues and poles, conformal mapping.
PR: MTH527.
3 hours
General syllabus for MTH 640
 MTH 641  Complex Variables II
 Continuation of MTH640.
PR: MTH640.
3 hours
General syllabus for MTH 641
 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
General syllabus for MTH 642
 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
General syllabus for MTH 643
 MTH 650  Real Variables I
 A study of measure and integration and related topics.
PR: MTH528.
3 hours
General syllabus for MTH 650
 MTH 651  Real Variables II
 Continuation of MTH650.
PR: MTH650.
3 hours
General syllabus for MTH 651
 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
General syllabus for MTH 655
 MTH 660  Stochastic Processes
 Theory and applications of Markov chains.
PR: MTH545.
3 hours
General syllabus for MTH 660
 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
General syllabus for MTH 661
 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
General syllabus for MTH 662
 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
General syllabus for MTH 663
 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
General syllabus for MTH 667
 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