Mathematics Course Catalog

Also available: Department of Mathematics courses offered this semester and the Schedule of Courses. The authoritative source for course information is the Marshall University Catalog.

MTH 98 - 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 99 - 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 101 - Introduction to the Graphing Calculator

Getting started, menus, syntax, order of operations, evaluating functions, solving equations, graphing, plotting data, finding best fit approximations, performing matrix operations, and solving linear systems.
1 hour.

MTH 104 - Spreadsheets for Mathematics

Spreadsheet skills useful in mathematics. Data entry, entering and applying formulas, charts/graphs, elementary statistics, formatting output.
1 hour.

MTH 106 - Intro to Computer Algebra Systems

A survey of computer algebra techniques including entering data, algebraic manipulations, solving equations, graphing, calculus applications, elementary programming, and statistics.
1 hour.

MTH 121 - Concepts and Applications of Mathematics (CT)

Critical thinking course for non-science majors that develops quantitative reasoning skills. Topics include logical thinking, problem-solving, 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 non-science 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 Sci Applica

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 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 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 vector-valued functions. PR: MTH230.
4 hours.

MTH 280-283 - 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 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: MTH300.
4 hours.

MTH 335 - Differential Equations

First and second-order 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 400 - Structure of Algebra

Informal development of modern elementary algebra. Recommended for pre-service middle school teachers and for elementary and secondary in-service teachers. May not be used for either a 5-12 mathematics specialization or for a degree offered by the Department of Mathematics. PR: MTH130.
3 hours.

MTH 401 - Structure 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 in-service teachers. May not be used for either a 5-12 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 content-specific 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 real-world 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 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 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 Box-Jenkins procedures. PR: MTH230.
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 point-set 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 480-483 - Special Topics

Courses on special topics not listed among the current course offerings. PR: Permission of instructor.
1 to 4 hours.

MTH 485-488 - 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 pre-service middle school teachers and for elementary and secondary in-service teachers. May not be used for a 5-Adult (or 5-12) 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 pre-service middle school teachers and for elementary and secondary in-service teachers. May not be used for a 5-Adult (or 5-12) mathematics specialization. May not be used for any degree offered by the Department of Mathematics.
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 519 - Forensic Statistics

Basic theory of probability and statistics, odds from Bayes' theorem for transfer evidence, likelihood ratio, population and statistical genetics, statistical issues in paternity testing and mixtures, and presenting evidence. May not be used for any degree offered by the Department of Mathematics. PR: Admission to the M.S. program in Forensic Science.
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 540 - Graph Theory/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 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 580-583 - Special Topics

Courses on special topics not listed among the current course offerings. PR: Permission of instructor.
1 to 4 hours.

MTH 585-588 - 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 first-year course in modern algebra. PR: MTH552.
3 hours.

MTH 613 - Mathematical Modeling

Students will work in teams to construct mathematical models of various real-world 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 (maximum-liklihood and liklihood-ratio 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 Box-Jenkins 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 690-693 - Special Topics

Courses on special topics not listed among the current course offerings. PR: Permission of instructor.
1 to 4 hours.