General Course Syllabi

Mathematics Course Catalog

Also available: Department of Mathematics courses offered this semester and the Schedule of Courses. Schedules are also available showing when upper-division undergraduate and graduate courses are planned for future semesters. The authoritative source for course information is the Marshall University Catalog.

100-level courses

MTH 100 - Preparation for College Mathematics A
A mastery-based 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 mastery-based 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 mastery-based 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 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
General syllabus for MTH 121
MTH 121B - Concepts and Applications of Mathematics with Algebra Review (CT)
A quantitative reasoning skills course for non-science 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 17-18 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 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 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

200-level 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 vector-valued functions.
PR: MTH230.
4 hours
General syllabus for MTH 231
MTH 280-283 - Special Topics
Courses on special topics not listed among the current course offerings.
PR: Permission of instructor.
1 to 4 hours

300-level 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 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
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 n-dimensional calculus: the derivative, the integral, and applications. Coordinate-free methods are emphasized.
PR: MTH 231.
3 hours
General syllabus for MTH 361

400-level courses

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
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 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
General syllabus for MTH 401
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
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 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
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 split-plot 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 distribution-free 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 Box-Jenkins 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 point-set 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 non-parametric methods, models and inferences for survival data, and regression diagnosis.
PR: 445, or permission.
3 hours
General syllabus for MTH 470
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 490 - Internship
A supervised internship in an area of mathematics, applied mathematics, or statistics. By permission only.
PR: MTH 300 and permission
2-12 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 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
General syllabus for MTH 500
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
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 least-squares); 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 distribution-free 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 non-parametric 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 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 - Graduate Mathematics Seminar
A seminar on topics relevant to graduate students in mathematics, including college-level 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 first-year 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 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
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 (maximum-liklihood and liklihood-ratio 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 Box-Jenkins 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 690-693 - Special Topics
Courses on special topics not listed among the current course offerings.
PR: Permission of instructor.
1 to 4 hours
 
 
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