Graduate Courses in Mathematics and Statistics

Below are listings for Graduate Courses offered through the Department of Mathematics. The authoritative source for course information is the Marshall University Catalog.

View the Mathematics Graduate Course Offering and Course Rotation (PDF) schedule for future semesters.

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500 Level Math Courses


600 Level Math Courses


 
 

500 Level Math 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 Credit 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 Credit Hours

STA 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 Credit Hours

STA 513 – Experimental Designs
Principles of experimentation; analysis of variance; Latin square and related designs; factorial designs, response surface; robustness; nested and split-plot designs.
3 Credit Hours

STA 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 Credit Hours

STA 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 Credit 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 Credit 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 Credit Hours

STA 545 – Probability and Statistics I
Probability spaces, conditional probability, and applications. Random variables, distributions, expectation, and moments.
3 Credit Hours

STA 546 – Probability and Statistics II
Parametric statistics: sampling methods, estimation of parameters, tests of hypotheses. Regression, analysis of variance.
PR: STA 545.
3 Credit Hours

MTH 548 – Modern Geometries
Finite geometrics, basic background material for the modern development of Euclidean Geometry, other geometries.
3 Credit Hours

MTH 549 – Projective Geometry
Projective geometry using both synthetic and algebraic methods.
3 Credit Hours

MTH 550 – Modern Algebra I
Structure of the abstract mathematical systems; groups, rings, fields, with illustrations and applications from number theory.
3 Credit Hours

MTH 552 – Modern Algebra II
Continuation of MTH 550.
PR: MTH 550.
3 Credit Hours

STA 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 Credit Hours

STA 570 Applied Survival Analysis
Survival and hazard functions, parametric and non-parametric methods, models and inferences for survival data, proportional hazard, and regression diagnosis.
PR: STA 545, or permission
3 Credit Hours


MTH 580-583 – Special Topics
Courses on special topics not listed among the current course offerings.
PR: Permission of instructor.
1 to 4 Credit Hours

MTH 585-588 – Independent Study
PR: Permission of instructor.
1 to 4 Credit 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 Credit Hours

 
 

600 Level Math Courses


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 Credit 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 Credit 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 Credit 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 Credit Hours

MTH 630 – Topology I
General topology including separation axioms, connectedness, compactness, convergence, continuity, metric spaces, product and quotient spaces.
3 Credit Hours

MTH 631 – Topology II
First course in algebraic topology. Homotopy, fundamental group, simplicial homology.
PR: MTH550 and MTH630.
3 Credit Hours

MTH 632 – Advanced Topology
Advanced topics in topology, applications, and related topics beyond a first year course in topology.
PR: MTH631.
3 Credit 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 Credit Hours

MTH 640 – Complex Variables I
Complex numbers, analytic functions, properties of elementary functions, integrals, series, residues and poles, conformal mapping.
PR: MTH527.
3 Credit Hours

MTH 641 – Complex Variables II
Continuation of MTH640.
PR: MTH640.
3 Credit 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 Credit 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 Credit Hours

MTH 650 – Real Variables I
A study of measure and integration and related topics.
PR: MTH528.
3 Credit Hours

MTH 651 – Real Variables II
Continuation of MTH650.
PR: MTH650.
3 Credit 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 Credit Hours

STA 660 – Stochastic Processes
Theory and applications of Markov chains.
PR: MTH545.
3 Credit Hours

STA 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 Credit Hours

STA 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 Credit Hours

STA 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 Credit 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 Credit 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 Credit Hours

MTH 681 – Thesis
Graduate students have the option of including a thesis in their program of study.
1 to 6 Credit Hours

MTH 690-693 – Special Topics
Courses on special topics not listed among the current course offerings.
PR: Permission of instructor.
1 to 4 Credit Hours