## Graduate Courses in Mathematics

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* - 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 Credit 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 Credit 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. May not be used for any degree offered by the Department of Mathematics.

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

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

PR: MTH545.

*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 MTH550.

PR: MTH550.

*3 Credit Hours* - 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 Credit Hours* - 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.

PR: MTH 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* - MTH 660 – Stochastic Processes
- Theory and applications of Markov chains.

PR: MTH545.

*3 Credit 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 Credit 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 Credit 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 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*