For more information regarding mathematics graduate courses offered through the Department of Math and Statistics, please contact a program assistant.

Course Number | Course Name | Description | Credit Hours |
---|---|---|---|

MATH6001 | Real Analysis | Review of measure theory; introduction to Hilbert and Banach spaces, Fourier transforms of LP functions; elementary theory of analytic functions including Cauchy's theorem and its consequences; Banach algebras and applications. | 3 ch |

MATH6013 | Topcs in Complex Analysis | Complex analytic functions, contour integrals and Cauchy's theorems; Taylor's, Laurent's and Liouville's theorems, residue calculus. | 3 ch |

MATH6021 | Group Representation Theory | Introduction, representation modules, the regular representation, the principle indecomposable representation, the Wedderburn structure theorems for semi-simple rings, multiplicities, generalized characters, representation of abelian groups. induced characters, representation of direct products, some applications. | 3 ch |

MATH6022 | Group Theory | Topics from: p-groups; solvable and nilpotent groups; permutation groups; direct sums; Abelian groups (elementary theory); free groups; group extensions; group representations, free amalgamated products. | 3 ch |

MATH6023 | Functional Analysis with Application | Normed spaces, the Hahn-Banach theorem, uniform boundedness theorem. Wavelets. The contraction mapping theorem. Existence and uniqueness for nonlinear differential equations. | 3 ch |

MATH6032 | Ring Theory | Topics to be covered may include rings, ideals, prime and maximal ideals. Semi-simple rings and the Artin-Wedderburn theorem, localization, completion, the spectrum, Dedekind Domains, discrete valuation rings, the Hilbert Basis theorem, Hilbert's Nullstellenstatz and the Brauer group. | 3 ch |

MATH6043 | Topics in Advanced Algebra I | Prime fields and characteristic, extension fields, algebraic extensions, theory of finite fields, Galois theory, and topics which may include some of: rings, topological algebra, multilinear and exterior algebra, quadratic forms. | 3 ch |

MATH6053 | Topics in Advanced Algebra II | Group Theory: Simplicity of An, Sylow Theorems, Fundamental Theorem of Abelian Groups, Jordan-Holder Theorem; Rings and Modules: Localization, Noetherian Rings, Wedderburn Theorem; Multilinear Algebra: Tensor Products and Alternating Products. | 3 ch |

MATH6102 | Graph Theory and Progrmming | With a graph there are associated its adjacency matrix and its group of automorphisms. In this course a study is made of the properties of these structures including spectral properties of the matrix and transitivity properties of the group. The course demonstrates the interaction of techniques from linear algebra, group theory and graph theory. | 3 ch |

MATH6103 | Measure Theory | An introduction to measure and integration theory with applications to probability. Measures, integration, Radon-Nikodym theorem, Lp-spaces, product measures and Fubini's Theorem. Topics selected from the following: probability spaces, random variables, characteristic functions, independence, conditional probability martingales, limit theorems, and stochastic processes. | 3 ch |

MATH6131 | Qualitative Theory of Differential Equations | Topics selected from: Stability theory, periodic solutions, limit cycle, differential-difference equations, controllability and stability. | 3 ch |

MATH6132 | Theory of Partial Differential Equations | Cauchy-Kowalewski Theorem. Equations of the first Order: Characteristics, Monge Cone, complete integral. Classification of Partial Differential Equaitons: Canonical forms of linear equations, quasi-linear systems. Cauchy Problems: Characteristics, Riemann Function. Additional topics to be chosen by the instructor. | 3 ch |

MATH6142 | Advanced Ordinary Differential Equations | Systems of differential equations, existence and uniqueness of solutions, properties of linear systems, introduction to qualitative methods, phase-plane analysis, stability of non-linear systems, Lyapunov method. Further topics chosen from numerical methods, boundary value problems and Sturm-Liouville systems, shooting method for non-linear boundary value problems. | 3 ch |

MATH6151 | Advanced Topology | Review of point-set topology. Fundamental groups, covering spaces, Jordan curve theorem, hairy ball theorem, classification of closed surfaces, introduction to simplicial complexes and homology. | 3 ch |

MATH6153 | Topology | Advanced topological concepts. Basic results in point-set topology. | 3 ch |

MATH6201 | Graph Theory | Graph symmetries, graph enumerations using Polya's theorem, power group theorem and its applications, generalizations of Redfield's enumeration theorem and its applications to super-positions, unsolved enumeration problems. | 3 ch |

MATH6222 | Topics in Optimization | Necessary and sufficient conditions of optimality including the Pontryagin maximum principle, the discrete maximum principle, Kuhn-Tucker and F. John Theory. Multivalued criteria optimization. Optimization under uncertainty. | 3 ch |

MATH6231 | Topics in Differential Equations | Topics to be chosen by instructor with approval of MATH/STAT department. | 3 ch |

MATH6313 | Computorial Optimization | Brief review of linear programming duality theory; time-tabling and ranking problems; optimum network flow and applications; efficiency of algorithms, totally unimodular matrices, integer programming, optimum matchings and constrained subgraphs; introduction to boolean and pseudo-boolean programming. | 3 ch |

MATH6321 | Principles of Combinatorics | Various principles of combinatorics will be elucidated, and applications of a non-elementary nature studied: Enumeration theory; Mobius inversion; permutation groups and Polya's theorem; combinatorial problems related to convex polytopes; totally unimodular matrices, and integer programming. | 3 ch |

MATH6331 | Rational Mechanics | Dynamics of particles and rigid bodies. Generalized co-ordinates and equations of motion. Existence and uniqueness theorems. Perturbation theory. Conditional rigid systems. Oscillations. Approximation methods. Hamiltonian mechanics and the n-body problems Various principles of combinatorics will be elucidated, and applications of a non-elementary nature studied: Enumeration theory; Mobius inversion; permutation groups and Polya's theorem; combinatorial problems related to convex polytopes; totally unimodular matrices, and integer programming. |
3 ch |

MATH6332 | Mathematical Theory of Relativity | Introduction to the special and general theories of relativity with emphasis on the geometry of space time. | 3 ch |

MATH6363 | Enumeration Theory | Use of generating functions and Polya's theorem. Emphasis is on the understanding of these methods and their applications to a wide variety of problems. | 3 ch |

MATH6392 | Seminar in Pure and Applied Mathematics | Students in the Master's program will review the literature in one or more areas of pure or applied mathematics and present a minimum of four but not more than six seminars throughout the year. | cr |

MATH6413 | Fluid Mechanics | Derivation of the Equations of Motion: Euler's equations, rotation and vorticity, Navier-Stokes equations. Potential Flow: complex potentials, harmonic functions, conformal mapping, potential flow in three dimensions. Slightly Viscous Flow: boundary layers and Prandtl boundary layer equations. Gas Flow in one dimension: characteristics and shocks. | 3 ch |

MATH6423 | Mathematical Theory of Control | Topics selected according to the interests of students and faculty which may include the following: optimal control of linear systems, Pontryagin's maximum principle, controllability, observability, distributed parameter systems, differential games, stochastic systems. | 3 ch |

MATH6433 | Calculus of Variations | Introduction to functionals and function spaces. Variation of a functional. Euler's equations, necessary condition for an extremum, case of several variables, invariance of Euler's equation, fixed end point problem for unknown functions, variational problems in parametric form, functionals depending on high order derivatives. | 3 ch |

MATH6443 | Introduction to Quantum Field Theory | Relativistic quantum mechanics. The negative energy problem. Classical field theorem symmetries and Noether's theorem. Free field theory and Fock space quantization. Thee interfacing field: LSZ reduction formula, Wick's theorem, Green's functions, and Feynman diagrams. Introduction to Quantum electrodynamics and renormalization. | 3 ch |

MATH6453 | Special Functions | Covers in depth those functions which commonly occur in Physics and Engineering, namely, the Gamma, Beta, Bessel, Legendre, hypergeometric, Hermite and Laguerre functions. Additional or alternative special functions may be included. Applications to Physics and Engineering will be discussed. | 3 ch |

MATH6463 | Integral Equations | Classification. Comparison of integral and differential equations. Green's functions. Analytical solutions of Fredholm equations with degenerate kernels. Approximate solutions of Frenhold equations with non-degenerate kernels. The Neumann series and resolvent kernels. Volterra equations of the second kind. Non-linear integral equations. | 3 ch |

MATH6473 | Introduction to Differential Geometry | Geometry of embedded curves and surfaces, n-dimensional manifolds, tensors, Riemannian geometry. | 3 ch |

MATH6483 | Introduction to General Relativity | Special relativity, foundations of general relativity, solutions of Einstein's equations, classical tests, cosmology, additional topics. | 3 ch |

MATH6492 | Advanced Seminar in Pure and Applied Mathematics | Students in the PhD program will review the literature in one or more areas of pure or applied mathematics and present a minimum of four but not more than six seminars throughout the year. | cr |

MATH6501 | Advanced Topics in Mathematics I | Topics to be chosen by instructor with approval of MATH/STAT department. | 3 ch |

MATH6503 | Numerical Methods for Differential Equation | The numerical solution of ordinary differential equations, and partial differential equations of elliptic, hyperbolic and parabolic type. The course is a basic introduction to finite difference methods, including the associated theory of stability, accuracy and convergence. Students will gain practical experience using state-of-the-art numerical solvers and visualization tools, while solving problems from the physical and biological sciences. | 3 ch |

MATH6512 | A continuation of topics offered in MATH 6501 . | 3 ch | |

MATH6615 | Linear Programming | This course includes: simplex method, duality theory, parametric and post-optimality analysis, geometry and complexity of simplex method, bounded variable linear programs and piece-wise linear programming, ellipsoid algorithms and interior point methods. | 3 ch |

MATH6625 | Network Flows | This course includes: shortest path algorithms, maximum flow, minimum flows and multicommodity flows. | 3 ch |

MATH6633* | Calculus Revisited | A course for high school mathematics teachers. The course is built around a set of optimization problems, whose solution requires review of topics in first and second year calculus and linear algebra. Connections are made with topics in the Common Atlantic High School Mathematics Curriculum. *This course may not be taken for credit by graduate students in Mathematics & Statistics degree programs. | 3 ch |

MATH6634* | Fundamental Principles of School Mathematics | A course for graduate students and students with and undergraduate degree with experience teaching school mathematics. Topics build around the K-12 syllabus, with extensions beyond the classroom, to show the 'how' and 'why' behind school mathematics. Mathematical language; real numbers and other mathematical structures; Euclidean geometry; functions; mathematical connections; problem solving. *This course may not be taken for credit by graduate students in Mathematics and Statistics degree programs. | 3 ch |

MATH6635 | Approximation Algorithms | This course includes: hard combinatorial optimization problems, approximation algorithms, worst-case analysis, probabilistic analysis, domination analysis, E-approximation schemes and fully polynomial approximation schemes, metaheuristics and experimental analysis of algorithms. | 3 ch |

MATH6853 | Mathematics of Financial Derivatives | Basics of options, futures, and other derivative securities. Introduction to Arbitrage. Brief introduction to partial differential equations. Stochastic calculus and Ito's Lemma. Option pricing using the Black-Scholes model. Put-call parity and Hedging. Pricing of European and American call and put options. Numerical methods for the Black-Scholes model: binary trees, moving boundary problems, and linear complementarity. The barrier, and other exotic options. | 3 ch |

MATH6903 | Independent Study in Mathematics | Topics to be chosen jointly by student, advisor, and Math/Stat graduate committee. May be taken for credit more than once. Title of topic chosen will appear on transcript. | 3 ch |

MATH6991 | Reading Course | Reading courses on advanced topics may be taken for graduate credit subject to departmental approval. | 3 ch |

MATH6992 | Reading Course | Reading courses on advanced topics may be taken for graduate credit subject to departmental approval. | 3 ch |

MATH6996 | Master's Report | cr | |

MATH6997 | Master's Thesis | cr | |

MATH6998 | PhD Thesis | cr |