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North Carolina Central University

(p) 919-530-6100

1801 Fayetteville St.

Durham, NC 27707

ClassID |
Name |
Description |
Credits |

MATG 5010 | Modern Algebra I | Part 1 of a two course study of algebraic systems including groups, rings and fields, vector spaces, and linear algebras, and other algebraic systems. | 3 |

MATG 5020 | Modern Algebra II | Part 2 of a two course study of algebraic systems including groups, rings and fields, vector spaces, and linear algebras, and other algebraic systems. | 3 |

MATG 5040 | Advanced Topics in Geometry | A study of topics chosen from Euclidean and non-Euclidean geometries using analytic and synthetic approaches. Studies may include topics from finite, projective, algebraic and differential geometries. | 3 |

MATG 5060 | Applied Mathematics | A study of advanced mathematical techniques as needed in the solution of mathematical models and application problems. Various models and problems will be studied, including those based on differential equations and requiring techniques for solving differential equations. Model formulation, solution evaluation, and interpretation of results will also be incorporated. | 3 |

MATG 5080 | Operations Research | Prerequisites: MATH 4410. A study of mathematical models and methods for optimal decision-making regarding the usage of constrained analysis, transportation and transshipment problems, assignment models and game theory, dynamic programming, activity networks, Markov chains, queuing theory, and an introduction to simulation. | 3 |

MATG 5210 | Theory of Numbers | A study of congruences, non-linear congruences, number theoretic functions, primitive roots, quadratic residue, Legendre symbol, Gauss's lemma, quadratic reciprocity law, and the theory of binary forms. | 3 |

MATG 5240 | Theory of Groups | A study of group properties, subgroups and cyclic groups, normal subgroups, homomorphism and isomorphism theorems, Abelian groups, Sylow's theorems, composition series, and Jordon-Holder Theorem. | 3 |

MATG 5310 | Point Set Topology | A study of elementary point set theory of the line and the plane, topological spaces and properties, product separation, compactness, connectedness and path connectedness, metrication and compactification, continuous mappings and topological algebra. | 3 |

MATG 5400 | Foundations of Mathematics | A study of axiomatic set theory, operations on sets, relations and functions, axiom of choice, well ordering, maximal principles, cardinal and ordinal numbers, and the generalized continuum hypothesis. | 3 |

MATG 5410 | Numerical Analysis | An analysis of errors in approximate calculation, solutions of nonlinear equations, finite differences and interpolating polynomials, numerical differentiation and integration, quadrature in n dimensions, computational methods and error analysis of matrix inversion, eigenvalues, and eigenvectors. | 3 |

MATG 5510 | Theory of Functions of a Real Variable | A study of the real number system, linear point sets, theory of limits, continuity and differentiability properties of functions of one or more variables, sequences and series of functions, Reimann, Lesbesgue, and Stieltjes integrals, implicit function theorem, and existence theorems for differential equations. | 3 |

MATG 5520 | Theory of Functions of a Complex Variable | A study of complex numbers and their geometric representation, analytic functions, elementary functions, complex integration, Taylor and Laurent series, the calculus of residues, conformal mapping, series and product expansion, power series with finite radius of convergence, Abel's theorem and its consequences, and an introduction to transforms. | 3 |

MATG 5640 | Numerical Methods for Partial Differential Equations I | Prerequisites: MATH 3020 and MATH 4410 or equivalent. An in-depth study of numerical methods for solving parabolic, elliptic, and hyperbolic partial differential equations. Topics include finite difference schemes in one, two, and three dimensions including explicit and implicit methods, as well as variational methods. A detailed discussion of consistency, convergence and stability is covered for each method introduced. | 3 |

MATG 5790 | Nonlinear Optimization | Prerequisites: COMP 1520, MATH 2030 and MATH 4410. A study of theory and algorithms of finite dimensional nonlinear programming. Topics include first and second order optimality conditions, convergence, rate of convergence, convexity, and duality; unconstrained optimization algorithms including line search, conjugate gradient, Newton, and quasi-Newton methods; constrained optimization algorithms including quadratic programming, sequential quadratic programming, penalty, Lagrangian, and augmented Lagrangian methods. | 3 |

MATG 5810 | Special Topics in Mathematics | Approval, by the department chairman, is required prior to registering. A course in which content varies from semester to semester. Possible topics include actuarial mathematics, partial differential equations, mathematical logic, and analysis of variance. Repeatable for a maximum of 9 credits. | 3 |

MATG 5820 | Independent Study | Approval, by the department chairman, is required prior to registering. Independent research under the direction of a professor. The faculty mentor directs the study and assesses the studentâ€™s knowledge through oral and written reports. Repeatable for a maximum of 6 credits. | 1 to 3 |

MATG 5890 | Supervised Research | Before registering, the student must submit an outline of the proposed research for approval by the faculty member who will supervise the work and by the department chairman. An advanced study, using the research facilities of the department, under the supervision of a professor in the department. Repeatable for a maximum of 6 credits. | 1 to 3 |

MATG 5900 | Thesis | Before registering, the student must submit an outline of the proposed research for approval of the faculty member who will supervise the thesis , approval by the student's thesis committee, and by the department chairman. Students should register for this course during the semester in which they intend to complete thesis research and writing. A minimum of 3 credits in MATG 5900 is required for graduation. | 1 to 6 |

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2014

North Carolina Central University

1801 Fayetteville St., Durham, NC 27707