**403G.** |
** ** |
**Vector Analysis (3)**. Prerequisite: MS 227 and see “Prerequisite for all Mathematics Courses.” Algebra and calculus of vectors, Stokes theorem, and divergence theorem; applications to geometry, mass potential functions, electricity, and fluid flow. |

**404G.** |
** ** |
**Mathematical Statistics II (3)**. Prerequisites: MS 227 and MS 304, and see “Prerequisite for all Mathematics Courses.” Continuation of MS 304; selected topics from multivariate probability distributions, functions of random variables, approximations to probability distributions, methods of estimation, linear models and least squares estimators, analysis of variance, and nonparametric statistics. |

**416G.** |
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**Advanced Calculus II (3)**. Prerequisite: MS 415 and see “Prerequisite for all Mathematics Courses.” Selected topics from advanced calculus; elements of partial differentiation including the general theorems, Jacobians; topics on theory of integration. |

**423G.** |
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**Survey of Geometries (3)**. Prerequisite: MS 323 and see “Prerequisite for all Mathematics Courses.” Selected topics from advanced Euclidean geometry, finite geometries, non-Euclidean geometry, and other geometries. |

**451G.** |
** ** |
**Functions of a Complex Variable (3)**. Prerequisites: MS 227 and MS 300 and MS 415, and see “Prerequisite for all Mathematics Courses.” Fundamental operations with complex numbers, differentiation and integration theorems, mapping, series, and residues. |

**480G.** |
** ** |
**Introductory Topology (3)**. Prerequisite: MS 415 and see “Prerequisite for all Mathematics Courses.” Basic topological concepts to include topological spaces, mapping, compactness, connectedness, and separation axioms. |

**484G.** |
** ** |
**Partial Differential Equations (3)**. Prerequisites: MS 227 and MS 344, and see “Prerequisite for all Mathematics Courses.” Standard methods of solution; separation of variables, Fourier Series, Laplace Transforms; selected applications. |

**504.** |
** ** |
**Applied Statistical Methods (3)**. Prerequisite: See “Prerequisite for all Mathematics Courses.” Fundamental concepts of descriptive and inferential statistics, probability distributions, estimation, and hypothesis testing; statistical software packages are used to facilitate valid analysis and interpretation of results; emphasis is on method and selection of proper statistical techniques for analyzing real situations. |

**505.** |
** ** |
**Basic Logic and Set Theory (3)**. Prerequisite: MS 415 or MS 441, and see “Prerequisite for all Mathematics Courses.” Basic topics in symbolic logic and naive set theory, including sets and set operations, symbolic logic, the language of set theory, and applications of set theory. |

**515.** |
** ** |
**Real Variables I (3)**. Prerequisite: MS 416 or permission of the instructor, and see “Prerequisite for all Mathematics Courses.” Selected topics from real analysis with emphasis on functions of one and several variables, measure, and the Riemann and/or Darboux integral. |

**516.** |
** ** |
**Real Variables II (3)**. Prerequisite: MS 515 and see “Prerequisite for all Mathematics Courses.” Selected topics from real analysis emphasizing Lebesgue integration, sequences and series of functions. |

**517.** |
** ** |
**Introduction to Functional Analysis (3)**. Prerequisites: MS 352 and MS 415 and see “Prerequisite for all Mathematics Courses.” Introduction to the fundamental topics of functional analysis. Topics include metric spaces, completeness, linear operators, normed spaces and Banach spaces, inner product spaces, and Hilbert spaces. Objectives include the Riesz Representation Theorem, the Hahn-Banach Theorem, and the Contraction Mapping Theorem. |

**523.** |
** ** |
**Topics in Geometry for Teachers (3)**. Prerequisite: See “Prerequisite for all Mathematics Courses.” Classical theorems, ideas, and constructions of Euclidean and non-Euclidean geometry in theorems of Ceva, Menalaus, Pappus, and Feuerbach; homothetic transformations, inversion, harmonic sets of points, and cevians. |

**526.** |
** ** |
**Topics in Analytic Geometry for Teachers (3)**. Prerequisite: See “Prerequisite for all Mathematics Courses.” Applications of Euclidean and homogeneous coordinates, geometric transformations, trigonometric, and vector techniques to geometric problems. |

**528.** |
** ** |
**Theory of Equations and Functions for Teachers (3)**. Prerequisite: See “Prerequisite for all Mathematics Courses.” Topics in the theory of polynomial and other equations, and in the properties of transcendental functions. (The goal is the development of a deeper understanding of the equations and functions commonly encountered in precalculus mathematics.) May require the use of computer software. |

**530.** |
** ** |
**Foundations in Calculus for Teachers (3)**. Prerequisite: See “Prerequisite for all Mathematics Courses.” Theory, problem-solving techniques, and applications of differential and integral calculus, including the use of graphing calculators and computer software. (Recommended for students who are teaching or planning to teach Advanced Placement Calculus.) |

**533.** |
** ** |
**Topics in Modern Analysis for Teachers (3)**. Prerequisite: See “Prerequisite for all Mathematics Courses.” Logic and set theory, functions and sequences, structure and development of the real number system including completeness. |

**535.** |
** ** |
**Topics in Finite Mathematics for Teachers (3)**. Prerequisite: See “Prerequisite for all Mathematics Courses.” Elementary combinatorial analysis, probability, vectors and matrices, game theory, linear programming, and model building in the social and physical sciences. |

**537.** |
** ** |
**Foundations in Algebra for the Secondary Teacher (3)**. Prerequisite: MS 441 and see “Prerequisite for all Mathematics Courses.” Concepts of high school algebra from the perspective of ring theory. |

**541.** |
** ** |
**Abstract Algebra I (3)**. Prerequisite: MS 441 and see “Prerequisite for all Mathematics Courses.” General group theory including cyclic groups and permutation groups, homomorphism and isomorphism theorems. |

**542.** |
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**Abstract Algebra II (3)**. Prerequisite: MS 441 and see “Prerequisite for all Mathematics Courses.” Theory of rings, ideals, fields, and integral domains. |

**549.** |
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**Selected Topics in Mathematics for the Secondary Teacher (3)**. Prerequisite: See “Prerequisite for all Mathematics Courses.” Selected topics suitable for the secondary teacher; problem solving; secondary school mathematics from an advanced standpoint. |

**552.** |
** ** |
**Linear Algebra (3)**. Prerequisites: MS 352 and MS 441 and see “Prerequisite for all Mathematics Courses.” Abstract treatment of finite dimensional vector spaces. Linear transformations, determinants, eigenvalues and eigenvectors, invariant subspaces, Rational and Jordan Canonical Forms, inner product spaces, unitary and normal operators, bilinear forms. |

**591.** |
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**Seminar in Algebra (3,3)**. Prerequisites: MS 541 and MS 542 or permission of instructor and see “Prerequisite for all Mathematics Courses.” Selected topics in modern algebra beyond the scope of the graduate algebra sequence. Topics may be chosen from the theory of groups, rings, fields, or modules; linear algebra; homological algebra; or other topics, depending on student and instructor interests. |

**595.** |
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**Seminar in Analysis (3,3)**. Prerequisites: MS 515 and MS 516 or permission of instructor and see “Prerequisite for all Mathematics Courses.” Selected topics in modern analysis beyond the scope of the graduate analysis sequence. Topics may be chosen from the fields of real analysis (measure theory and integration, special functions, finite differences, functional equations, sequences and series), complex variables, Fourier and harmonic analysis, integral transforms, operator theory, or other topics, depending on student and instructor interests. |

**598.** |
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**Directed Readings (3,3)**. Prerequisites: Students must have two courses in the topical area chosen and approval by the faculty advisor in mathematics and the instructor and see “Prerequisite for all Mathematics Courses.” Algebra, analysis, geometry, and topology. |

**599.** |
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**Thesis (3,3)**. (Grade of Pass or Fail only.) Prerequisite: Approval of Application for Thesis Option. See “Thesis Options and Procedures" in the Thesis Guide on this website. |