Math Courses
4103 Finite Dimensional Vector Spaces (D)
Linear functions, matrix representation of linear transformations, scalar product, special representation of linear transformations.
Prerequisite: MATH 3083 or consent.
4113 Introduction to Abstract Algebra II (D)
Topics in abstract algebra including finite abelian groups, linear groups, factorization in commutative rings, quadratic field extensions, Gaussian integers. Wedderburn's theorem, and multilinear algebra.
Prerequisite: MATH 3113.
4153 Mathematical Modeling (D)
Mathematical techniques for formulating, analyzing, and criticizing models taken from the biological, social, and physical sciences. Techniques include graphical methods, stability, optimization, and phase plane analysis.
Prerequisite: MATH 3404.
4163 Dynamic Models in Biology (D)
Mathematical and computational techinques for developing,executing, and analyzing dynamic models arising in the biological sciences. Both discrete and continuous time models are studied. Applications include population dynamics, cellular dynamics, and the spread of infectious diseases.
Prerequisite: MATH 2554.
4203 Linear Programming and Game Theory (D)
Solution sets, duality, and pivoting in linear programming. Feasible solutions and the simplex method. The transportation problem. Matrix games.
Prerequisites: MATH 3083 and proficiency in a high level computer language.
4253 Symbolic Logic I (D)
Rigorous analyses of the concepts of proof, consistency, equivalence,validity, implication, and truth. Full coverage of truth-functionallogic and quantification theory (predicate calculus). Discussionof the nature and limits of mechanical procedures (algorithms) for proving theorems in logic and mathematics. Informal accountsof the basic facts about infinite sets. (Same as PHIL 4253)
4263 Symbolic Logic II (D)
Topics include: soundness and completeness of propositional logic,soundness and completeness of quantification theory, the elementsof model theory and recursion theory, Gödel's incompleteness theorems, and the limitative theorems of Tarski and Church (Same as PHIL 4263).
4353 Numerical Linear Algebra (II)
Numerical methods for problems of linear algebra, including the solution of very large systems, eigenvalues, and eigenvectors.
Prerequisite: programming experience and MATH 3083.
4363 Numerical Analysis (I)
General iterative techniques, error analysis, root finding, interpolation, approximation, numerical integration, numerical solution of differential equations
Prerequisite: programming experience and MATH 4513 or consent.
4503 Differential Geometry and Vector Calculus (D)
Topics include: Vector differential and integral calculus, Stokes Theorem in 3-space, classical differential geometry in 3-space (curves, surfaces), differential forms, general Stokes Theorem, applications to hydrodynamics, and electromagnetism.
4513 Advanced Calculus I (I)
The real and complex number systems basic set theory and topology sequences and series continuity differentiation Taylors theorem Emphasis is placed on careful mathematical reasoning.
Prerequisite: MATH 2574 and MATH 3083 or consent of instructor.
4523 Advanced Calculus II (II)
The Riemann-Stieljes integral uniform convergence of functions Fourier series, implicit function theorem, Jacobians, and derivatives of higher order.
Prerequisite: MATH 4513.
5013 Topics in Algebra for Teachers (D)
Topics from abstract algebra and linear algebra of current interest to teachers. May be repeated for credit.
Prerequisite: graduate standing and consent.
5033 Topics in Analysis for Teachers (D)
Topics related to calculus that are of current interest to secondary school teachers. May be repeated for credit.
Prerequsite: graduate standing and consent.
504V Special Topics for Teachers (D)
Current topics in mathematics of interest to secondary schoool teachers. May be repeated for credit.
Prerequisite: graduate standing and consent.
510V Mathematics Seminar (1-3) (D)
Members of the faculty and advanced students meet for presentation and discussion of topics.
Prerequsite: graduate standing.
5123 Algebra I (I)
Beginning algebra for graduate students: groups, rings, modules, algebras, categories, homological algebra, Galois theory, Lie algebras.
Prerequisite: MATH 4113.
5133 Algebra II (II)
Prerequisite: MATH 5123.
5303 Ordinary Differential Equations (I)
Existence, uniqueness, stability, qualitative behavior, and numerical solutions.
Prerequisites: programming experience, MATH 3404 and MATH 4513 , or consent.
5313 Partial Differential Equations (II)
Classification, boundary value problems, applications, numerical solutions.
5363 Scientific Computation and Numerical Methods (D)
An introduction to numerical methods used in solving various problems in engineering and the sceinces.
5453 Functional Analysis I (I)
Linear vector spaces, linear operators.
Prerequisite: MATH 5513.
5503 Theory of Functions of Real Variable I (I)
Prerequisite: MATH 4523.
5513 Theory of Functions of a Real Variable II (II)
Prerequisite: MATH 5503.
5523 Theory of Functions of Complex Variable I (I)
Complex numbers, analytic functions, power series, complex integration, Cauchy's Theorem and integral formula, maximum principle, singularities, Laurent series, Mobius maps.
Prerequisite: MATH 4513 and consentof instructor.
5533 Theory of Functions of Complex Variable II (II)
Riemann Mapping Theorem, analytic continuation, harmonic functions, entire functions.
Prerequisite: MATH 5523.
5703 Foundations of Topology (I)
Metric and general topological spaces, separation axioms, Urysohn's lemma, Tietze extension theorem, connectedness, compactness, and the Tychonoff theorem.
Prerequisite: MATH 4513.
5713 Algebraic Topology (II)
Homotopy, singular and relative homology, excision theorem, the Mayer-Vietoris sequence, Beti numbers, and the Euler characteristic.
Prerequisite: MATH 5703.
600V Master's Thesis (1-6) (I,II)
Prerequisite: graduate standing and consent.
610V Directed Readings (1-6) (D)
Prerequisite: graduate standing and consent.
619V Topics in Algebra (D)
Current research interest in algebra. May be repeated for credit.
659V Topics in Analysis (D)
Current research inrerests in analysis. May be repeated for credit.
679V Topics in Topology (D)
Current research interests in topology. May be repeated for credit.
700V Doctoral Dissertation (1-18) (D)
Original research to be published in a recognized journal, presented, and defended.