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Untitled - University of New Orleans

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MATH 4711 Graph Theory<br />

3 cr.<br />

Prerequisite: MATH 2511 or MATH 2721 or consent <strong>of</strong> department.<br />

An introduction to graph theory and its applications; the basic<br />

theorems and algorithms. Paths and cycles, colorings, planarity,<br />

directed graphs, networks.<br />

MATH 4711G Graph Theory<br />

3 cr.<br />

Prerequisite: MATH 2511 or MATH 2721 or consent <strong>of</strong> department.<br />

An introduction to graph theory and its applications; the basic<br />

theorems and algorithms. Paths and cycles, colorings, planarity,<br />

directed graphs, networks.<br />

MATH 4721 Combinatorics<br />

3 cr.<br />

Prerequisite: MATH 2511 or 2721 or consent <strong>of</strong> department. Permutations,<br />

combinations, and partitions; inclusion-exclusion principle;<br />

generating functions and recurrence relations; matchings; combinatorial<br />

designs.<br />

MATH 4721G Combinatorics<br />

3 cr.<br />

Prerequisite: MATH 2511 or 2721 or consent <strong>of</strong> department. Permutations,<br />

combinations, and partitions; inclusion-exclusion principle;<br />

generating functions and recurrence relations; matchings; combinatorial<br />

designs.<br />

MATH 4990 Special Topics<br />

3 cr.<br />

Prerequisite: consent <strong>of</strong> department. Six hours maximum will be<br />

accepted for graduate credit.<br />

MATH 4990G Special Topics<br />

3 cr.<br />

Prerequisite: consent <strong>of</strong> department. Six hours maximum will be<br />

accepted for graduate credit.<br />

MATH 4991 Special Topics<br />

3 cr.<br />

Prerequisite: consent <strong>of</strong> department. Six hours maximum will be<br />

accepted for graduate credit.<br />

MATH 4991G Special Topics<br />

3 cr.<br />

Prerequisite: consent <strong>of</strong> department. Six hours maximum will be<br />

accepted for graduate credit.<br />

MATH 4992 Special Topics<br />

3 cr.<br />

Prerequisite: consent <strong>of</strong> department. Six hours maximum will be<br />

accepted for graduate credit.<br />

MATH 4992G Special Topics<br />

3 cr.<br />

Prerequisite: consent <strong>of</strong> department. Six hours maximum will be<br />

accepted for graduate credit.<br />

MATH 4998 Selected Readings in Math<br />

1-3 cr.<br />

Prerequisite: consent <strong>of</strong> department. This course may be repeated<br />

to a total <strong>of</strong> six credits. The course consists <strong>of</strong> directed readings<br />

designed to meet the needs and interests <strong>of</strong> the individual student;<br />

regular conferences between the student and the instructor are<br />

required. The section number will correspond with credit to be<br />

earned.<br />

MATH 4998G Selected Readings in Math<br />

1-3 cr.<br />

Prerequisite: consent <strong>of</strong> department. This course may be repeated<br />

to a total <strong>of</strong> six credits. The course consists <strong>of</strong> directed readings<br />

designed to meet the needs and interests <strong>of</strong> the individual student;<br />

regular conferences between the student and the instructor are<br />

required. The section number will correspond with credit to be<br />

earned.<br />

MATH 6005 Higher Algebra<br />

3 cr.<br />

Prerequisites: a working knowledge <strong>of</strong> college algebra and consent<br />

<strong>of</strong> department. (This course is intended for candidates in the M.A.<br />

in Science Teaching program.) Topics covered include inequalities,<br />

complex numbers, theory <strong>of</strong> equations, mathematical induction,<br />

binomial theorem, progressions, infinite series and applications.<br />

MATH 6006 Analytic & Vector Geometry<br />

3 cr.<br />

Prerequisites: a working knowledge <strong>of</strong> plane geometry and college<br />

algebra and consent <strong>of</strong> department. (This course is intended for<br />

candidates in the M.A. in Science Teaching program.) Plane and<br />

solid geometry by analytic methods. Topics covered include vectors,<br />

lines, conic sections, translation and rotation <strong>of</strong> axes, polar coordinates,<br />

parametric representations; plane and three-space curves<br />

and surfaces.<br />

MATH 6007 Topics in High Alg & Geometry<br />

3 cr.<br />

Prerequisite: MATH 6005 or 6006 or consent <strong>of</strong> department. (This<br />

course is intended for candidates in the M.A. in Science Teaching<br />

program.) Topics selected from inequalities, theory <strong>of</strong> equations,<br />

Euclidean geometry, and non-Euclidean geometry.<br />

MATH 6020 Geometry<br />

3 cr.<br />

Prerequisite: MATH 4020. Space figures: similarity and trigonometry,<br />

area and volume measurement, elements <strong>of</strong> spherical geometry,<br />

plane coordinate geometry. This course may be used for degree<br />

credit only in the elementary education curriculum.<br />

MATH 6201 Introduction to Applied Math<br />

3 cr.<br />

Prerequisites: MATH 4101. MATH 4101 may be taken concurrently.<br />

System <strong>of</strong> linear ordinary differential equations, fundamental<br />

matrices, nonlinear systems <strong>of</strong> ODE’s, stability, limit cycles, separation<br />

<strong>of</strong> variables, heat equation, wave equation, Laplace’s equation,<br />

Sturm-Liouville boundary value problems, Green’s functions, integral<br />

transforms, conformal mapping, complex integration.<br />

MATH 6202 Introduction to Applied Math<br />

3 cr.<br />

Prerequisites: MATH 4101 or consent <strong>of</strong> department. Dynamical systems,<br />

elementary bifurcations, chaos, nonlinear PDE, characteristics,<br />

shocks, calculus <strong>of</strong> variations, Euler-Lagrange equation, normed linear<br />

spaces, linear operators, convex analysis, optimization.<br />

MATH 6211 Applied Analysis<br />

3 cr.<br />

Prerequisite: MATH 4104 or 4411. Calculus <strong>of</strong> residues, Fourier and<br />

Laplace transforms, orthogonal expansion; special functions; solution<br />

<strong>of</strong> boundary value problems <strong>of</strong> partial differential equations<br />

by various methods; separation <strong>of</strong> variable, transform techniques;<br />

Sturm-Liouville theory; perturbation and asymptotic developments;<br />

Green’s functions; the method <strong>of</strong> characteristics.<br />

MATH 6221 Adv Differential Equations<br />

3 cr.<br />

Prerequisites: MATH 4101 or 4221. Ordinary differential equations in<br />

the real and complex domains, existence and uniqueness theorems,<br />

linear systems with constant and periodic coefficients. Linear differential<br />

equations or order n, self-adjoint eigenvalue problems,<br />

nonlinear equations, and stability theory.<br />

MATH 6224 Partial Differential Eqs II<br />

3 cr.<br />

Prerequisite: MATH 4224 or consent <strong>of</strong> department. Topics in modern<br />

linear and nonlinear partial differential equations, distributions<br />

and weak solutions, method <strong>of</strong> characteristics, shock waves, Green<br />

functions, fixed point theorems, reaction diffusion equations.<br />

MATH 6230 Adv Finite Element Analysis<br />

3 cr.<br />

Prerequisites: MATH 4224 or consent <strong>of</strong> department; Mathematics<br />

4230 is recommended; some knowledge <strong>of</strong> computer programming<br />

is required. Galerkin method, linear triangular elements, bilinear<br />

rectangular elements, axisymmetric elements, isoparametric elements,<br />

heat transfer by conduction and convection, torsion <strong>of</strong> noncircular<br />

sections, ground water with sources and sinks, biharmonic<br />

equation, vibration <strong>of</strong> membrane, iterative methods, s<strong>of</strong>tware<br />

maintenance and development.<br />

MATH 6242 Functional Analysis<br />

3 cr.<br />

Prerequisite: MATH 4102 or consent <strong>of</strong> department. Topics will be<br />

selected from the following: metric spaces, normed spaces, Banach<br />

<strong>University</strong> <strong>of</strong> <strong>New</strong> <strong>Orleans</strong>/303

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