university college - Department of Extended Studies - Florida ...

discrete optimization and dynamic programming.
(Requirement: At least one upper-level undergraduate
math course.)
MTH 5009 INTRODUCTION TO PROBABILIS-
TIC MODELS (3 credits). An applied treatment of
modeling, analysis and solution of problems involving
probabilistic information. Topics chosen from
decision analysis, inventory models, Markov chains,
queuing theory, simulation, forecasting models and
game theory. (Requirement: Instructor approval or
prerequisite course.) Prerequisites: MTH 2401.
MTH 5050 SPECIAL TOPICS (3 credits). Contents
may vary depending on the needs and interests
of the students and the fields of expertise of the
faculty. (Requirement: Instructor approval.)
MTH 5051 APPLIED DISCRETE MATHEMAT-
ICS (3 credits). Logic fundamentals, induction,
recursion, combinatorial mathematics, discrete
probability, graph theory fundamentals, trees,
connectivity and traversability. Applications from
several fields of science and engineering, including
computer science, operations research, and computer
and electrical engineering. Prerequisites:
MTH 2051.
MTH 5070 EDUCATIONAL STATISTICS (3
credits). Includes sampling procedures, frequency
distributions, measures of central tendency, estimation
of variability, the normal distribution, differences
between two groups, analysis of variance
and correlation. Also includes nonparametric
techniques, multivariate techniques and computer
analysis of educational data.
MTH 5101 INTRODUCTORY ANALYSIS (3
credits). Rigorous treatment of calculus. Includes
sequences and series of real numbers, limits of functions,
topology of the real line, continuous functions,
uniform continuity, differentiation, Riemann integration,
sequences and series of functions, Taylor’s
theorem, uniform convergence and Fourier series.
Prerequisites: MTH 2001, MTH 2201.
MTH 5102 LINEAR ALGEBRA (3 credits). Linear
algebra, systems of linear equations and Gauss
elimination method; inverses, rank and determinants;
vector spaces; linear transformations, linear
functional and dual spaces; eigenvalues, eigenvectors;
symmetric, Hermitian and normal transformations;
and quadratic forms. (Requirement:
Undergraduate course in multivariable calculus
or linear algebra.)
MTH 5107 OPTIMIZATION MODELS AND
METHODS (3 credits). Surveys popular optimization
models and algorithms. Topics chosen from
linear, integer, nonlinear, dynamic and combinatorial
optimization. (Requirement: At least one upperlevel
undergraduate math course.)
MTH 5111 REAL VARIABLES 1 (3 credits). Studies
basic topology, continuous and semicontinuous
functions, metric spaces, differentiation, measures,
132 Florida Institute of Technology
product measure, Lebesgue integration, Radon-
Nikodym Theorem, Lp-spaces and measures on
topological spaces. Prerequisites: MTH 5101.
MTH 5112 REAL VARIABLES 2 (3 credits). Studies
basic topology, continuous and semicontinuous
functions, metric spaces, differentiation, measures,
product measure, Lebesgue integration, Radon-
Nikodym Theorem, Lp-spaces and measures on
topological spaces. Prerequisites: MTH 5111.
MTH 5115 FUNCTIONAL ANALYSIS (3 credits).
Banach spaces, Hilbert spaces, topological vector
spaces, bounded and unbounded linear operators,
spectral theory. Prerequisites: MTH 5101.
MTH 5120 CALCULUS OF VARIATIONS AND
OPTIMAL CONTROL (3 credits). Includes necessary
conditions for smooth and nonsmooth problems,
Euler-Lagrange equations, Pontryagin’s maximum
principle and its applications, elements of convex
analysis, special problems and sufficient conditions
and existence theory. Prerequisites: MTH 2201.
MTH 5125 APPLIED COMPLEX VARIABLES
(3 credits). Analytic functions, Cauchy-Reimann
equations, contour integration, Cauchy theorem,
Cauchy integral formula, Taylor and Laurent series,
residue theorem and applications, linear fractional
transformations, conformal mapping, Schwarz-
Christoffel transformation. Inversion integral for
Laplace transform with complex argument; inverse
Laplace transforms. Prerequisites: MTH 2001,
MTH 2201.
MTH 5130 THEORY OF COMPLEX VARI-
ABLES (3 credits). Topology of the complex plane,
analytic functions, Cauchy’s integral formula,
Liouville’s theorem, maximum modulus theorem,
Taylor and Laurent series, singularities, residue
theorem, analytic continuation, entire functions,
infinite product representation and conformal mapping.
Prerequisites: MTH 2201, MTH 4101.
MTH 5201 MATHEMATICAL METHODS IN
SCIENCE AND ENGINEERING 1 (3 credits).
Fourier series and their convergence properties;
Sturm-Liouville eigenfunction expansion theory;
Bessel and Legendre functions; solution of heat,
wave and Laplace equations by separation of variables
in Cartesian coordinates. Prerequisites: MTH
2001, MTH 2201.
MTH 5202 MATHEMATICAL METHODS IN
SCIENCE AND ENGINEERING 2 (3 credits).
Solution of heat, wave and Laplace equations by
separation of variables in cylindrical and spherical
coordinates. Associated Legendre functions,
hypergeometric functions and spherical harmonics.
Fourier transforms and separation of variables for
heat and wave equations on infinite intervals. Vector
integral calculus. Prerequisites: MTH 5201.
MTH 5203 MATHEMATICAL METHODS IN
SCIENCE AND ENGINEERING 3 (3 credits).
General perturbation techniques for linear and