2008–2009 - Florida Institute of Technology

MTH 1702 APPLIED CALCULUS (3 credits). Elements of differential and integral
calculus with application to business, economics, management and the social
and life sciences, as well as maxima, minima, rates, exponential growth and decay,
and some techniques of integration. Prerequisites: MTH 1701.
MTH 1801 TRIGONOMETRY REVIEW (1 credit). Reviews trigonometric topics
necessary for calculus, including trigonometric functions, graphs, identities and
solving trigonometric equations. May be taken with MTH 1001. (Requirement: High
school trigonometry and appropriate score on placement test.)
MTH 2001 CALCULUS 3 (4 credits). Cylindrical and spherical coordinates, vectors,
functions of several variables, partial derivatives and extrema, multiple integral,
vector integral calculus. Prerequisites: MTH 1002.
MTH 2051 DISCRETE MATHEMATICS (3 credits). Formulation of precise
definitions and their negations using propositional and predicate logic; argument
analysis and proof techniques including induction; number theory; and sets,
relations, functions, directed graphs and elementary counting arguments. (Requirement:
Passing score on placement test or prerequisite course.) Prerequisites: MTH
1000 or MTH 1001 or MTH 1702.
MTH 2201 DIFFERENTIAL EQUATIONS/LINEAR ALGEBRA (4 credits).
First-order differential equations, linear differential equations with constant coefficients,
first-order systems of differential equations with constant coefficients,
numerical methods, Laplace transforms, series solutions, algebraic systems of
equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors.
Prerequisites: MTH 1002.
MTH 2202 LINEAR ALGEBRA FOR DIFFERENTIAL EQUATIONS
(1 credit). Includes systems of equations, matrices, determinants, vector spaces,
eigenvalues, and eigenvectors. Supplements differential equations. (Requirement:
Instructor approval.) Prerequisites: MTH 1002.
MTH 2332 PRIMER FOR BIOMATH (1 credit). Introduces the separate languages
of mathematics and biology such that students from the different disciplines
can efficiently develop a biomath glossary to communicate with one another. Focuses
on the current research projects in biology and ecology, and the relevant mathematical
analysis. (Requirement: Instructor approval.) Prerequisites: MTH 1000.
MTH 2401 PROBABILITY AND STATISTICS (3 credits). Random variables,
expectations, sampling and estimation of parameters, normal and other distributions
and central-limit theorem, tests of hypothesis, linear regression and design experiments.
Prerequisites: MTH 1002.
MTH 3051 COMBINATORICS AND GRAPH THEORY (3 credits). Elementary
and advanced counting techniques including permutations, combinations,
multisets, inclusion-exclusion, generating functions, recurrence relations and topics
in graph theory including graphs, trees, binary tree, graph traversals and network
flow. Prerequisites: MTH 1001, MTH 2051.
MTH 3101 COMPLEX VARIABLES (3 credits). Algebra of complex numbers,
elementary analytic functions, complex integration, series representations for analytic
functions, residue theory and conformal mapping and its applications. Prerequisites:
MTH 2001.
MTH 3102 INTRODUCTION TO LINEAR ALGEBRA (3 credits). Includes
vectors and matrices, linear equations, vector spaces and subspaces, orthogonality,
determinants, eigenvalues and eigenvectors, and linear transformations. Introduces
students to solution and manipulation of matrix equations using a standard package
of mathematical software. Prerequisites: MTH 1002.
MTH 3201 BOUNDARY VALUE PROBLEMS (3 credits). Solutions of the
heat, wave and potential equations by separation of variables; orthogonality; Fourier,
Bessel and Legendre series; and properties of Bessel functions, Legendre polynomials
and the gamma function. Prerequisites: MTH 2001, MTH 2201.
MTH 3301 FINITE DIFFERENCES AND FINITE ELEMENTS (3 credits).
Numerical methods for BVPs in one and two dimensions; finite difference methods
for solving PDEs, finite element methods, variational formulation and Galerkin
approximations for ODEs and two-dimensional PDEs, and writing programs. Prerequisites:
CSE 1502 or CSE 1503 or CSE 2050, MTH 3201.
MTH 3311 APPLIED NUMERICAL METHODS (3 credits). Numerical
methods, use and modification of existing software and computer arithmetic, linear
systems of equations, interpolation, numeric quadrature, linear least-squares data
fitting, eigenvalues, solutions of nonlinear equations. Prerequisites: CSE 1502 or
CSE 1503 or CSE 2050, MTH 1002.
MTH 4051 ABSTRACT ALGEBRA (3 credits). Groups, cyclic groups, permutation
groups, isomorphisms, cosets and Lagrange’s theorem, rings, integral domains,
vector spaces, and fields. Prerequisites: MTH 3102.
MTH 4082 INTRODUCTION TO PARALLEL PROCESSING (3 credits).
Introduces parallel algorithm development, architectures for parallel computers, programming
paradigms SIMD and MIMD for shared and distributed memory computers.
Presents parallel algorithms for matrix computations, sorting and searching, and
various numerical algorithms. Includes analysis of performance of parallel algorithms
and scalability of algorithms. (Requirement: Programming ability in FORTRAN
or C.) Prerequisites: CSE 1502 or CSE 1503 or CSE 2010 or CSE 2050.
198 Florida Tech
MTH 4101 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 or MTH 2201.
MTH 4105 TOPOLOGY (3 credits). Metric and topological spaces, continuity,
homeomorphism connectedness, compact spaces, separation axioms, product spaces,
homeotypic and fundamental group. Prerequisites: MTH 2051, MTH 3102.
MTH 4201 MODELS IN APPLIED MATHEMATICS (3 credits). Allows students
to formulate and construct mathematical models that are useful in engineering,
physical sciences, biological sciences, environmental studies and social sciences.
(Requirement: Junior standing.) Prerequisites: MTH 2201.
MTH 4311 NUMERICAL ANALYSIS (3 credits). Introduces numerical methods
for solving equations in one variable, polynomial approximation, interpolation,
numerical differentiation and integration, initial-value problems for ODE and
direct methods for solving linear systems. Prerequisites: CSE 1502 or CSE 1503 or
CSE 2050, MTH 2201.
MTH 4320 NEURAL NETWORKS (3 credits). Includes basic existence
theory, differential and integral inequalities, qualitative and quantitative theory, and
Lyapunov’s second method. Prerequisites: CSE 1502 or CSE 1503 or CSE 2050,
MTH 2201.
MTH 4801 ADVANCED GEOMETRY (3 credits). Topics in Euclidean and non-
Euclidean geometry with an emphasis on proofs and critical thinking. Satisfies the
state of Florida requirement for teacher certification in mathematics. (Requirement:
Instructor approval or prerequisite course.) Prerequisites: MTH 2001.
MTH 4920 SPECIAL TOPICS IN APPLIED MATHEMATICS (3 credits).
Selected topics from mathematics. Content varies from year to year depending on
the needs and interests of the students and expertise of the instructor. (Requirement:
Instructor approval.)
MTH 4990 UNDERGRADUATE RESEARCH (3 credits). Participation in a
research project under the direction of a faculty member. (Requirement: Instructor
approval.)
MTH 5007 INTRODUCTION TO OPTIMIZATION (3 credits). An applied
treatment of modeling, analysis and solution of deterministic (e.g., nonprobabilistic)
problems. Topics include model formulation, linear programming, network flow,
discrete optimization and dynamic programming. (Requirement: At least one upperlevel
undergraduate math course.)
MTH 5009 INTRODUCTION TO PROBABILISTIC 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 MATHEMATICS (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
upper-level undergraduate math course.)
MTH 5111 REAL VARIABLES 1 (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 5101.