2012–2013 UNIVERSITY CATALOG - Florida Institute of Technology

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, CSE 1400 or 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 3210 INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
AND APPLICATIONS (3 credits). Includes heat, wave and Laplace equations,
initial and boundary value problems of mathematical physics and Fourier series.
Also covers Dirichlet problem and potential theory, Dalambert’s solutions for wave
equation, Fourier and Laplace transforms, and Poisson integral formula. Also
includes PDEs in higher dimensions and special functions of mathematical physics.
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 or MTH 3210.
MTH 3663 MATHEMATICAL METHODS FOR BIOLOGY AND
ECOLOGY (3 credits). Examines biological processes and mathematically reformulates
the biological information into linear and nonlinear systems, and differential
equations, and studies these formulations via matrix algebra, numerical techniques,
approximation theory, stability and bifurcation analysis. (Requirement: Junior standing
and instructor approval.) Prerequisites: BIO 2332 or MTH 2332, MTH 1002.
MTH 3993 SELECTED TOPICS ON BIOSTOCHASTICS (3 credits). Studies
the influence of stochasticity on biological processes using statistical methods and
Markov processes to analyze vital biological rates, including mutation rates for diseaseassociated
DNA repeats, organismal growth and per-capita survival. (Requirement:
Instructor approval.) Prerequisites: MTH 1002, BIO 2332 or MTH 2332.
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.
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.
276 Florida Tech
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.) (Q)
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 upper-level
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 upperlevel
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.
MTH 5115 FUNCTIONAL ANALYSIS (3 credits). Banach spaces, Hilbert spaces,
topological vector spaces, bounded and unbounded linear operators, spectral theory.
Prerequisites: MTH 5101.
MTH 5130 THEORY OF COMPLEX VARIABLES (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.