2013–2014 UNIVERSITY CATALOG - Florida Institute of Technology

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 3401 INTRODUCTION TO NUMBER THEORY (3 credits). Covers divisibility,
prime numbers, unique factorization, congruences. quadratic reciprocity,
Diophantine equations, properties of rational numbers, polynomials and dynamical
systems. Includes computation, formulating conjectures, writing proofs and
extended projects. (Requirement: Junior standing.) Prerequisites: MTH 1002.
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 disease-associated 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.
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 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.
MTH 5115 FUNCTIONAL ANALYSIS (3 credits). Banach spaces, Hilbert spaces,
topological vector spaces, bounded and unbounded linear operators, spectral theory.
Prerequisites: MTH 5101.
2013–2014 Course Descriptions 279