2008–2009 - Florida Institute of Technology

which it complements other courses and furnishes breadth and
depth to the program. The work should consist of advanced studies
and scientific research that lead to a significant contribution
and knowledge of a particular area.
Each student must pass a preliminary examination covering the
core courses, complete an approved program of studies, pass the
comprehensive examination (usually oral), complete a program
of significant original research work and defend a dissertation
concerning the research work completed.
General degree requirements are presented in the Academic
Overview section of this catalog.
Curriculum
After a bachelor’s degree in mathematical sciences, a minimum
of 75 credit hours is required for the doctoral program, including
the courses listed below:
Core Areas (30 credit hours)
Linear Algebra............................................................................................3
Real and Complex Variables.......................................................................9
Numerical and Computational Mathematics .............................................6
Probability and Statistics ...........................................................................6
Differential Equations ...............................................................................6
Areas of Specialization (21–27 credit hours)
Nonlinear Analysis
Stochastic Analysis
Optimization
Numerical Analysis and Scientific Computing
Statistics
Considerable flexibility is allowed in the selection of courses in
core areas and areas of specialization. Selected course offerings
from the mathematics department and other areas of science and
engineering may be taken to fulfill the requirements.
Doctoral Dissertation
The dissertation consists of 24–30 credit hours of work and is
expected to be completed within two years. The doctoral dissertation
is expected to represent original research in mathematics.
It may present new theoretical developments or new areas of
application or both. The dissertation should contain results that
constitute a significant contribution to the literature of the field
of investigation. These results should be worthy of publication in
an established technical journal.
Operations Research ________________________
The doctor of philosophy program provides a more advanced
level of education, as well as demonstrated ability to perform
independent research. These additional strengths should qualify
the graduate for vital positions of leadership in industry, business,
government and academia.
Admission Requirements
An applicant for the doctoral program will normally have completed
a master’s degree in operations research or a related discipline.
If the master’s degree is not in operations research, then
the student will be required to take the core courses for Florida
Tech’s master’s degree in operations research. These courses may
be used toward fulfilling the credit requirements for the Ph.D. in
operations research. Students also will be required to pass a written
qualifying examination equivalent to Florida Tech’s master’s
final program examination.
General admission requirements are discussed in the Academic
Overview section of this catalog.
134 Florida Tech
Degree Requirements
A minimum of 48 credit hours beyond the requirements for the
master’s degree is required to earn the doctoral degree. These
credits include 24 credit hours of dissertation research in addition
to normal course work.
Each student must complete an approved program of study, pass
a comprehensive examination, complete a program of significant
original research, and defend a dissertation concerning the
research. General degree requirements are presented in the
Academic Overview section of this catalog.
Curriculum
The individual doctoral program of study must be approved by
the student’s doctoral committee and the program chair. Students
who have not taken MTH 5051 and MTH 5102, or their equivalents,
will be required to take them. Students are also required
to take at least two courses from the Computation/Computer
Science list above.
The doctoral program in operations research does not fall within
the traditional boundaries of a single discipline. The scope is
broad and interdisciplinary. Consequently, every course in a
student’s program of study is evaluated in terms of how it complements
other courses and provides breadth and depth to the
program. Considerable latitude is permitted in course selection,
provided the core requirements for operations research/mathematics/computation
are met. The remaining courses are selected
in collaboration with the Doctoral Committee according to the
interests and research objectives of the student.
research
Active areas of research in the mathematics program include
methods of nonlinear analysis, qualitative and quantitative
properties of nonlinear evolution equations (including differential
equations with delay), integro-differential equations and stochastic
differential equations, spectral theory of operators, reactiondiffusion
equations, approximation theory, applied statistics,
sequential analysis, mathematical programming, combinatorial
optimization, operations research, queuing theory, stochastic
processes, mathematical modeling, neural networks, numerical
and computational mathematics with emphasis on numerical
methods for ordinary and partial differential equations, numerical
algorithms and parallel processing.
Current active research in operations research include the modeling
of controlled queuing systems, stochastic processes, applied
statistics, design of experiments, neural networks, parallel
processing and algorithms, decision-making under uncertainty,
simulation, engineering management, quality control, optimization
models and methods, scheduling and timetabling algorithms,
applied graph theory and integer programming.