2011–2012 UNIVERSITY CATALOG - Florida Institute of Technology

General degree requirements are presented in the Academic
Overview section.
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)
Areas of specialization include nonlinear analysis; stochastic
analysis; optimization; numerical analysis and scientific computing;
and 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, Ph.D. ____________________
Major Code: 9074 Degree Awarded: Doctor of Philosophy
Age Restriction: N Admission status: graduate
Delivery Mode/s: classroom only Location/s: main campus
Admission Materials: 3 letters of
recommendation, résumé, objectives
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.
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 coursework.
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.
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.
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. The student may
opt to concentrate study in the area of human-centered design
(described below).
Computation Electives
MTH 5301 Numerical Analysis
MTH 5305 Numerical Linear Algebra
MTH 5320 Neural Networks
ORP 5050 Discrete System Simulation
Human-Centered Design
The program in human-centered design (HCD) is offered for
students who wish to carry out advanced research, innovation and
leadership in the academic world, as well as fill equivalent positions
in industry and government. The program may be completed
through one of three areas: aerospace engineering, operations
research or computer science. Other research areas within the
field may be pursued depending on current trends in the Human-
Centered Design Institute (HCDi) of Florida Tech.
The program is designed to attract students who have the greatest
potential for expanding the frontiers of knowledge and art of
HCD, and in transferring this knowledge and art to others. It is
open to graduate students who have a strong interest in people and
are ready to learn about applied human and social sciences. HCD
requires significant breadth and depth of understanding in engineering,
mathematics and science, the mastery of several specialized
subjects and the creativity to extend the body of knowledge
and art on a particular subject through significant original research.
Each candidate is expected to publish major portions of their dissertation
in refereed conferences and journals, and is strongly encouraged
to actively participate in research activities of the HCDi while
pursuing the degree. The student’s advisory committee and the
director of the HCDi must approve the doctoral program of study.
RESEARCH
Applied Mathematics
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, reaction-diffusion
Degree Programs—College of Science 191