Mathematics
Chair of the Department: John R. Cannon
Graduate Program Coordinator: Ahmed Zayed
MAP 212, (407) 823-5989.
E-mail: zayed@pegasus.cc.ucf.edu
Faculty
Professors: L. C. Andrews, Ph.D.; L. H. Armstrong, Ph.D.; R. C. Brigham, Ph.D.; J. R. Cannon, Ph.D.; L. Debnath, Ph.D.; P. Hilton, Ph.D., Distinguished Professor; P. Mikusinski, Ph.D.; R. N. Mohapatra, Ph.D.; G. D. Richardson, Ph.D.; B. K. Shivamoggi, Ph.D.; M. D. Taylor, Ph.D.; K. Vajravelu, Ph.D.; A. I. Zayed, Ph.D.Associate Professors: J. M. Anthony, Ph.D.; R. M. Caron, Ph.D.; S. R. Choudhury, Ph.D.; M. N. Heinzer, Ph.D.; X. Li, Ph.D.; C. P. Rautenstrauch, Ph.D.; R. S. Rodriguez, Ph.D.; D. K. Rollins, Ph.D.
Assistant Professors: C. Hopen, Ph.D.; R. C. Jones, Ph.D.; A. Katesvich, Ph.D.; H. M. Martin, Ph.D.; M. Y. Pensky, Ph.D.; F. L. Salzmann, Ph.D.; A. Tovbis, Ph.D.; Y. Zhao, Ph.D.
Instructor: R. Pyle, M.S.
Visiting Instructors: L. Dunlop, M.S.; M. Langfield, M.S.
Joint Appointees: T. Clarke, Ph.D., Associate Faculty; R. Dutton, Ph.D., Professor of Computer Science; L. Hoffman, Ph.D., Associate Professor of Statistics; A. J. Kassab, Ph.D., Associate Professor of Engineering; D. W. Nicholson, Ph.D., Professor of Engineering; R. L. Phillips, Ph.D., Professor of Engineering
The Department of Mathematics offers a Master of Science degree in Mathematical Science and a Doctor of Philosophy degree in Mathematics. Both degrees are intended to provide a broad base in applied and industrial mathematics. Research interests of the faculty include applied analysis, differential equations, methods of mathematical physics, probability and mathematical statistics, functional analysis, numerical analysis, approximation theory, nonlinear dynamics, fluid mechanics, wave propagation, algebra, number theory, and combinatorics and graph theory.
Application Deadlines
| Fall admission | July 15 |
| Spring admission | December 1 |
| Summer admission | April 15 |
Admission
The Graduate Record Examination (GRE) is required of all graduate students. Admission requirements are the standard university criteria of either: (1) at least the equivalent of a 3.0 (out of 4.0) grade point average (GPA) for the last 60 attempted semester hours of credit earned toward the baccalaureate; or (2) a GRE score of at least 1000 for the combined verbal-quantitative sections of the General (Aptitude) Test; or (3) a prior graduate degree from an accredited institution. GRE results must be less than five years old. Transfer of credits from other programs will be considered on a course-by-course basis. The department requires international students and students whose native language is not English to have a minimum score of 220 (computer-based test; or equivalent score on the paper-based test) on the Test of English as a Foreign Language (TOEFL).Additionally, students entering the graduate program with regular status are assumed to have a working knowledge of undergraduate calculus, differential equations, linear algebra (or matrix theory), boundary value problems, statistics, computer programming, and maturity in the language of advanced calculus (at the level of MAA 4226). Those students who find they are not adequately prepared in one or more of these areas can select appropriate courses from the undergraduate curriculum to make up such deficiencies. Such courses, unless specially approved, will not count toward the graduate degree. Applicants not qualified for regular status may be admitted initially to the university in a non-degree-seeking status, although only nine hours in this status can be transferred into a graduate program.
Admission to the Ph.D. Program
Admission to the Ph.D. Program in Mathematics is formalized by the university upon the recommendation of the Department of Mathematics. To be eligible to take the Ph.D. Qualifying Examination, the student must have a minimum grade point average of 3.0 (out of 4.0) in all work beyond baccalaureate.Master of Science in Mathematical Science
There are two options for the master’s degree, thesis and non-thesis. In either option, a student should find an adviser who participates in designing a program of study. A program of study is presented to either the Graduate Curriculum Committee or the graduate program coordinator for approval.
Electives
Electives should be chosen in consultation with the graduate program coordinator or the student’s
thesis adviser and may be chosen from the suggested options: discrete mathematics, general applied
mathematics, image processing and computer graphics, mathematical optics, mathematical physics,
pure mathematics, rational mechanics, signal analysis, and statistics. A list of courses for these
elective options can be obtained from the graduate program coordinator. Approved graduate courses
outside the department may also be used. The student can take up to six credit hours of approved
4000-level mathematics courses. If a student takes MAP 4363 (Applied Boundary Value Problems I),
then MAP 5435 (Advanced Mathematics for Engineers) cannot be applied toward the graduate program
of study.
Thesis Option
In this option, the Mathematical Science degree requires a total of at least 30 semester hours
composed of at least 27 semester hours of course work and 3 semester hours of thesis. An oral
defense of the thesis will be required. It is strongly recommended that the student select a
thesis adviser by the completion of 18 semester hours of course work.
A typical plan of study:
MAA 5210 Topics in Advanced Calculus (4 hours)
MAA 5405 Complex Variables (3 hours)
MAP 5336 Ordinary Differential Equations and Applications (3 hours)
MAP 5385 Applied Numerical Mathematics (3 hours)
MAP 5407 Applied Mathematics I (3 hours)
MAS 5145 Advanced Linear Algebra and Matrix Theory (3 hours)
Electives (9 hours)
MAP 6971 Thesis (3 hours)
Minimum Hours Required for M.S. with Thesis Option—30-31 Semester Hours
Non-Thesis Option
In this option the student takes 36 semester hours of course work with at least 21 in the
Department of Mathematics. The student must pass a comprehensive examination given in the final
semester of the student’s program, based on the program of study. The examination will be
supervised by a committee composed of the adviser and at least two other faculty members from the
Department of Mathematics. A “P” or “NP” (or “S” or “U”) grade is given on the examination. The
examination may be repeated twice if necessary.
A typical plan of study:
MAA 5210 Topics in Advanced Calculus (4 hours)
MAA 5405 Complex Variables (3 hours)
MAP 5336 Ordinary Differential Equations and Applications (3 hours)
MAP 5385 Applied Numerical Mathematics (3 hours)
MAP 5407 Applied Mathematics I (3 hours)
MAS 5145 Advanced Linear Algebra and Matrix Theory (3 hours)
Electives (18 hours)
Minimum Hours Required for M.S. with Non-Thesis Option—36-37 Semester Hours
Industrial Mathematics Track
A track in Industrial Mathematics is offered to prepare graduate students to pursue careers in industry by providing them with a high quality of professional training in branches of mathematics that are valuable to high-technology industry. Graduates of the program will be able to pursue a wide variety of jobs at the local and national levels.This track offers a thesis or non-thesis option. In either option, a student will work with an adviser to design a program of study. A program of study is presented to either the Graduate Curriculum Committee or the program coordinator for approval. If a student has an industry sponsor, the student’s program of study will be developed in consultation with a representative from his sponsoring company. Students are expected to obtain hands-on experience by working at sponsoring companies during summer semesters.
There are several courses required as pre-requisites to this track. Those courses are as follows: Calculus with Analytic Geometry I, II, and III; Differential Equations; Elementary Linear and Matrix Algebra (or a course equivalent); Numerical Calculus (or a course equivalent); and Statistics.
Required Courses
MAP 5407 Applied Mathematics I (3 hours)
MAP 5XXX Mathematical Modeling (3 hours)
MAP 5XXX Scientific Computing (3 hours)
MAP 5385 Applied Numerical Mathematics (3 hours)
MAP 6111 Mathematical Statistics (3 hours)
Electives
Electives should be chosen in consultation with the graduate program coordinator or the student’s
adviser. A list of elective courses can be obtained from the graduate program coordinator.
Approved graduate courses outside the department may also be used. The student can take up to
six credit hours of approved 4000-level mathematics courses.
Minimum Hours Required for M.S.—30-36 Semester Hours
Thesis Option
The thesis option requires 27 credit hours of courses, including the required courses and 3 credit
hours of thesis. The student must take at least 15 credit hours from the Mathematics Department
and at least 6 credit hours from outside the department (with the approval of the advisor or the
graduate program coordinator). It is recommended that the theses subjects have potential for
industrial applications. An oral defense of the thesis will be required.
Non-Thesis Option
The non-thesis option requires 36 credit hours of courses, including the required courses and a
comprehensive examination. The student must take at least 21 credit hours from the Mathematics
Department and at least 9 credit hours from outside the department (with the approval of the
advisor or the graduate program coordinator). The comprehensive examination will be given in the
final semester of the student’s program of study, based on the program of study. The examination
will be supervised by a committee composed of the advisor and at least two other faculty members
from the Department of Mathematics. A pass/fail grade is given on the examination; and it may be
repeated twice if necessary.
Doctor of Philosophy in Mathematics
The Doctor of Philosophy (Ph.D.) program consists of at least 75 semester hours of course work, of which a minimum of 15 hours are required for the dissertation. In addition to the dissertation hours, the program requirements include 18 hours of core courses, 6-12 hours of course work at the graduate level outside the department, and the remainder made up of electives and independent study courses. No more than 12 semester hours of independent study may be credited toward the degree.Electives should be chosen in consultation with the student’s advisory committee and may be chosen from the suggested options: Discrete Mathematics, General Applied Mathematics, Image Processing and Computer Graphics, Mathematical Optics, Mathematical Physics, Pure Mathematics, Rational Mechanics, Signal Analysis, and Statistics. A list of courses for these elective options can be obtained from the graduate program coordinator. If a student takes MAP 4363 (Applied Boundary Value Problems I), then MAP 5435 (Advanced Mathematics for Engineers) cannot be applied toward the graduate program of study.
Courses taken outside the department are to be in a single area of application of mathematics that is related to the student’s doctoral work. These courses are to be selected in consultation with the student’s advisory committee. Students are encouraged to include in their plan of study a maximum of 12 semester hours of course work outside the department. Students can take up to 6 semester hours of approved 4000-level mathematics courses. In addition to the 75 semester hours of the program, a minimum of 3 hours of an approved computer language are required. The language and computer courses may have been taken at any point in the student’s post-secondary career.
Core Courses—18-19 Semester Hours
MAA 5210 Topics in Advanced Calculus (4 hours)
MAA 6404 Complex Analysis (3 hours)
MAA 6306 Real Analysis (3 hours)
MAP 5336 Ordinary Differential Equations and Applications (3 hours)
MAP 5407 Applied Mathematics I (3 hours)
MAS 5145 Advanced Linear Algebra and Matrix Theory (3 hours)
Electives—42 Semester Hours
Dissertation—15 Semester Hours
Minimum Hours Required for Ph.D.—75-76 Semester Hours
Examinations
In accordance with university requirements, a prospective doctoral student has to successfully pass the following examinations:- Qualifying Examination
- Candidacy Examination
- Dissertation Defense
Qualifying Examination
The qualifying examination is composed of six parts, with each part based on one of the six core
courses. The student must pass all six parts. All six parts must be completed within three attempts
with any number of parts being taken in each attempt. If a student cannot complete these
examinations in the three attempts, the student must leave the doctoral program.
The qualifying examination is a written examination that will be administered twice a year. Students must obtain permission from the Graduate Program Coordinator to take the examination. Students normally start taking this exam at the end of the first year and are expected to have completed the exams by the end of the second year unless a written request for a postponement has been approved by the Graduate Committee at least two months prior to the examination date.
After passing the qualifying exam, the student must select a dissertation adviser. Finding a dissertation adviser is the responsibility of the student and should be done as soon as possible. In consultation with the dissertation adviser, the student should form an advisory committee. The dissertation adviser will be the chair of the student’s advisory committee. This committee will approve a plan of study for the doctoral student and will recommend which courses outside the department should be taken.
Candidacy Examination
The candidacy examination will be administered by the student’s committee and will be tailored to
the student’s individual program. It can be attempted anytime after passing the qualifying
examination, and after the student has begun research but prior to the end of the third year
following the qualifying examination. The candidacy examination can be taken no more than two
times.
Dissertation Defense
Upon completion of a student’s research, the student’s committee will schedule an oral defense of
the dissertation. The student has seven years from the date of admission to the doctoral program to
complete the dissertation.
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