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Description
The University of Central Florida 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.
The master's program offers a track in Industrial Mathematics to prepare graduate students to pursue careers in industry by providing them with high quality 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 industrial jobs at the local and national levels.
Students in the doctoral program specialize in one of many different aspects of mathematics, including propagation through random media, nonlinear waves, graph theory, operator algebra and frame theory, tomography, approximation theory, differential equations, nonlinear dynamics and mathematical physics, as well as abstract algebra, real and complex analysis, and probability theory. In response to this wide variety of interests, the program offers more flexibility in the composition of the core as well as the qualifying examination. The program is comprehensive with opportunities for prospective students to pursue research in a variety of disciplines.
The goal of the doctoral program is to produce students with a broad base who will attain distinction in their fields of research. In order to achieve this, the program has a required core as well as a set of electives providing cross-disciplinary subjects. All Ph.D. students are required to take electives outside the department.
Research interests of the faculty include applied analysis, differential equations, methods of mathematical physics, nonlinear waves, probability and mathematical statistics, functional analysis, numerical analysis, approximation theory, nonlinear dynamics, fluid mechanics, wave propagation, algebra, number theory, combinatorics and graph theory, inverse problems, special functions and orthogonal polynomials, financial mathematics, and medical imaging.
Degrees Offered
- Master of Science in Mathematical Science
- Industrial Mathematics Track
- Doctor of Philosophy in Mathematics
Admission
For information on general UCF graduate admissions requirements that apply to all prospective students, please visit the Admissions and Registration section of the Graduate Catalog. Applicants must apply online. Please be sure to submit all requested material by the established deadline(s).
The Graduate Record Examination (GRE) is required of all applicants to the master's and doctoral programs. 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 competitive GRE score on the combined verbal-quantitative sections of the General (Aptitude) Test; or (3) a prior graduate degree from an accredited institution. In addition, all doctoral applicants are required to submit a resume, goal statement, and three letters of recommendation. Both the general test of the Graduate Record Examination (GRE) and the subject test in Mathematics are required of all doctoral applicants to this program. GRE results must be less than five years old.
Meeting minimum UCF admission criteria does not guarantee program admission. Final admission is based on evaluation of the applicant's abilities, past performance, recommendations, match of this program and faculty expertise to the applicant's career/academic goals, and the applicant's potential for completing the degree.
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 nondegree-seeking status, although only nine hours in this status can be transferred into a graduate program.
Application Due Dates
All students applying for fellowships must apply by the Fall Priority deadline date.
U.S. Applicants
| Program(s) | Fall Priority | Fall | Spring | Summer |
| Doctor of Philosophy in Mathematics | Jan 15 | Jul 15 | Dec 1 | Apr 15 |
| Master of Science in Mathematical Science | Jan 15 | Jul 15 | Dec 1 | Apr 15 |
| Industrial Mathematics Track | Jan 15 | Jul 15 | Dec 1 | Apr 15 |
International Applicants
| Program(s) | Fall Priority | Fall | Spring | Summer |
| Doctor of Philosophy in Mathematics | Jan 15 | Jan 15 | Jul 1 | Nov 1 |
| Master of Science in Mathematical Science | Jan 15 | Jan 15 | Jul 1 | Nov 1 |
| Industrial Mathematics Track | Jan 15 | Jan 15 | Jul 1 | Nov 1 |
International Transfer Applicants
| Program(s) | Fall Priority | Fall | Spring | Summer |
| Doctor of Philosophy in Mathematics | Jan 15 | Mar 1 | Sep 1 | Dec 15 |
| Master of Science in Mathematical Science | Jan 15 | Mar 1 | Sep 1 | Dec 15 |
| Industrial Mathematics Track | Jan 15 | Mar 1 | Sep 1 | Dec 15 |
Master of Science in Mathematical Science
There are two options for the master’s degree: thesis and nonthesis. 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 director for approval.
The nonthesis master’s requires students to take MAP 5407 Applied Mathematics I, where they apply mathematical principles to independent projects. Other courses also have substantial research projects, including MAP 5117 Mathematical Modeling, MAT 5711 Scientific Computing, and MAP 6111 Mathematical Statistics. The research study and final report will focus on reviewing and analyzing contemporary research in a student’s particular specialization within mathematics in order to help students acquire knowledge and skills pertaining to research-based best practices in that specialization area.
Electives
Electives should be chosen in consultation with the graduate program director 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 director. Approved graduate courses outside the department may also be used. At least one-half of the program courses must be taken at the 6000 level.
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.
Requirements for M.S. with Thesis Option—30 Credit Hours Minimum
A typical plan of study:
- MAA 5210 Topics in Advanced Calculus (4 credit hours)
- MAA 5405 Complex Variables (3 credit hours)
- MAP 5336 Ordinary Differential Equations and Applications (3 credit hours)
- MAP 5385 Applied Numerical Mathematics (3 credit hours)
- MAP 5407 Applied Mathematics I (3 credit hours)
- MAS 5145 Advanced Linear Algebra and Matrix Theory (3 credit hours)
Electives (9 credit hours)
- MAP 6971 Thesis (3 credit hours)
Nonthesis Option
In this option the student takes 36 credit hours of course work with at least 21 credit hours in the Department of Mathematics. The student must pass a comprehensive written examination given in the final semester of the student’s program, based on the program of study. The examination will be on four of the six courses in the plan 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.
Requirements for M.S. with Nonthesis Option—36 Credit Hours
A typical plan of study:
- MAA 5210 Topics in Advanced Calculus (4 credit hours)
- MAA 5405 Complex Variables (3 credit hours)
- MAP 5336 Ordinary Differential Equations and Applications (3 credit hours)
- MAP 5385 Applied Numerical Mathematics (3 credit hours)
- MAP 5407 Applied Mathematics I (3 credit hours)
- MAS 5145 Advanced Linear Algebra and Matrix Theory (3 credit hours)
Electives (18 credit hours)
Industrial Mathematics Track
A track in Industrial Mathematics is offered to prepare graduate students to pursue careers in industry by providing them with high-quality 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 nonthesis 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 director 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.
Note: The following courses are required as prerequisites to this track: 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 credit hours)
- MAP 5117 Mathematical Modeling (3 credit hours)
- MAP 5385 Applied Numerical Mathematics (3 credit hours)
- MAP 6111 Mathematical Statistics (3 credit hours)
- MAT 5711 Scientific Computing (3 credit hours)
Electives
Electives should be chosen in consultation with the graduate program director and the student’s adviser. A list of elective courses can be obtained from the graduate program director. 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. At least one-half of the program courses must be taken at the 6000 level.
Thesis Option
Minimum Requirements for M.S. with Thesis Option—30 Credit Hours
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 adviser or the graduate program director). It is recommended that the thesis topics have potential for industrial applications. An oral defense of the thesis will be required.
Nonthesis Option
Requirements for M.S. with Nonthesis Option—36 Credit Hours
The nonthesis option requires 36 credit hours of courses, including the required courses and a written 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 adviser or the graduate program director). 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 on the required courses with the exclusion of Scientific Computing. 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 pass/fail grade is given on the examination; and it may be repeated twice if necessary.
Doctor of Philosophy in Mathematics
Total Hours Required for Ph.D.—Minimum of 75 credit hours beyond the bachelor’s degree; minimum of 45 credit hours beyond the master’s degree
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 or independent research may be credited toward the degree. At least one-half of the program courses must be taken at the 6000 level.
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) previously as part of an undergraduate progrm, then MAP 5435 (Advanced Mathematics for Engineers) cannot be applied toward the graduate program of study, and another can be taken.
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. In addition to the 75 semester hours of the program, a minimum of 3 credit hours of an approved computer language are required. The language and computer courses may have been taken at any point in the student’s postsecondary career.
Core Courses—18 Semester Hours
Students must take six of the following courses. The choices must be approved by the graduate director.
- MAA 5405 Complex Variables (3 credit hours)
- MAA 5416 Foundations of Analysis (3 credit hours)
- MAA 6404 Complex Analysis (3 credit hours)
- MAA 6506 Functional Analysis (3 credit hours)
- MAP 5336 Ordinary Differential Equations and Applications (3 credit hours)
- MAP 5407 Applied Mathematics I (3 credit hours)
- MAA 6238 Measure and Probability (3 credit hours)
- MAP 6356 Partial Differential Equations (3 credit hours)
- MAP 6408 Applied Mathematics II (3 credit hours)
- MAS 5311 Abstract Algebra with Applications (3 credit hours)
Electives—42 Semester Hours
Dissertation—15 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 a written examination that will be administered twice a year. Students must obtain permission from the graduate program director 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. 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.
Depending on the choice of core courses, students may choose to complete qualifying exams in either one of the following two groups of courses:
- MAA 5416 Foundations of Analysis (3 credit hours)
- MAA 6404 Complex Analysis (3 credit hours)
- MAA 6506 Functional Analysis (3 credit hours)
- MAS 5311 Abstract Algebra with Applications (3 credit hours)
- MAA 5405 Complex Variables (3 credit hours)
- MAP 5336 Ordinary Differential Equations and Applications (3 credit hours)
- MAP 5407 Applied Mathematics I (3 credit hours)
- MAP 6356 Partial Differential Equations (3 credit hours)
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.
Financial Support
Graduate students may receive financial assistance through fellowships, assistantships, tuition support, or loans. For more information, see Financing Grad School, which describes the types of financial assistance available at UCF and provides general guidance in planning your graduate finances. The Financial Information section of the Graduate Catalog is another key resource.
Key points about financial support:
- If you are interested in financial assistance, you are strongly encouraged to apply for admission early. A complete application for admission, including all supporting documents, must be received by the priority date listed for your program under "Admissions."
- You must be admitted to a graduate program before the university can consider awarding financial assistance to you.
- If you want to be considered for loans and other need-based financial assistance, review the UCF Student Financial Assistance website at http://finaid.ucf.edu and complete the FAFSA (Free Application for Federal Student Aid) form, which is available online at http://www.fafsa.ed.gov. Apply early and allow up to six weeks for the FAFSA form to be processed.
- UCF Graduate Studies awards university graduate fellowships, with most decisions based on nominations from the colleges and programs. To be eligible for a fellowship, students must be accepted as a graduate student in a degree program and be enrolled full-time. University graduate fellowships are awarded based on academic merit and therefore are not affected by FAFSA determination of need.
- Please note that select fellowships do require students to fill out a fellowship application (either a university fellowship application, an external fellowship application, or a college or school fellowship application). For university fellowship applications, see Financing Grad School.
- For information on assistantships (including teaching, research, and general graduate assistantships) or tuition support, contact the graduate program director of your major.
Contact Info
Doctor of Philosophy in Mathematics
Ram Mohapatra, Ph.D., Professor
Phone Number: 407-823-5080
ramm@mail.ucf.edu
Master of Science in Mathematical Science
Ram Mohapatra, Ph.D., Professor
Phone Number: 407-823-5080
ramm@mail.ucf.edu
Industrial Mathematics Track
Ram Mohapatra, Ph.D., Professor
Phone Number: 407-823-5080
ramm@mail.ucf.edu