Mathematics PhD

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College : Sciences Degree :PHD
Department : Mathematics Option : Dissertation
Program Websites :


The Mathematics PhD program prepares students with a broad base in pure, applied and industrial mathematics.


The Mathematics PhD program consists of at least 75 credit hours of course work beyond the bachelor's degree, of which a minimum of 39 hours of formal course work, exclusive of independent study, and 15 credit hours of dissertation research (7980) are required. The program requires 18 credit hours of core courses, and 6 to 12 credit hours in two 2-semester sequences.
Total Credit Hours Required:
75 Credit Hours Minimum beyond the Bachelor's Degree

Required Courses—18 Credit Hours

The remaining 30 to 36 credit hours consist of additional dissertation research (7980 or 7919), at least 15 credit hours of regular classroom elective courses, and at most 12 credit hours of independent study or independent directed research. Electives require the approval of the adviser and the graduate program director; up to 12 credit hours may be taken outside the department. At least one-half of the program courses must be taken at the 6000 level. Students who pass the qualifying examination may substitute some of the core courses at the approval of the adviser and the graduate program director.

All students are required to complete the following courses with grade of "B" or better.

  • MAA 5228 Analysis I (3 credit hours)
  • MAA 6229 Analysis II (3 credit hours)
  • MAT 5712 Scientific Computing (3 credit hours)
  • MAP 6385 Applied Numerical Mathematics (3 credit hours)
  • MAS 5145 Advanced Linear Algebra and Matrix Theory (3 credit hours)
  • MAA 6405 Complex Variables (3 credit hours) or MAP 5336 Ordinary Differential Equations and Applications (3 credit hours)

Elective Courses—42 Credit Hours

At least 21 hours of course work here must be formal course work, exclusive of independent study.

Restricted Electives—6-12 Credit Hours

All students are required to complete two 2-semester sequences. Sequences are pairs of related courses that give advanced knowledge in an area of mathematics.

Each sequence must be approved by the dissertation adviser, dissertation committee, and the graduate program director. The following shows examples of acceptable sequences using current courses. We expect that other sequences will be developed as our program grows. Note that some sequences consist of a core course plus one elective, while others consist of two electives. Thus, the credit hours in this requirement are variable (6 to 12 credit hours). A written examination on two such sequences will be required as part of the candidacy examination (see more details in Candidacy Examination section).

  • MAP 6407 Integral Equations and the Calculus of Variations (3 credit hours) / MAP 6408 Perturbations and Asymptotic Methods (3 credit hours)
  • MAA 6405 Complex Variables (3 credit hours) / MAA 6404 Complex Analysis (3 credit hours)
  • MAD 5205 Graph Theory I (3 credit hours) / MAD 6309 Graph Theory II (3 credit hours)
  • MAP 5336 Ordinary Differential Equations with Applications (3 credit hours) / MAP 6356 Partial Differential Equations (3 credit hours)
  • MAA 6238 Measure and Probability I (3 credit hours) / MAP 6111 Mathematical Statistics (3 credit hours)
  • MAA 6306 Real Analysis (3 credit hours) / MAA 6506 Functional Analysis (3 credit hours)

Unrestricted Electives—30-36 Credit Hours

Electives are chosen in consultation with the student’s advisory committee and may be chosen from the suggested options: Discrete Mathematics, General Applied Mathematics, Mathematical Computer Tomography, Image Processing and Computer Graphics, Mathematical Finance, Mathematical Physics, Pure Mathematics, and Mathematical Statistics. A list of elective course options can be obtained from the graduate program director. 

Courses taken outside the Mathematics department must be approved by the adviser and graduate program director. These courses are selected in consultation with the student’s advisory committee.

Dissertation—15 Credit Hours Minimum

  • XXXX 7980 Dissertation Research (15 credit hours minimum)

Qualifying Examination

The qualifying/comprehensive examination is based on the core course work (MAA 5228 Analysis I, MAA 6229 Analysis II, MAS 5145 Advanced Linear Algebra and Matrix Theory). To continue in the PhD program students must pass the examination at the PhD level. Two attempts are permitted. The examination will be administered twice a year: one in the Fall semester and the other in the Spring semester. To take the examination, students must have earned a "B" or better in each core course, must have a minimum grade point average of 3.0 (out of 4.0) in the program, or must obtain permission from the graduate program director. Students will normally take the examination after the first year and are expected to have passed it by the end of the second year of study unless a written request for a postponement has been approved by the Graduate Committee at least two months before the examination date. The student must pass the Qualifying Examination in at most two attempts.

It is strongly recommended that the student select a dissertation adviser by the completion of 18 credit hours of course work, and it is strongly recommended that the student works with the dissertation adviser to form a dissertation committee within two semesters of passing the Qualifying Examination.

Candidacy Examination

The Candidacy Examination consists of a written examination based on the materials from two of the selected two-semester sequence courses taken by the students beyond the core courses on Analysis and Advanced Linear Algebra (MAA 5228, MAA 6229, MAS 5145). A committee formed or selected by the Graduate Committee or the graduate program director is responsible for preparing and grading the written examinations.

After passing the candidacy examination and meeting other requirements, the student can register for Doctoral Dissertation (MAP 7980 or MAA 7980). A minimum of 15 Doctoral Dissertation credit hours are required. The Candidacy Examination can be attempted after passing the qualifying examination. The Candidacy Examination must be completed within three years after passing the qualifying examination. A student must successfully pass the Candidacy Examination within at most two attempts.

Admission to Candidacy

The following are required to be admitted to candidacy and enroll in dissertation hours:

  • Completion of all course work, except for dissertation hours.
  • Successful completion of the candidacy examination.
  • The dissertation advisory committee is formed, consisting of approved graduate faculty and graduate faculty scholars.
  • Submittal of an approved program of study.

Dissertation Proposal Examination

After passing the candidacy examination, the student will prepare a dissertation proposal and orally present it to the dissertation advisory committee for approval. The proposal will include a description of the research performed to date and an agenda for the research planned to be completed for the dissertation. In addition to standards of correctness, indicating a suitable level of mastery of the material of the area of the dissertation, and suitability of the proposed dissertation topic, the presentation must meet current standards for professional presentations within the discipline of mathematics. For the successful completion of the Dissertation Proposal Examination the presentation must be judged as passing the requirements for the examination by the majority of the dissertation committee. This exam must be passed within 18 months of passing the candidacy examination and not later than the end of the sixth year of graduate study. A candidate must pass this examination within at most two attempts.

Dissertation Defense

Upon completion of a student’s research, the student’s committee schedules an oral defense of the dissertation. Most students complete the program within five years after obtaining their bachelor's degree. Students are expected to complete the dissertation in no more than seven years from the date of admission to the program.

Independent Learning

The required 15 credit hours of dissertation will provide ample opportunities for students to gain the independent learning experience through studying published research papers and deriving, on their own, new and meaningful research results.

Application Requirements

For information on general UCF graduate admissions requirements that apply to all prospective students, please visit the Admissions section of the Graduate Catalog. Applicants must apply online. All requested materials must be submitted by the established deadline.

In addition to the general UCF graduate application requirements, applicants to this program must provide:

  • One official transcript (in a sealed envelope) from each college/university attended.
  • Bachelor's degree in related field.
  • Official, competitive GRE score, taken in the last five years.
  • Three letters of recommendation.
  • Goal statement.
  • Résumé.

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 the 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. 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), and maturity in the language of advanced calculus (at the level of MAA 4226). Students who 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, do not count toward the graduate degree.

Application Deadlines

Mathematics PhD *Fall Priority Fall Spring Summer
Domestic Applicants Jan 15Jul 15Dec 1Apr 15
International Applicants Jan 15Jan 15Jul 1Nov 1
International Transfer Applicants Jan 15Mar 1Sep 1Dec 15
*Applicants who plan to enroll full time in a degree program and who wish to be considered for university fellowships or assistantships should apply by the Fall Priority date.


Graduate students may receive financial assistance through fellowships, assistantships, tuition support, or loans. For more information, see the College of Graduate Studies Funding website, 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.


Fellowships are awarded based on academic merit to highly qualified students. They are paid to students through the Office of Student Financial Assistance, based on instructions provided by the College of Graduate Studies. Fellowships are given to support a student’s graduate study and do not have a work obligation. For more information, see UCF Graduate Fellowships, which includes descriptions of university fellowships and what you should do to be considered for a fellowship. 

The department offers over 20 Graduate Teaching Assistantships every year on a competitive basis. A few Graduate Research Assistantships are also available for qualified students.