Ph.D. in Applied Mathematics

Doctor of Philosophy
Main Campus - Melbourne
Major Code: 9073 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 doctoral program in mathematics is designed to produce a mathematician with a broad background in analysis and a strong field of specialization in applied analysis, modeling or numerical analysis and scientific computing. This combination of training will prepare the student for a career in a variety of areas, such as government or industrial research, or academic research and teaching. Doctoral graduates have the necessary experience in areas of application to be able to work successfully with other members of multidisciplinary research teams. Graduates also have the critical ability to think independently and analytically. They are able to make significant contributions to knowledge in their chosen fields of inquiry.

A preliminary program of study should be prepared by the student and advisor during the first semester of graduate studies. The final doctoral program of study must be approved by the student's advisory committee and program chair.

Admission Requirements

Applicants for the doctoral program in mathematics usually have a bachelor's or master's degree in mathematics. However, applications are also invited from graduates in physical and engineering sciences. In these cases, necessary undergraduate courses have to be taken to offset deficiencies before the student enters the doctoral program. In evaluating international applicants, due consideration is given to academic standards in the country in which the graduate studies were performed. Graduate teaching assistants carry on a variety of teaching assignments and in view of this, evidence of good English-speaking skills is an important criterion in processing the applications. For admission, a student should have a superior academic record and letters of recommendation. Preference will be given to applicants who have good scores on the GRE.

General admission requirements and the process for applying are presented in the Academic Overview section.

Degree Requirements

The degree of doctor of philosophy (Ph.D.) is conferred primarily in recognition of the breadth of scientific accomplishment and the power to investigate scientific problems independently, rather than for the completion of a definite course of studies. Although demanding a strong mathematical orientation, the doctoral program in mathematics does not fall within the traditional boundaries of a single academic unit and the scope is quite broad. Consequently, every course in a student's program of study is evaluated not only as to content, but also as to the way in 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.


The doctoral program in applied mathematics requires a minimum of 72 semester credit hours after the bachelor's degree or 42 semester credit hours after the master's degree. Students entering the Ph.D. program with a bachelor's degree must follow the master of science degree requirements listed above for 30 semester credit hours. Students entering the Ph.D. program with a master's degree in mathematics, or continuing doctoral students with 30 credit hours equivalent to master's degree requirements in applied mathematics must take six 5000- or 6000-level mathematics course on-site at Florida Tech (equivalent to 18 semester credit hours).

A course used for a master's degree cannot be used to fulfill the doctoral requirements. Transfer course substitutions must be approved by the department head. All students must successfully complete a preliminary examination; a series of three qualifying written examinations and one oral examination; and present and orally defend a written dissertation proposal.

In addition, all students must successfully complete a virtual written grant proposal and defend it orally; submit a written dissertation and defend it orally; and complete a minimum of 24 semester credit hours of dissertation research.

Doctoral Dissertation

Each student must take a preliminary examination by the end of the first year (offered twice a year). The examination includes the calculus sequence, linear algebra and differential equations, and may be retaken only once. A passing grade on the preliminary examination is 80 percent and students who score 60-80 percent will continue in the master's program.

Before acceptance to the first proposal defense, students must take a series of qualifying comprehensive examinations (three written, two-hour examinations and one oral examination) on three topics chosen with the approval of their major advisor, and based on the student's coursework. Written examinations must be taken within one week, followed by the oral examination within two weeks after passing the written examinations. Passing grades for each of the qualifying examinations is 75 percent and a failed examination should be retaken within three weeks. Any examination may be retaken only once. Students who fail the written qualifying examination series may earn a master's degree on passing a final program examination.

Further examination and committee requirements include:

  • Examinations taken after completion of coursework.
  • At least 60 days before the examination series, the examination committee must be formed, the corresponding document signed by all committee members and the department head to be filed with the graduate school.
  • The examination series must be taken within a three-week period.
  • The oral examination should include advanced topics in the area(s) of the proposed research at the discretion of student's advisor.

The doctoral dissertation includes:

  • Two proposals
  • Dissertation coursework (a minimum of 24 credit hours)
  • Defense

The first proposal will be based on forthcoming research. A proposal defense must be preceded by at least three credit hours of research (six hours are recommended). A student can take as many hours as needed for the completion of the proposal defense. However, only a maximum of nine credit hours will be counted toward the dissertation. A minimum of 15 credit hours of dissertation must be taken after the proposal defense.

At least 60 days before the proposal defense, the dissertation committee must be formed unless it is identical to the examination committee. In the former case, a corresponding document signed by all dissertation committee members must be filed with the graduate school. On successful oral defense of the proposal, the student is allowed to continue their research.

Before the dissertation defense, the student defends a second proposal, which must include a virtual submission of a written grant proposal to a funding agency (such as NSF) and approved by the dissertation committee, followed by an oral presentation and discussion. The topic of the research must be related to the dissertation.

The dissertation is expected to represent original research that expands the boundary of knowledge in modern mathematics. Before the defense, the student is expected to present at a conference and have at least one paper published or accepted for publication in an established academic journal with ranking.

The dissertation must be written and orally defended. A written thesis of the dissertation must be sent to each committee member at least 30 days before the scheduled defense.