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College of Liberal Arts and Sciences

Department of Mathematics

Doctor of Philosophy

PhD degree requirements

NOTE: this page contains degree requirements for students who entered the program prior to the Fall 2025 academic term. For the requirements effective Fall 2025, see this page.

First Year Examination

Pass three parts of the First Year Exam, including at least one of the first four parts listed below, at least one of the last four parts listed below, and one of the exams on MAA 5228, MAA 5229, MAS 5311, MAS 5312 with grades of Pass or High Pass.

  1. MAA 5228 Modern Analysis 1
  2. MAA 5229 Modern Analysis 2
  3. MAD 6407 Numerical Analysis
  4. MTG 5316 Introduction to Topology 1
  5. MTG 5317 Introduction to Topology 2
  6. MAD 6406 Numerical Linear Algebra
  7. MAS 5311 Introduction to Algebra 1
  8. MAS 5312 Introduction to Algebra 2

After completing one of the core courses, a student may take the corresponding part of the First Year Exam only the first three times the exam is offered. The section Satisfactory Progress below has deadlines by which the parts must be passed.

2. Language proficiency

Demonstrate proficiency in reading mathematical works in French, German or Russian by receiving a grade of Pass on an exam by a member of one of the departmental language exam committees or by scoring in the 40th percentile or higher on the corresponding ETS language exam. (Students entering the program from Fall 2019
onwards will not be subject to the language proficiency requirement.)

3. Qualifying Examination

Pass the written and oral parts of the Qualifying Examination.
The written part of the exam is chosen with advice from the Supervisory Committee from the list exams given by departmental committees in the following areas: Algebra, Analysis, Combinatorics, Complex Analysis, Differential Geometry, Ergodic Theory and Dynamical Systems, Functional Analysis, Logic, Numerical Analysis, Partial Differential Equations, Probability, and Topology. The Ph.D. exams are administered in May and August each year, and each written Ph.D. exam may be taken at most twice.
The oral exam is conducted by the Supervisory Committee. It is scheduled only after the written part has been passed. It focuses on the intended area of research and includes other appropriate material at the Supervisory Committee’s discretion.

4. Research and Dissertation

Conduct research under the guidance of a faculty member and prepare, present and defend a dissertation which shows independent investigation and is acceptable in form and content to the Supervisory Committee and the Graduate School.

5. Courses and Grades

Complete 90 credits of graduate work, including MAS 5311-2 and MAA 5228-9 or equivalent, with a minimum of 36 credits in 6000+ graduate mathematics courses for the extent part of the distribution requirements, and fulfill the breadth part of the distribution requirements by completing sequences in two of the following four categories, two semesters in a third, and a semester in the fourth (see distribution requirements for a list of suitable courses):

  • Algebra, Combinatorics and Number Theory
  • Analysis
  • Applied Mathematics
  • Topology and Foundations

Achieve a grade point average of 3.0 or better in all course work and a grade point average of 3.0 or better in all course work in mathematics.

6. Teaching requirement

Teach a minimum of two semesters at the college level.

7. Residence Requirement

Complete 30 credits enrolled at the University of Florida campus beyond the first 30 credits counted toward the doctoral degree.

Remarks

  • The sections on Admission to Candidacy and Satisfactory Progress have information on expected timing of the various milestones.
  • The Department of mathematics also offers PhD Comajor with Statistics (See below)
  • The requirements for the PhD degree changed on May 18, 2012. The rules below may still be applied to students who have enrolled or signed up for the PhD program in Mathematics prior to May 18, 2012: PhD requirements prior to May 18, 2012

Admission to Candidacy

Students normally are admitted to candidacy when they have a dissertation topic approved by their supervisory committee and have passed the written and oral parts of the qualifying examination.

Satisfactory Progress Criteria

Graduate students in mathematics are required to make satisfactory progress. Students not making satisfactory progress will be placed on probation. If probationary status is not resolved by the end of the semester in which it is initiated, the student will not be allowed to continue as a graduate student in mathematics and any guarantee of support will be terminated. Exceptions to the rules will be made through written appeals to the Graduate coordinator or the Graduate Committee. Graduate students in mathematics must meet university requirements for satisfactory progress (see the subsection on Unsatisfactory Progress or Unsatisfactory Scholarship in the General Regulations section of the Graduate Catalog). In addition, the Department of Mathematics requires the following:

  • Course and Grade Requirements
    • During their first year, PhD students must take at least two 5000+ mathematics courses each semester.
    • During their second year, PhD students normally take two 6000+ sequences leading to PhD written exams and complete their schedule with courses that fulfill their degree goals, either applied courses for an applied degree, additional 6000+ courses for a proposed area of research or for the distribution requirements.
    • After the first two years, PhD students must take at least one 5000+ mathematics course per semester. A student can count a reading/research course, e.g. MAT 6905, MAT 6910, MAT 7979, MAT 7980, for at most two non-summer terms. At most five credits of MAT 6910 count toward the degree.
    • The distribution requirements are normally completed by the end of the fourth year of graduate study and must be completed by the fall of the fifth year of graduate study.
    • Each mathematics graduate student must maintain a cumulative grade point average of 3.0 or better.
  • First Year, Qualifying and Language Exams
    • PhD students must pass at least one First Year Semester Exam by May of the first full academic year of graduate study, at least two by August of that year, and three parts by the following February. Students who fail to achieve one of these three milestones will be transferred to the master’s program.
    • Students must complete the written part of the Qualifying Exam by the Spring of the third year of graduate study, a year later than normal progress. Students who are granted a waiver of the First Year Examination must complete the written part of the Qualifying Exam by the Fall offering of exams at the start of the third year of study.
    • Students must take the oral part of the Qualifying Exam prior to the midpoint of the fall semester of the fourth year of graduate study.
    • The Language Exam must be passed prior to the oral part of the Qualifying Exam
  • Dissertation Advisor and Supervisory Committee
    • A PhD student is expected to have a dissertation advisor and supervisory committee by the end of the Spring semester of the second year; failure to have one by January of the third year will result in academic probation.
    • At no time after the end of the third year may a PhD student be without a dissertation advisor and supervisory committee. If you change advisors at any time, you must notify the Graduate Secretary.
    • A PhD supervisory committee should consist of five approved faculty members: the advisor, an external member (a graduate faculty member not affiliated with the Department of Mathematics), and three additional members. Usually at least three members of the committee are graduate faculty in the UF Department of Mathematics.
  • Time Limits
    • The Ph.D. requirements must be completed by the end of the Summer B/C semester of the eighth calendar year after the first term enrolled in any University of Florida mathematics graduate program.

Co-major with Statistics

Overview of the program

The Departments of Mathematics and Statistics jointly offer a Doctor of Philosophy degree with a comajor in mathematics and statistics for graduate students who wish to combine the strengths of both departments in a single degree program.

Admission to the program

Students completing the M.S. or M.A. degree in Mathematics or the M.S. or MSTA degree in Statistics at the University of Florida who wish to continue into the Ph.D. Comajor program must request approval from the Graduate Committee of the Department of Mathematics or the Graduate Program Committee of the Department of Statistics. This should be done in writing during the final semester of the Master’s program. The appropriate Graduate (Program) Committee will determine suitability of master’s students for entry into the Ph.D. Comajor program based on their overall performance in the master’s program.
Students in the Ph.D. program of either department who wish to enter the Ph.D. Comajor program must also apply in writing to one of the Graduate (Program) Committees.

Courses

Each student will plan with the Graduate Committee an appropriate program of courses to give the student a broad knowledge of the major areas of mathematics and statistics, as well as to prepare the student to do research in a particular field.
The total number of semester hours required is 90. Of the 90 hours, at least 6 courses (including at least 4 at the 6000+ level) must be in Mathematics, with a grade of B or better. At least 5 courses (including at least 3 at the 6000+ level) must be in Statistics, with a grade of B or better.
Note that students will not be required to take the full complement of Master’s level courses in both disciplines, provided they meet the above course requirements. Examinations
Students must

  1. demonstrate mastery of basic concepts of real analysis and algebra
  2. demonstrate mastery of basic concepts of theoretical statistics and applied statistics
  3. demonstrate all-round competence expected of a Ph.D. Comajor in Mathematics and Statistics
  4. prepare, present and defend a dissertation

The requirements in (1) may be fulfilled by either obtaining grades of Pass or High Pass on both parts of the First Year written examination given by the Department of Mathematics during the first two weeks of each semester, in May, September and January. In normal circumstances, a student is expected to pass each part in no more than three attempts.
The requirements in (2) may be fulfilled by either obtaining grades of Pass or High Pass on both parts of the Masters Comprehensive Examination given by the Department of Statistics. In normal circumstances, a student is expected to pass each part in no more than two attempts.
To fulfill (3), the student must pass the Ph.D. Qualifying Examination which consists of three parts, two written and one oral. One written exam must be from the Department of Mathematics and the other from the Department of Statistics, in areas determined by the Supervisory Committee. The student must pass each written part in no more than two attempts.
The oral exam is on the research proposal and other appropriate material at the Supervisory Committee’s discretion. The two written exams must be passed before the oral part of the Qualifying Exam is taken. The oral examination must be taken no later than the beginning of the fourth year of graduate study. A student may normally take the exam only once. The student is normally “admitted to candidacy” when these requirements are satisfied.
The dissertation in (4) must show independent investigation and be acceptable in form and content to the supervisory committee and the Graduate School.

Supervisory Committee

At the doctoral level, each student in the comajor program will form a supervisory committee which shall consist of no fewer than 5 members, at least two from each department and at least one from a discipline other than the two comajor fields. Formed with the approval of both departmental chairs, this supervisory committee will be responsible for determining both written Ph.D. examinations and administering the oral Ph.D. qualifying examination and the final defense.