### 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, 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 36 hours must be from the following listed courses. The 36 hours must include year-long sequences in three categories and at least one semester course from the fourth category. (Please consult the Course Guide for course abbreviations.)

**Analysis:**- MAA 6616-7, MAA 6406-7, MAA 7526-7.
**Algebra/Combinatorics:**- MAS 6331-2, MAS 7396-7, MAD 6206-7, MAS 7215-6.
**Topology/Foundations:**- MTG 6346-7, MTG 6401-2, MTG 6256-7, MTG 7396-7, MTG 7493-4, MHF 6306-7.
**Applied Mathematics:**- MAD 6406-7, MAP 6327-8, MAP 6356-7, MAP 6375-6, MAP 6467-8, MAP 6472-3, MAP 6487-8.

Additional courses may be offered which fulfill these requirements. Such courses will be approved by the Graduate Committee at the time they are offered.

All courses taken by the student are subject to approval by the Graduate Committee and the student’s supervisory committee. The Graduate Committee will interview each student at least once each year to review progress and approve the course schedule.

### Examinations

Students must:

- demonstrate mastery of basic concepts of real analysis and algebra
- demonstrate all-round competence expected of a PhD in Mathematics
- demonstrate proficiency in reading mathematical works in French, German or Russian
- demonstrate knowledge of one of the major scientific computer programming languages
- 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, or by petitioning the Graduate Committee to waive the First Year examination. The Graduate Committee expects the petitioning student to have a Master’s degree from the University of Florida or a comparable institution. The first year exam is given during the first two weeks of each semester, in May, September and January. After completing the MAS 5311-2 or MAA 5228-9 sequence, students may take the corresponding exam up to three times, if necessary, out of the four times the exam is given, one year following the completion of the corresponding course sequence. Students in the applied mathematics program may replace the Algebra or Analysis part of the First Year Examination by a Ph.D. pass on the Numerical Analysis exam.

To fulfill (2), the student must pass the Ph.D. Qualifying Examination which consists of three parts, two written and one oral. One written exam must be on one of the three sequences: MAA 6616-7 (Measure and Integration), MAS 6331-2 (Algebra) and MTG 6346-7 (Topology). The second written exam must be on either a second of those three sequences or else on one of the sequences: MAA 6406-7 (Complex Analysis), MAA 7526-7 (Functional Analysis), MHF 6306-7 (Logic), MAD 6206-7 (Combinatorics), MAP 6472-3 (Probability), MAP 6356-7 (Partial Differential Equations), MTG 6256-7 (Differential Geometry), and MAD 6406-7 (Numerical Analysis). The oral exam is on the research area 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. Students must complete all written exams by the end of the third year of graduate study. Students who waive the first-year examinations must complete the remaining Ph.D. exams by the end of the second year of graduate study. The Ph.D. exams are administered in May and September each year, and each written Ph.D. exam may be taken at most twice. Passing grades should reflect basic competence in the subject, although non-routine problems may be included.

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 language requirement in (3) is satisfied by a passing grade on a departmental examination given by the Language Examination Committee or by ETS exam with a score of 40th percentile or better.

The computer language requirement can be fulfilled either by experience or course work.

The dissertation in (5) must show independent investigation and be acceptable in form and content to the supervisory committee and the Graduate School.

### Teaching Requirement:

Two semesters of college level teaching experience are required.