# Ph. D. Requirements

The purpose of the Doctor of Philosophy program is to prepare the student for research and teaching.

It is expected that each graduate student who is a U.S. citizen or permanent resident should begin the process of establishing North Carolina residency during the first semester of graduate study. Detailed information can be found here.

### Time and residency requirements

Ph.D students are required to take a minimum of 48 semester hours of course work, including at least 3 units of Math 994, Ph.D. dissertation. Ph.D students must complete their degree within eight years unless special permission is given for an extension of time. Students who remain beyond 10 semesters are responsible for the payment of tuition.

### First Year Courses

Courses taken during the first year are usually chosen from the following list, which is designed to prepare students for the Ph.D. qualifying examinations. Master’s students will typically take these courses as well in the first year before focusing in the second year on the requirements for a Master’s degree.

**653, 656, 661, 662, 668, 669, 676, 677, 680, 681.**

### Qualifying Exam Requirements

There are five qualifying exams:

- Algebra: Math 676 and 677
- Analysis: Math 653 and 656
- Geometry-Topology: Math 680 and 681
- Methods of Applied Mathematics: Math 668 and 669
- Scientific Computation: Math 661 and 662

Ph.D. qualifying exams are given twice each year, near the beginning of classes in August and January. Ph.D. students are encouraged to take the Ph.D. qualifying exams early and in principle would be ready to take them in August after the first year. The qualifying exams, sometimes called comps, are subject to the following rules:

- A Ph.D. student can pass either the Pure Math option for the for the qualifying examination or the Applied Math option.
- To pass the Pure Math Option, a student is required to pass three of the five qualifying exams by the beginning of the sixth semester. Any three of the five can be passed.
- To pass the Applied Math option, a student is required to pass Methods of Applied Math and Scientific Computation by the beginning of the sixth semester.
- In each examination period a student can take any number of qualifying examinations, from one to five.
- A graduate student who passes a Ph.D. qualifying examination, as determined by the Graduate Committee, will receive credit for that examination toward the Ph.D. requirements.
- If a student does not pass at least one Ph.D. exam by the beginning of the fourth semester, the department will not guarantee financial support past the end of the fourth semester. However, if such a student passes one exam by the beginning of the fifth semester, then reinstatement of financial support will be considered.
- To remain in the Ph.D. program, a graduate student must pass the written qualifying exam, with either the Pure Math or the Applied Math option, by the beginning of the sixth semester. A student who does not do this will be out of the Ph.D. program.
- Any exceptional cases will be decided by the graduate committee.

### Course Requirements

All Ph.D. students must take and receive a grade of P or higher in at least six courses from the following two lists:

- Comprehensive courses that are not basic courses for any of the three comprehensive exams passed by the student
- Second tier courses
- Algebra: Math 641, 643, 771, 774, 775
- Analysis: Math 657, 751, 753, 754, 857
- Applied Mathematics: Math 635, 761, 762, 768, 769, 892
- Geometry-Topology: Math 781, 782, 773, 775, 776

Furthermore, of these six courses every Ph.D. student must take and receive a grade of P or higher in three courses numbered over 700 from the second tier list

A student taking a pure math option, respectively an applied math option, may replace one, respectively one or more, course/s in the second tier requirement with other graduate level courses inside or outside of the department. For each replacement course, the student must obtain permission, prior to registration, from both the adviser and the graduate director.

### Oral Examination Requirement

When the student is prepared and has selected a direction for the Ph.D. dissertation, the Ph.D. candidate must pass an oral examination on material basic to the proposed dissertation area. The examination will be conducted by the Ph.D. committee of the student, which consists of five faculty members and is chaired by the student’s adviser. The committee will recommend action to correct any deficiencies noted during the oral examination.

After passing the oral examination the candidate continues working in the area of concentration to complete the Ph.D. dissertation.

It is strongly recommended that the oral examination be taken no later than one year after passing the Ph.D. qualifying examinations.

### Dissertation Defense

After finishing the dissertation the candidate gives a public oral presentation of the thesis and is examined on it by the Ph.D. committee. For information about paper and electronic submission of dissertations consult the Thesis and Dissertation guide.

### Computer Language Requirement

A Master’s or Ph.D. student must pass a computer language requirement by demonstrating a certain level of programming ability. Please note the following guidelines:

- Computer language requirements are the same for Ph.D. and Master’s students.
- Passing the following courses at UNC will be sufficient to satisfy the computer language requirement:

**MATH 565, MATH 566, MATH 661, MATH 662, MATH 761, MATH 762, COMP 110, COMP 116, COMP 121, COMP 401** - Any computer science course which lists one of these courses as a prerequisite is also acceptable.
- A Master’s or Ph.D. student may also satisfy the computer language requirement by passing an approved one semester undergraduate course on computer programming at any university.
- If the course title title on the transcript is not self-explanatory, then a syllabus, text or other information may be required. In all cases where there is some question about whether a course fulfills the requirement the Graduate Director will decide in consultation with the Faculty Computer Chair and possibly others from the Graduate Committee.

### Teaching Requirement

Students are required to take and successfully pass the TA Teaching Seminar, a special section of Math 920, during their first fall semester of their program. Students are also required to perform a minimum of two semesters of instructional service.

A semester of instructional service can be satisfied by any of the following:

- Teach one course: 12 hours
- Lead 4 recitations (includes 110L and 231L): 3 hours each
- Lead 2 labs (383L, 528L, 529L): 6 hours each

Recitations and labs can be completed in different semesters and combined to satisfy the requirement. For example, if a student leads two recitations in a fall semester, and two recitations in a spring semester, these duties can be combined to count for one semester of instructional service.