# Degree Requirements

## Ph.D. Degree Requirements

In addition to general requirements, the department requires the student to meet the following requirements before being admitted to the comprehensive examination.

- Pass 2 written qualifying examinations, 1 exam in either algebra or analysis and a second exam in either numerical analysis or probability/statistics and complete the required qualifying exam coursework. The qualifying examinations must be completed by the beginning of the student’s fifth semester. The qual course requirement must be met before taking the preliminary exam.
- Pass 1 preliminary examination in an area close to the focus of the eventual doctoral dissertation. The preliminary examination must be completed by the beginning of the student’s eighth semester.
- Satisfy the research skills and responsible scholarship requirement by demonstrating a working knowledge of a programming language such as C++ or FORTRAN and by completing the departmental training in responsible scholarship. To meet the research skills requirement students must complete an introductory programming language course approved by the graduate committee. Alternately, students may complete an approved computing project demonstrating competence in either a programming language or the use of specialized software that supports the student’s research.
- Pass a set of required courses, differing in different tracks.

**Note:** Contact your department or program for more information about the qualifying exam coursework requirement, the research skills and responsible scholarship, and the current requirements for doctoral students. Current policies on Doctoral Research Skills and Responsible Scholarship are listed in the Graduate Studies section of the online catalog and in the KU Policy Library.

### Pure Mathematics

This track requires MATH 800, MATH 810, MATH 820, MATH 830, and an approved course in geometry (e.g., MATH 840, MATH 910, or MATH 920).

### Applied Mathematics

This track requires MATH 727 (or the corresponding qualifying examination); MATH 781 (or the corresponding qualifying examination); MATH 800; MATH 810; MATH 881 and MATH 882 or MATH 865 and MATH 866 or MATH 850 and MATH 851; and one of MATH 840, MATH 850, or MATH 950.

### Examination Preparation

Normally the work required to prepare a student for the oral comprehensive examination (and to do research) includes 1 or more semesters of advanced courses, directed readings, and seminars. In the oral comprehensive examination, a student must show proficiency in the chosen area of mathematics. Precise areas of responsibility on this examination are discussed in detail with the advisory committee (the student’s advisor and two other members of the department’s Graduate Faculty).

The student must complete 4 additional courses at the 800 level or above before the final examination. Mathematics courses at the 700 level, or courses outside the department at the 700 level or higher, may be substituted with the approval of the graduate studies committee.

## Ph.D. Degree Requirements

In addition to general requirements, the department requires the student to meet the following requirements before being admitted to the comprehensive examination.

- Pass 2 written qualifying examinations, 1 exam in either algebra or analysis and a second exam in either numerical analysis or probability/statistics and complete the required qualifying exam coursework. The qualifying examinations must be completed by the beginning of the student’s fifth semester. The qual course requirement must be met before taking the preliminary exam.
- Pass 1 preliminary examination in an area close to the focus of the eventual doctoral dissertation. The preliminary examination must be completed by the beginning of the student’s eighth semester.
- Satisfy the research skills and responsible scholarship requirement by demonstrating a working knowledge of a programming language such as C++ or FORTRAN and by completing the departmental training in responsible scholarship. To meet the research skills requirement students must complete an introductory programming language course approved by the graduate committee. Alternately, students may complete an approved computing project demonstrating competence in either a programming language or the use of specialized software that supports the student’s research.
- Pass a set of required courses, differing in different tracks.

**Note:** Contact your department or program for more information about the qualifying exam coursework requirement, the research skills and responsible scholarship, and the current requirements for doctoral students. Current policies on Doctoral Research Skills and Responsible Scholarship are listed in the Graduate Studies section of the online catalog and in the KU Policy Library.

### Pure Mathematics

This track requires MATH 800, MATH 810, MATH 820, MATH 830, and an approved course in geometry (e.g., MATH 840, MATH 910, or MATH 920).

### Applied Mathematics

This track requires MATH 727 (or the corresponding qualifying examination); MATH 781 (or the corresponding qualifying examination); MATH 800; MATH 810; MATH 881 and MATH 882 or MATH 865 and MATH 866 or MATH 850 and MATH 851; and one of MATH 840, MATH 850, or MATH 950.

### Examination Preparation

Normally the work required to prepare a student for the oral comprehensive examination (and to do research) includes 1 or more semesters of advanced courses, directed readings, and seminars. In the oral comprehensive examination, a student must show proficiency in the chosen area of mathematics. Precise areas of responsibility on this examination are discussed in detail with the advisory committee (the student’s advisor and two other members of the department’s Graduate Faculty).

The student must complete 4 additional courses at the 800 level or above before the final examination. Mathematics courses at the 700 level, or courses outside the department at the 700 level or higher, may be substituted with the approval of the graduate studies committee.