All applicants for the degree of Doctor of Philosophy with a major in mathematics are urged first to study the general University requirements for this degree and to plan their programs so that all those requirements are fulfilled in the proper order and at the proper times. Listed below are the major steps in earning this degree. Specific requirements of the Department of Mathematics are included.


Admission to this program is contingent upon admission to the Graduate School; see Admission, Regular. Doctoral applicants must have completed a master's degree in mathematics or reached an equivalent level of advancement. The Department Graduate Committee may make exceptions to this rule in cases where unusual ability has been demonstrated. Admission to the doctoral program will be granted only to those whose records indicate an ability to succeed in advanced study and research.


Candidates for the doctoral degree must complete ninety credits in course work beyond the bachelor's degree, including thirty credits of dissertation direction. The thirty credit dissertation registration requirement is fulfilled in one of two ways: 1) Students who have accumulated credits in the course numbered 9999 (Doctoral Dissertation Research and Direction) register for a total of thirty credits in 9999; or 2) Students who have not accumulated any credits in the course numbered 9999 and who attain Candidacy after Summer semester 2001 register for the courses 9991, 9992, 9993, and 9994 (Doctoral Dissertation Research and Direction I, II, III, and IV, respectively), in consecutive academic year semesters. Additional specific requirements for this degree in mathematics are as follows:

Preliminary Examinations:  These are 2-hour written examinations covering undergraduate level material from a sophisticated point of view.  Students are required to pass a preliminary exam in Algebra or Analysis, as well as one additional exam from the following four choices: Algebra; Analysis; Applied Mathematics; and Probability and Statistics. Here are the syllabi for the examinations.

Students may choose to take exams in their first semester in the Ph.D. program, in which case they must satisfy the requirements by the end of their second semester; or they may choose to take exams in their second semester, in which case they must satisfy the requirements by the end of their third semester. Students must select exams at the beginning of each semester, to be taken later in that semester.

Under special circumstances, the Departmental Graduate Committee may approve petitions on an individual basis for exceptions to these rules.

Course Requirements: In addition to the examinations described above, before advancement to candidacy every student in the Ph.D. program must earn a grade of ‘B’ or better in one course in each of the three subject areas in which they do not pass a Preliminary Examination. The courses may be selected from the following choices:

  1. Algebra: MAT 7400
  2. Analysis: MAT 7600
  3. Applied Mathematics: MAT 7200 or MAT 7210
  4. Probability and Statistics: MAT 7700 or MAT/STA 7810
  5. Topology: MAT 7500 or MAT 7510

As a general rule, students are expected to take at least one required course each semester until they fulfill their course requirements.  Under special circumstances, the Departmental Graduate Committee may approve petitions on an individual basis for exceptions to these rules.

QUALIFYING EXAMINATIONS consist of two sections, a written and an oral examination. A student must begin the written qualifying examination by the end of the third year in the Ph.D. program, and must pass all parts of the examination by the end of the fourth year in the Ph.D. program. All parts of the examination must be passed before a student can advance to Candidacy Status.

Written Qualifying Examinations: These consist of two 3-hour parts, a major and a minor area exam. The examination committee will give the student a list of topics in the student's area of specialization. These topics should both reflect the student's particular research interest and be of sufficient breadth to cover the entire area. The committee will also designate a minor area on which the student will be examined. The minor area is to be supportive of the major area but sufficiently different to avoid compromising the diversity of the total two-part exam.

Oral Qualifying Examinations: After passing the written Qualifying Examinations, a student must take an oral Qualifying Examination; the exam must be taken within thirty days after certification of passing the written exam. The oral examination committee consists of the written examination committee, and a representative of the Graduate Committee. The oral examination normally covers material similar to that of the written examinations, but may also include material outside the written examination areas which is deemed relevant to the student's research work.

Defense of Dissertation: Candidates must pass a final oral examination covering their research after the candidate's adviser has approved the completed dissertation.

Scholarship: All course work must be completed in accordance with the academic procedures of the College of Liberal Arts and Sciences and the Graduate School governing graduate scholarship and degrees: see the sections of this bulletin under Academic Regulations for the College of Liberal Arts and Sciences and Academic Regulations, Graduate, respectively.


Forms for PhD Students

Petition for Directed Study

See the Graduate School for more forms.


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