IV. Doctor of Philosophy Program

Besides satisfying the general regulations of the Graduate School for the degree of Doctor of Philosophy, the student must comply with the following requirements.

1. Qualifying Examinations. The student must pass four written examinations chosen as described below. The exams are based on material that is covered in the courses listed and on material from undergraduate prerequisites. Credit for passing a similar examination at another university cannot be transferred.
   
   

   The Qualifying Examinations are written examinations offered twice a year during week long Qualifier Exam Sessions the week before classes start in August and January. Each examination is written and graded by a faculty member or a committee of faculty members chosen by the Graduate Committee.

   The following four subject areas are called the Core 4 Areas:.

   • Complex Analysis (MA 530)
   • Real Analysis (MA 544)
   • Abstract Algebra (MA 553)
   • Linear Algebra (MA 554)
   
   

   The qualifier exam subject areas are the Core 4 Areas plus the following Area Exams:

   • Numerical Analysis (MA 514)
   • Probability (MA 519)
   • Partial Differential Equations (MA 523)
   • Differential Geometry (MA 562)
   • Topology (MA 571)
   • Mathematical Logic (MA 585)
   
   

   The student must pass at least two exams from the Core 4 Areas, including at least one of 544 or 553. They must also pass two more exams from the Area Exams and the unused two exams from the Core 4.

   The Qualifier Deadline for students who enter the program with a master's degree is the January Qualifier Exam Session of their second year. The Qualifier Deadline for students without a master's degree is the January Qualifier Exam Session of their third year. Students who have not passed the four exams on or before the session of their Qualifier Deadline will have their privileges to continue in the mathematics PhD program terminated.

   Each qualifier exam can be attempted a maximum of three times and students may attempt as many qualifier exams as they wish at any Qualifier Session on or before their Qualifier Deadline.

   Once an exam is passed, it cannot be retaken to improve the grade from B to A.

   A syllabus for each area is given in section VI. Previous exams are available at

   http://www.math.purdue.edu/academic/grad/qualexams/

2. Language. The student must satisfy the foreign language requirement in one of French, German, or Russian. Any of the five options approved by the Graduate School may be used to meet this requirement. (See the section on Regulations in the Graduate Bulletin.)
   


3. Advanced Topics Examinations. A student becomes eligible to take the Advanced Topics Examination after passing the Qualifying Examinations and satisfying the foreign language requirement.

After passing the Qualifying Examinations, a student must find a faculty member willing to serve as the Advanced Topics Examination Coordinator. This Coordinator, once identified, begins to serve as the student's academic advisor, counseling the student and signing course registration forms. Usually the Coordinator becomes the student's thesis advisor, provided the student passes the Advanced Topics Examination.

The student must meet with the Coordinator to prepare an Advanced Topics Examination Proposal Form, which is to be filed in the Graduate Office at least one month prior to the examination date. The form lists the Coordinator, two courses beyond the qualifying level on which the student is to be examined (or a body of mathematics roughly equivalent to this), and one other faculty member who, with the Coordinator, administers the Advanced Topics Examination. At the discretion of the Coordinator, the examination may also cover a third subject, possibly with a third examiner. The examinations may be oral or written, and may be given separately or together. The conditions of the examination are specified on the Advanced Topics Examination Proposal Form, which must be approved and signed by the Coordinator, the student, and the Graduate Committee Chair. To pass the examination requires agreement of all members of the committee and the consent of one to serve as the student's thesis advisor. While this is usually the Coordinator it need not be.

A student may take the Advanced Topics Examination at most twice; however, the examination should be passed within 1 1/2 years of passing the Qualifying Examinations. In special cases the Graduate Committee may grant an extension of this time limit. Each time the examination is taken, a new Advanced Topics Examination Proposal Form must be filed in the Graduate Office. Below is a list of some possible combinations of courses for the Advanced Topics Examination.

• Algebra (MA557, 558) (MA642, 643) (MA558, 650)
• Analysis (MA531, 631)
• App. Math (MA611, 642)
• Control Theory (MA545, 620) (MA558, 664)
• Geometry (MA562, 661)
• Logic (MA586, 587) (MA538, 545) (CS584, MA586) (MA546, 646)
• Numerical Analysis (CS614, 615) (MA642, 643)
• Probability (MA538, 539) (MA647, 648)
• Topology (MA572, 672)


4. Plan of Study. The plan of study should be submitted electronically to the Graduate School through the department by each student preparing for Ph.D. candidacy within one semester after passing the Advanced Topics Examinations. The student must arrange for an advisory committee to approve the plan of study, with the chair being the supervisor of thesis research. This advisory committee must have at least half of its members with a faculty appointment over 50% in the Department of Mathematics. Substitutions in course requirements and the transfer of credits from other universities may be permitted with the approval of the advisory committee and the Graduate Committee. The Plan of Study Generator (POSG) may be accessed via the mypurdue portal at http://mypurdue.purdue.edu (see section X). The plan of study must include:
   
   
   1. Normally at least a total of 42 hours of graduate work, however due to a recent policy change by the Graduate School all applicable courses (graduate courses with a letter grade) should be listed on the plan of study. This includes up to 30 credits from a master's degree. A completed plan of study must list courses with at most two grades of C and all other grades of A or B. (A total of 90 credit hours are required for the Ph.D. degree, but this total includes thesis research MA 699, which is not included on the plan of study.)
   2. At least three courses (nine credit hours) at an advanced level in the field of specialty or closely related to it. Reading courses and seminars may be included.
   3. The courses MA 530, 544, 553, and 554 and two courses from among MA 514, 519, 523, 562, 571, 572, and 585. A student can avoid taking any of these courses by passing the qualifier exam in the subject.
   4. For students in applied mathematics, at least two courses selected from CS 514, 515, 614, 615, and one course that uses advanced mathematics, taken outside the mathematical sciences.
   5. For students in numerical analysis, at least two courses selected from MA 523, 543, 611, 642, 643.
      


5. Preliminary Examination. The preliminary examination for most students will only require the completion of a form for the Graduate School. An oral or written examination may be required by the student's advisory committee for admission to candidacy. Graduate School regulations require that at least two sessions (including summer sessions) must elapse between the preliminary examination and the thesis defense. A request form must be submitted to the Graduate Office at least two weeks prior to the examination date. This should be done by the student as soon as the student has fulfilled items (A)-(D). If a student has an advisor who is not in the Department of Mathematics then an advisory committee must be approved by the Graduate Committee of the Department of Mathematics. (For example, this could be the case for a student in the CS&E program.) This advisory committee must have at least half of its members with a faculty appointment over 50% in the Department of Mathematics. In this case, a preliminary examination may be required. The purpose of this exam is to ensure that the proposed thesis problem(s) is chiefly mathematical in nature, and that a thesis on this topic is appropriate as a thesis in the Department of Mathematics. A report on the preliminary examination shall be made in writing to the Graduate Committee of Mathematics discussing the proposed project, with particular emphasis on the mathematical content. The Graduate Committee will then make the final decision whether the thesis topic is acceptable.
   


6. Admission to Candidacy. To be admitted to candidacy for the Ph.D. degree, the student must have fulfilled the preceding requirements.
   


7. Dissertation. A thesis must be submitted in final form presenting new results of sufficient importance to merit publication. The thesis must be accepted by the major professor and four copies must be submitted at least three weeks before the end of the semester in which the degree is expected. The student must present the contents of the thesis before an examining committee consisting of a minimum of four faculty members in an open colloquium or seminar. At least half of the examining committee must have a faculty appointment over 50% in the Department of Mathematics. The thesis must be acceptable to this committee. A request form for the appointment of the final examining committee must be received by the Graduate School not later than two weeks preceding the examination. The thesis must meet departmental and University format requirements. The Graduate Office will provide the necessary information.
   


8. Recommendation for the Ph.D. Degree. If the above requirements are met within the time limits stated below, the candidate will be recommended to the faculty to receive the degree of Doctor of Philosophy.
   


9. Time Limits for Completion of the Ph.D. Degree. Seven years from entry into the graduate program (i.e., 14 semesters plus the intervening summers -plus one additional summer to finish if necessary) is the maximum time allowed to complete the Ph.D. in the College of Science. An additional year may be allowed if requested by the student's Thesis Committee and approved by the department's Graduate Committee. Any exceptions to this policy will require approval by the Department Head.
   


10. Financial Support. Continued financial support by the Mathematics Department will depend on satisfactory academic progress and satisfactory performance in teaching and/or research duties (see section VII.). The Graduate Committee urges students to complete the Ph.D. within seven years since financial support will be terminated after that time.
    


11. Research in Absentia. Research in absentia is possible only for students who have fulfilled the requirements (A) through (E) in section IV. and are well into a research program. A request for permission from the Mathematics Department to do research in absentia requires the approval of the major professor, the Graduate Committee Chair, and the Graduate School. This form must be filed one month prior to the start of the session in which research in absentia registration is requested.