The Preliminary Examination
The preliminary examination covers the two foundational course sequences, MAT 601-602 and MAT 631-632. It consists of two written exams lasting no more than three hours and each of which may be taken separately. There are only two outcomes on each exam, Pass or Fail. Both exams must be passed to pass the Preliminary Examination. These exams will be given twice a year, before or near the beginning of each semester. The exact dates will be announced at least a month ahead of time.

Masters students who wish to continue into the Ph.D. program must take these exams by the beginning of their second year of graduate study and pass them by the end of their second year of graduate study. Students who pass one, but not both of these exams on their first attempt are required to retake only the exam that is not passed. Only two attempts at each of these exams are permitted.

With the approval of the Mathematics Graduate Committee, students who enter the Mathematics Graduate Program with extensive preparation in mathematics may attempt the Preliminary Examinations upon entering the Program. This attempt will not be counted as one of the two attempts at the Preliminary Examinations.

With the approval of the Mathematics Graduate Committee, students who enter the Mathematics Graduate Program with limited preparation in mathematics may postpone the Preliminary Examinations until their third year of graduate study.

The Qualifying Examination
The Qualifying Examination consists of written tests covering two areas selected from the following list:

• Algebra/Topology I: MAT 661, 731
• Algebra/Topology II: MAT 661, 761
• Analysis I: MAT 701, 712
• Analysis II: MAT 701, 721
• Combinatorics: MAT 645, 646
• Numerical Analysis I: MAT 682, 683
• Numerical Analysis II: MAT 683, 684
• Statistics MAT 651, 652

One of these exams is designated by the student as the Major Exam and is in the field in which he/she anticipates writing his/her thesis. The other exam is called the Minor Exam. The particular pair of exams a student takes depends on the area of the Major Exam as described in the following table:

Each part of the Qualifying Exam lasts no more than four hours. The parts may be taken separately. There are only two outcomes on each part, Pass or Fail. These exams will be given twice a year, before or near the beginning of each semester. The exact dates will be announced at least a month ahead of time.

Students first must take the Major Exam no later than the beginning of the third year of graduate study and pass it nolater than the end of their third year of graduate study.

After a student has passed the Major Exam, he/she should select the faculty member who will chair his/her Specialty Examination and begin working closely with that faculty member in preparation for the Specialty Examination.

Students must take the Minor Exam no later than the middle of their third year of graduate study and pass it no later than the beginning of their fourth year of graduate study.

The Mathematics Graduate Committee may recommend non-continuance in the Ph.D. program for a student in the Ph.D. program who fails to pass the full Qualifying Exam by the beginning of his/her fourth year of graduate study.

With the approval of the Mathematics Graduate Committee, students who postpone taking their Preliminary Examinations until their third year of graduate study may also postpone the Qualifying Examinations until their fourth year of graduate study.

Students who wish to change the area in which they plan to write their thesis may be required to retake all or part of the Qualifying Exam.

The Specialty Examination
The Specialty Examination serves at least two purposes:

• To acquaint faculty members with the research potential and interests of the student, and the student with the research interests of faculty members.
• To determine whether the student can read and assimilate advanced material in a specialized field.

The Specialty Examination is an oral examination. After a student has passed the Major Exam in his/her field of interest, he/she asks a faculty member to direct his/her preparation for the Specialty Examination and to chair a committee to conduct his/her Specialty Examination. The chair, in consultation with the student, selects at least two other faculty members to comprise the committee.

The committee members, in consultation with each other and the student, assign topics and a reading list to the student. To pass the examination, the student must demonstrate competence in and understanding of the assigned topics and prerequisite material. The examination may include a short presentation by the student, but will also include direct examination by the committee members.

The Specialty Examination must be passed by the end of a student's fourth year. The mathematics Graduate Committee may recommend non-continuance in the Ph.D. program for a student in the Ph.D. program who fails to pass the Specialty Exam by this time.

The Oral Examination (Dissertation Defense)
When the dissertation meets with the approval of the student's dissertation advisor and the student has acquired a total of 90 hours of graduate credit, the candidate is given a final oral examination of the dissertation and the immediately related field. The committee for this examination will consist of a chair appointed by the Graduate School, the student's dissertation advisor, and four other members appointed by the Mathematics Graduate Committee with advice from the student and the dissertation advisor. Upon final approval of this committee, a copy of the dissertation will be placed in the mathematics library.