2. Milestones
2.1. Preliminary Examination
All students must satisfy the department’s preliminary exam requirement in order to continue with the program. The Preliminary Examination consists of written examinations lasting three hours each in the following three subjects: algebra, analysis, and geometry/topology.
Incoming students are invited to take the Preliminary Examination upon entrance. There is no penalty for failing to pass a preliminary examination taken upon entrance to the program. Incoming students will be required to take the first-year course in each of the prelim subjects they do not pass upon entrance, unless they submit documentation of having passed a comparable course at another institution (or other compelling evidence of familiarity with a subject).
Syllabi for the preliminary examinations and copies of past examinations are avail- able online at the department website. The rules for the Preliminary Examination are posted here.
The Preliminary Examination is usually given around early September and at the end of the academic year (typically around Weinberg College’s final exam week in June). Graduate students must take the Preliminary Examination in all three subjects by the end of their first academic year. Each test is a closed book exam that should be completed in 3 hours. For students who take Preliminary Examinations in both September and June of their first academic year, we take the best scores for each of the three examination subjects. Students who do not pass the Preliminary Examination by the end of their first year must pass a make-up examination in September at the beginning of their second year in order to continue in the program beyond the first quarter of the second year. In the presence of strong evidence of other mathematical accomplishment, this rule may be modified or waived with the approval of the Graduate Committee.
An award may be offered by the Graduate Curriculum Committee at the end of each academic year to a student who has achieved an outstanding performance in the Preliminary Examination.
2.2. Master’s Degree.
Passing the Preliminary Examination and completing at least nine approved courses over at least three quarters of registration will satisfy the departmental requirements for a master’s degree. The deadline for filling out and submitting the Application for Degree and Master’s Degree Completion forms in GSTS in order to receive the degree in any quarter is published on the official Academic Calendar. Students intending to apply for a master’s degree should approach the Graduate Program Assistant at least 3 weeks prior to this deadline.
2.3. Qualifying Exam.
A student becomes a Ph.D. candidate after successfully completing six quarters of course work and the Qualifying Examination. This is the last examination before a student begins dissertation research. This 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 Qualifying Examination is an oral examination. After the student has decided upon a field of interest, they ask a faculty member to chair a committee to conduct their Qualifying 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. The committee must be comprised of at least three faculty members, at least two of whom are NU graduate faculty.
The Qualifying Examination is passed by majority vote of the committee and the chair of the committee must be in the majority.
The syllabus for the Qualifying Examination must be approved by the committee. The student must enter this and other information on the Qualifying Examination Form at least three weeks prior to the exam date. The student will receive a copy of the form by email and bring it to the exam for the members of the committee to sign. Afterwards the form should be handed to the Graduate Program Assistant for proper recording. The student must also submit their qualifying exam information to the Graduate School through its GSTS site.
The Qualifying Examination must be taken by the end of the first quarter of a student’s third year. Failure to pass the exam by the end of the third year may jeopardize financial support in the subsequent years.
2.4. Prospectus.
Students must have a prospectus (dissertation proposal) approved no later than the end of the fourth year of study, which falls on the last date of the 16th quarter. A student failing to meet this milestone will be considered not in good academic standing and therefore will be placed on academic probation. Deadlines will be altered in the case of an approved leave of absence or a childbirth accommodation. The prospectus must be approved by a faculty committee comprised of a minimum of three individuals. At least two members of this committee, including the chair, must be members of the Northwestern University Graduate Faculty.
Students may choose to have their prospectus approved by the faculty committee members via electronic communication or an in-person meeting. The student must then submit the PhD Prospectus form through TGS Form in GSTS for program apapproval. The student’s adviser must email the Graduate Program Assistant to confirm the student’s successful completion of the prospectus. The students will be notified via email by TGS of approval of their Prospectus form.
2.5. Dissertation and thesis defense.
Each student must complete original research and produce a dissertation acceptable to the student’s adviser and the Thesis Committee. The Thesis committee is comprised of a minimum of three faculty members. At least two members of this committee, including the chair, must be members of the Northwestern University Graduate Faculty. The last milestone of the graduate program is an oral defense of this dissertation.
The student must notify TGS of their thesis defense by submitting the Final Exam form at GSTS. Submission of a dissertation to TGS is performed electronically. Information on this process can be found in the Degree Requirements section of the Student Services page of the TGS website. Students must consult the TGS website for the latest information on submission requirements and guidelines. They must, however, give electronic or hard copies of the dissertation to each member of the committee at least three weeks prior to the scheduled date of the oral examination.
The student must also provide an electronic copy of the thesis, location and time of thesis defense to the graduate program assistant three weeks prior to the scheduled date of the thesis defense. The examination on the dissertation will be open to the public. The student must announce their thesis defense by email to the department and also enter the event in the department event calendar. The examining committee has discretion to exclude the public during part of the examination for additional questioning of the candidate and confidential deliberations.
2.6. Waivers.
In order to maintain flexibility in the graduate program, and, in particular, to accommodate exceptional cases, the Graduate Committee will consider written requests from students’ advisers to waive or modify requirements. However, it is expected that such requests will be granted only rarely.