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Our doctoral program provides a broad background coupled with intensive training in an area of specialization. We are proud that most of our students finish in five years.
We allow a great deal of flexibility in the specific courses you choose, focusing on your particular background and interests.
Before you begin graduate mathematics study at Northwestern, you should have substantial undergraduate preparation in mathematics, including courses in linear algebra, abstract algebra, and real analysis or advanced calculus. A course in point set topology would also be valuable. If you have deficiencies in one of these areas but are otherwise well qualified, you may make up the deficiency through course work in your first year. Entering students who have previously completed graduate-level work frequently enroll in more advanced courses offered by the department.
Our doctoral program provides a broad background in mathematics coupled with intensive training in a specialized area. We are proud that most of our students finish the total program in five years after the undergraduate degree. The curriculum is flexible, designed to prepare you for a career as a research mathematician in academia, industry, or other professional work. The program's various stages lead to increased intellectual independence, culminating in the doctoral thesis.
During the first year most of your time will be spent on course work. The standard full-time course load is three courses per quarter. This is also the minimum load, although it is possible to register for four courses with no increase in tuition. Although all graduate students are expected to know certain basic material, we allow a great deal of flexibility in the specific courses you choose, depending on your background and interests.
Ordinarily, you will take the written preliminary examination in the September preceding your second year. This examination covers three subjects, chosen from among the following topics:
We encourage you to take algebra and analysis plus one other subject.
During the second year, your course work should be chosen for both breadth and specialization. Your combined first- and second-year course work must include two one-year, graduate-level sequences from Group I along with two one-year, graduate-level mathematics sequences from Group II.
During your second and third years, you will begin individual, specialized work with a faculty member or committee to prepare for the oral qualifying examination, which you should take before the end of your third year. The examination is administered by a three-member faculty committee on advanced topics relevant to your forthcoming dissertation research. Its main purpose is to determine your ability to read and assimilate advanced material in specialized areas.
Once you have passed the qualifying examination and successfully completed the equivalent of six full- time quarters of course work, you will be eligible for admission to candidacy for the PhD. The final step in the PhD program is your dissertation, written under the guidance of a faculty member and based on your original research.
Although we have no formal foreign language requirement for the PhD, your course work and qualifying examination may require reading materials in languages other than English. Even if you have completed previous graduate work, the Graduate School has a residency requirement of nine quarters (three years) of full-time registration at Northwestern.
We have no program offering the exclusive goal of a master's degree. However, once you have been admitted to the PhD program, passed the preliminary examination, and completed three quarters of full-time work in approved courses, you may receive a master's degree upon application to the Graduate School.
Normally, during your first two years in the Graduate Program, your adviser will be a member of the Graduate Committee; the role of the adviser is to help you design your program of study. You may also request for another member of the department to be your adviser during these years. By the end of your second year, you will select a committee for your qualifying examination. While you prepare for the qualifying examination, your adviser is the chair of this committee, and usually, this faculty member becomes your dissertation supervisor on successful completion of the qualifying examination. You may also consult with the Director of Graduate Studies or any other member of the Graduate Committee about any aspects of requirements, planning your program, or any other matter regarding graduate studies.
Allowing you to gain teaching experience is a vital aspect of our graduate program. Our students take part in a workshop on teaching during their first year, and are assigned a teaching mentor (typically a more advanced graduate student).
If you receive financial aid from the university as a Teaching Fellow after the first year, you will be required to participate in teaching activities each quarter you are in residence after the first year. Usually, you will be assigned to assist particular faculty members with specific courses.
Normally you will assist with no more than seven courses over a year's time (in other words, two or three courses per quarter). We believe that this level of teaching responsibilities will give you enough time for your own graduate studies, allowing you to finish in five years, and still gain the experience you will need to prepare for future teaching positions.
TA duties vary with the course and the professor. Generally, you can expect to answer questions about homework in a weekly quiz section, to proctor and grade quizzes and homework, to assist in grading midterms and finals, and to hold office hours for student consultation. Regardless of the specific activities you agree on with the faculty member teaching your course, your total responsibility will be no more than four hours per course per week.
As a more advanced student, you may have an opportunity to teach your own course in University College (our continuing education division), Summer Session, or, occasionally, Northwestern's regular academic schedule.
In addition, advanced graduate students regularly take independent study courses with faculty on specialized topics.
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