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The graduate program in Mathematics is aimed at guiding the students toward original research. At the end of the program (normally by the end of the fifth year of study) students are expected to submit and defend a PhD thesis, which should contribute new results to the body of mathematical knowledge.
In order to successfully deal with problems arising in modern mathematics, graduate students need to acquire a considerable background. This is achieved through course work and independent study. The program provides for two sets of examinations to check the student's progress:
Each graduate student has an adviser to help design his/her program and to closely guide his/her mathematical development. The Chair of the Graduate Committee, or any member of the Graduate Committee, may also be consulted about any aspects of the requirements, planning the program of study, or any other matter pertaining to the graduate studies.
A student in his/her first and second year is assigned an adviser from the Graduate Committee in September of each academic year. A student preparing for the qualifying examination is advised by the chair of his/her committee. A student writing a dissertation is advised by the dissertation supervisor.
It is vitally important that the students think about a possible dissertation supervisor sufficiently early in the program (normally during the second year, or even earlier). While each faculty member would be happy to provide mathematical help to any graduate student, nothing can replace the student's own inner work such as thorough analysis of his/her mathematical inclinations.
Students are advised to learn more about the research of the faculty members as early as possible, starting with the current listings of faculty and their research interests.
The Preliminary Examination determines whether a student may continue further into the doctoral program.
The Preliminary Examination consists of written examinations in three subjects drawn from the following list:
We encourage you to take algebra and analysis plus one other subject.
Syllabi for the preliminary examinations and copies of past examinations are available. The rules for the Preliminary Examination are here.
The Preliminary Examination is given during New Student Week in September of each year, and make-up examinations are given in the first week of the Winter Quarter. Graduate students must take the Preliminary Examination in all three subjects before the beginning of their second year in the doctoral program unless specifically exempted by the Graduate Committee. In order to continue into the third year, he/she must pass the full Preliminary Examination by January of their second year.
A prize is offered each September to the student who has achieved the best performance in the Preliminary Examination, provided that sufficient funds are available.
Passing the Preliminary Examination and completing three quarters of full-time work in approved courses will satisfy the departmental requirements for a master's degree. The deadline for filing the Master's Degree Candidate Certification form with the Graduate School in order to receive the degree at the June degree ceremony is the end of Winter Quarter.
Graduate courses are designed so as to provide the introduction into mathematical subjects which are needed most commonly or most urgently by the graduate students. Mathematics is a vast discipline and accordingly, not all courses can be offered in all years. The students are therefore expected to actively try to get the most of the courses offered in any given quarter. The departmental and University legislation provides for certain minimal requirements related to the course work.
The minimal full-time course load for Mathematics graduate students is three courses per quarter. It is possible to register for four courses with no increase in tuition.
Graduate students must fulfill a residency requirement of 9 quarters (=3 years) of full-time registration in ordinary courses (subject to the distribution requirements above). After fulfilling this residency requirement and passing the Qualifying Examination, a student must register for three quarters of 599 (Post-candidacy research). Any registration after this is in 503 (Resident Research Continuation). The Graduate School Bulletin gives full details. Since 599 and 503 carry reduced tuition, those students granted tuition remission who qualify for 599 or 503 registration must so register. No tuition remission in excess of the 599 or 503 tuition will be granted such students except by prior written consent of the Graduate Committee.
From the third year of graduate study, students may enroll in at most two units of Independent Study (499) each quarter. Each third year student must be enrolled in at least one course other than 499 each quarter.
Students in the second year of graduate study may be permitted to enroll in Independent Study under exceptional circumstances.
A student wishing to enroll in 499 must file a brief syllabus, prepared by the faculty member supervising the Independent Study, with Melanie Rubin by the first day of class, using this form. Independent study courses should not duplicate regular courses offered by the department. In particular, if a course was offered in the near past or will be offered in the near future, then a request to enroll in a 499 course on a subject similar to this course, would most likely be denied.
By the end of the third year, a student must pass six one-year graduate level sequences: two from Group I below and two from Group II. A passed preliminary exam in a subject may be substituted for two courses.
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:
The Qualifying Examination is an oral examination. After the student has decided upon a field of interest, he/she asks a faculty member to chair a committee to conduct his/her 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.
Students preparing for the Qualifying Examination must submit for approval this qualifying examination form to the Graduate Program Assistant (Melanie Rubin) at least three weeks prior to the exam date.
To pass the examination, the student must demonstrate competence in and understanding of the assigned topics and prerequisite material. A short presentation may be made by the student, but adequate time should be allowed for direct examination by the committee.
The Qualifying Examination must be passed by the end of a student's third year. Failure to do so may jeopardize the financial support in subsequent year.
There are several types of financial aid awarded by the department and the University on the basis of merit. According to regulations of the United States IRS, all awards are taxable.
Financial aid is typically offered to graduate students for five academic years. The Graduate Committee decides whether to renew a student's support based upon his/her progress from year to year. For a first year student, progress will be determined from course grades and reports solicited by the Graduate Committee; for this purpose, a GPA of 3.0 or lower is not normally considered adequate preparation for further study. A student normally will be expected to pass the Preliminary Examination by February of the second year and the Qualifying Examination by the end of the third year.
It is a policy of the Graduate School that teaching assistants and University Fellows may not undertake other employment without the prior permission of the Graduate School.
Undergraduate teaching is one of the primary responsibilities of the Mathematics Department; graduate students play an important role in this function. As a part of their training, and as a necessary condition for most forms of financial aid, all teaching assistants are involved with departmental teaching activities each quarter they are in residence. Most often they assist faculty members by conducting the recitation sections of calculus and other lower level classes and/or assist in grading; they may on occasion be asked to grade for upper level or even graduate courses. All teaching assistants also participate in staffing the department's tutoring program. Especially experienced and capable graduate students are sometimes given the responsibility to teach a section of their own. Responsibilities to each course assignment begin on the first day of classes of that quarter and end 48 hours after the final examination. Normally, a student assists in no more than seven courses over a year's time. All teaching assignments are made by the department chairperson, with the aid of the Graduate Committee Program Assistant, Melanie Rubin.
The work of teaching assistants varies with the course and the faculty member who has primary responsibility but generally includes answering questions about homework problems in the recitation section (which meets weekly for each course), proctoring and grading quizes and homework, and assisting in grading mid-term and final exams. The faculty member teaching the course makes specific arrangements with his/her teaching assistants concerning their duties. Recitation sections meet on Tuesday or Thursday; the lectures are on Monday, Wednesday and Friday, although there may be occasional departures from this model. Classes begin on the hour and last for 50 minutes.
It is department policy that a teaching assistant's assigned instructional duties should take no more than four hours per course per week. A teaching assistant who feels he/she is overburdened should consult with the professor in charge of the course. If problems persist, the Director of Graduate Studies should be notified.
Teaching assistants should have at least three formal, announced office hours each week during which their students may meet with them; these serve for all of the classes for which you are a TA. You should choose times when your students are likely to be able to see you (so 9am is bad, as are the popular lecture hours like MWF 11) - otherwise they will be constantly harrassing you about making appointments at other times. Holding some of your office hours in the early evening is another possibility. One good strategy is to have your office hours straddle two class slots, for example 1:30-2:30 pm; this will make them available to more students. Finally, if you are a TA for a course with graded homework, try to schedule your office hours for the day before the homework is due, not the day after. But check with your professor to see what his/her preference is on this issue.
Each teaching assistant also serves as a departmental tutor for three hours each quarter; the tutoring sessions are open to any student who needs help in any lower level course. Teaching assistants sign up for their three hours in the department office at the beginning of each quarter.
The department and the graduate school organize several different training sessions for its new teaching assistants; all new teaching assistants are expected to attend. For first-year graduate students, there is a required teaching seminar during the Winter and Spring quarters.
Faculty members are required by College legislation to have their undergraduate courses evaluated by the students; this includes an opportunity for students to evaluate their recitation sections. The information collected is returned to the faculty member and to the department chairperson. This, and other methods of evaluation, are used by the department in assessing how well teaching assistants are carrying out their duties. A graduate student whose teaching is determined to be unsatisfactory may become ineligible for University financial support.
Summer School Teaching: In order to provide teaching experience and some summer support, some students are given the opportunity to teach in the Summer School. This is usually offered to advanced students, chosen on the basis of evaluations of performance as a teaching assistant.
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.
Teas
One of the best ways to get to know faculty and other graduate students is to attend the departmental teas. These are held in the Commons Room, Lunt 218, every afternoon at 3:45.
Seminars and Colloquia
Students are strongly encouraged to participate actively in departmental seminars and to attend department colloquia. The colloquia, in particular, are meant for a general mathematical audience with no specialized knowledge. A complete list of seminars and colloquia is available on the Mathematical Calendar webpage "http://www.math.northwestern.edu/calendar/".
Library
The R. P. Boas Mathematics Library is located on the first floor of Lunt Hall; it has a large collection of books and journals. Some books may be placed on reserve for beginning graduate courses so all the students can have access in the library. Journals must be used in the library, though they may be signed out briefly for copying. The librarian can explain the details of book circulation policies. Normal library hours are weekdays from 8:30 a.m. to 5:00 p.m. Graduate students may receive keys (for their personal use only) upon paying a $5.00 deposit to the librarian. This deposit will be refunded when the key is returned.
Other books and journals of interest, especially those in applied mathematics, can be found in the Science-Engineering Library, east of the Technological Institute.
The department has some funds to enable students to photocopy research articles. These are available to students who have been admitted to candidacy (passed the Qualifying Exam). See the office staff for details.
Computing Facilities
Many members of the Math Department at Northwestern University use computers in important ways in their research. To support this growing need, the Department has a network of computers running the Linux operating system. These computers and three laser printers are housed in Lunt Hall and are used exclusively by the faculty and graduate students in the Math Department. They support a C language compiler, and Maple for symbolic and numeric mathematical calculations as well as graphical display of their output. There are also more specialized packages in Algebra and Dynamical Systems. Of course TeX and related typesetting packages are available. This network is connected to the university computers via a fiber optic connection. Through this connection there is also access to the Internet and e-mail networks which allow mail to be sent electronically around the world.
Graduate students can obtain accounts on the department's internal computer network, and are encouraged to become familiar with its use. Each entering student should see Miguel A. Lerma to set up an account. The department discourages excessive personal use of departmental computer resources.
The university provides many additional computer services through Information Technology. One of the most useful of these is the campus WiFi network, accessible using your NetId.
Where to Find It
Mailboxes: Mailboxes for faculty and graduate students are located outside Room 201.
Photocopy machine: Room 202. Obtain a user number from the department office to use the machine.
Office supplies: Paper, pencils, pens, stationery, etc. are available in reasonable quantities from the office staff in Room 201.
Texts for TA's: Desk copies of textbooks are available from the Departmental Office.
Computers: Several linux computers and one Micosoft WindowsXT are in Room 215. There is one laser printer in the hall of the basement and two laser printers in Room 215.
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