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The graduate program in Mathematics is aimed at guiding 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, that contributes new results to the body of mathematical knowledge.

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:

- Preliminary Examination (normally passed by the end of the first year)
- Qualifying Examination (often passed by the end of the second year)

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 begin thinking about a possible dissertation supervisor sufficiently early in the program (normally toward the end of the first year, or beginning of the second). Students should be constantly browsing different areas of mathematics and discussing math informally with classmates and faculty, as they search for the fields which attract them most.

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. Graduate students may organize seminars in which they invite faculty to explain their areas of research.

Graduate students with learning disabilities are encouraged to contact the director of graduate studies and the Office of Services for Students with Disabilities (ssd(at)northwestern.edu).

All students must pass the Preliminary Examination in order to continue with the program.

The Preliminary Examination consists of written examinations in the following three subjects: algebra, analysis, and geometry/topology.

Incoming students are invited and encouraged 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).

Syllabuses for the preliminary examinations and copies of past examinations are available.

The rules for the Preliminary Examination are posted here.

The Preliminary Examination is given during New Student Week in September and at the end of the academic year (typically June). Graduate students must take the Preliminary Examination in all three subjects by the end of their first academic year. Students who do not pass the Preliminary Examination by the end of their first year must pass a make-up examination in September 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 is offered at the end of each academic year to the student who has achieved the best performance in the Preliminary Examination. The award is accompanied by a monetary prize when sufficient funds are available.

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 filing the form with the Graduate School in order to receive the degree at the June degree ceremony is the end of Winter Quarter. Students intending to apply for a master's degree should approach the Graduate Program Assistant (Deavon Mitchell) at least 3 weeks prior to this deadline.

Graduate courses are an essential component of a mathematician's training. Graduates of the Northwestern mathematics program are expected to be well-rounded, in part by having taken courses in a wide variety of subjects. In addition, several courses are research-oriented and presentation-based, offering training for some of the specific skills needed by research mathematicians. Beyond these general expectations, 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
in the first three years
is three (3) courses per quarter. It is possible to register for four
(4) courses with no increase in tuition. Graduate students in each of their
first three years are required to enroll in at least seven (7) regular
mathematics courses (i.e., **not** including 499 independent study
courses) each year, and at least one (1) such course per quarter.
Students who have passed their qualifying examination may count post-candidacy
research (TGS 500) toward this requirement. Substitutions or exceptions
require the advanced approval of the Graduate Committee.

Graduate students must fulfill a residency requirement of nine (9) quarters (=3 years) of full-time registration in ordinary courses. After fulfilling this residency requirement and passing the Qualifying Examination, a student should register for TGS 500 (Advanced Doctoral Study). This reduces the tuition and maintains full-time status.

*Summers:* By the end of each academic year, each student is
required to submit a list of the courses taken, in order to
demonstrate compliance with the course work and registration
requirements outlined herein. Each student receiving a
university fellowship for the upcoming summer must submit,
prior to the end of Spring quarter, to the
Graduate Program Assistant (Deavon Mitchell) a program of study for the
summer months, signed by a supervising faculty member.

Independent study courses ("499"; also called "reading courses") are an excellent way for students to explore specific topics not covered by the regular course offerings. They are also a way for students to learn of areas of research of the faculty. As such, they play an essential role for graduate students in search of an adviser.

A student wishing to enroll in 499 must file a brief syllabus, prepared by the faculty member supervising the Independent Study, with the Graduate Program Assistant (Deavon Mitchell) 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 in a similar subject would most likely be denied.

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, 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. The committee must be comprised of at least three faculty members, at least two of whom are NU graduate faculty.

Students preparing for the Qualifying Examination must submit for approval this qualifying examination form to the Graduate Program Assistant (Deavon Mitchell) at least three weeks prior to the exam date.

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 year.

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.

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.

Financial aid from Northwestern consists of a mixture of fellowships and graduate (teaching) assistantships. A student with a non-English speaking background may be required to demonstrate fluency in spoken English before he or she can hold a graduate assistantship. Failure to do so may result in academic probation, loss of funding, and even exclusion from the program. See Graduate Assistantship for the precise requirements.

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. This includes any stipend or fellowship at another institution.

**Residency during Fellowship Quarters.**
The department is required to certify that all graduate students on any
fellowship are working full-time on mathematics research; therefore, we
normally expect fellowship students to be in residence. Exceptions are
possible for extraordinary research opportunities. Such exceptions require
explicit permission of the student's advisor and the departmental graduate
committee.

Teaching experience is considered to be an integral part of the training of all graduate students, and is required each year of all students, with the exception of students in their final year of study. First-year students usually fulfill this requirement by assisting with grading. Upper-level students fulfill this requirement by serving as a teaching assistant for are least one course in an academic year.

Potential employers, particularly academic employers, often specifically inquire about the quality of teaching performed by job candidates from the department. Our students have found teaching experience to be a valuable asset.

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.

In some cases, senior students with exceptional teaching ability will be permitted to teach their own class. Permission would be granted after written application to the Director of Graduate Studies. The students must have the permission of the Department and their advisors, and there must be a clear fit for such teaching experience in the students' career plans. Students would work with a faculty mentor and perhaps in conjunction with a Searle Center Teaching Certificate Program. Students would teach during a fellowship quarter.

**Responsibilities to
each course assignment begin on the first day of classes of that
quarter and end 48 hours after the final examination.**

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 quizzes 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 students may meet with them. These office hours serve for all of the classes for which the graduate student is a TA. Teaching assistants should choose times when students are likely to be able to come (so 9am is bad, as are the popular lecture hours like MWF 11), so as to avoid multiple requests for appointments at other times. Holding some office hours in the early evening is another possibility. One good strategy is to have office hours straddle two class time-slots, for example 1:30-2:30 pm; this will make them available to more students. Finally, TA's for courses with graded homeworks should schedule office hours for the day before the homework is due, not the day after. Check with your professor to see what his/her preference is, as well.

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 second year graduate students, there is a required teaching seminar during the fall quarter (see below).

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.

*Training:* Graduate students undergo teacher
training during the fall quarter of their second year by participating
in Math 580 Seminar in College Teaching. First-year students perform
supervised grading of quizzes and exams in one undergraduate course
per quarter.

*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.

**Travel to Conferences and Seminars**

The mathematics department has limited funds allocated to support graduate student travel to present work or attend conferences and seminars of relevance to a student's educational and/or professional development.

The student should first approach his or her adviser to inquire about
funding through a grant held by the adviser. Please note that funding
from federal grants will carry additional limitations beyond the
standard University policy, such as requiring US air carriers for
foreign travel, and no alcohol. More information can be found at the
following link:

http://www.northwestern.edu/financial-operations/policies-procedures/policies/travel.pdf

The student should also seek funding from other sources, such as a hosting institution or conference organizers.

After these steps are taken, the student may apply for travel support from the mathematics department directly. The standard award is $750 per student per year, and the support is provided in the form of reimbursement.

To apply, the student should submit by e-mail to the Graduate Program Assistant (Deavon Mitchell) a description of the conference (including titles, dates, web URL's) and the intended use and total amount of funding requested. The application should also specify other sources and amounts of funding that the student has applied for/secured.

NOTE: A student seeking travel support for a conference or seminar at which he or she has an opportunity to contribute a presentation must concurrently apply for a Graduate School Travel Grant. Applications are available at the Graduate School Website. The student may consult with the Business Administrator regarding budgetary questions on the application as necessary.

The student should submit the application(s) as early as possible to secure funding before booking travel, but certainly at least one month prior to the date of travel. The student will receive a written response within 10 days.

After the travel is complete, the student should create an expense report and submit original receipts to the department office. The student also should submit by e-mail to the Graduate Program Assistant (Deavon Mitchell) a summary paragraph describing how the completed travel benefits the student's educational and/or professional development.

Once the summary paragraph has been received and approved, funds will be released for reimbursement.

Three awards are given annually to graduate students.

- An award for the
*best performance on the Preliminary Examination*is given at the end of the year. - The
*Gelfand Award*is given at the end of the year to that student who has contributed most to the department. - The
*Best Thesis Award*is given each year to a graduating student.

*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 Common 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.

*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.

*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 Mathematica 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 Microsoft Windows XP are in Room B10. There is one laser printer in the hall of the basement and one laser printer in Room 202.

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