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ACADEMIC ADVISING
ACADEMIC PROGRAM
Although these two requirements are somewhat different in the
Pure Math Program and in the
Applied Math Program, the programs have
many requirements in common.
DEPARTMENT REQUIREMENTS FOR THE DOCTORATE
While the Institute has no specific course requirement for doctoral students, the Department expects its students to pass at least 11 one-semester graduate courses, exclusive of thesis, (132 credit hours or units) with grades of A's and B's. One advanced undergraduate math subject and/or relevant graduate subjects from other departments may occasionally be used as substitutes. Note that many courses occur in pairs, filling up a full academic year. All students are expected to register for a minimum of three graduate classes per term each and every semester (usually 36 units) up until completion of the oral qualifying exams. Students choose their courses under the general guidance of a Department of Mathematics faculty registration advisor, even when the student's thesis advisor is a faculty member outside of the Department of Mathematics. No Pass/Fail graduate subjects are offered in the Department. All courses are graded A-F, with an internal plus and minus system currently in place. Grading in graduate subjects prior to completion of the oral qualifying examination is expected to be reflective of academic performance. Students are expected to complete all course requirements within the current semester: it is rare for a graduate student to receive an Incomplete. Graduate students are expected to maintain at least a B+ average. Satisfactory continuing thesis research in 18.THG, Thesis, is recorded as a "J"; unsatisfactory progress is graded "U" and would be cause for academic warning. The academic performance of all graduate students is reviewed at the end of each semester: i.e., units completed, progress through the academic requirements, grades, as is their performance in RA or TA positions. Students with external advisors: It is department policy to monitor the progress of all students both in Pure and Applied Math whose main thesis advisor is outside the Department of Mathematics and to foster active continuing communication between all parties. This policy applies to all registered students, those in residence at MIT and those on non-resident doctoral status. An informal summary of current research must be sent by each student with an external thesis advisor to the Graduate Administrator, room 2-233, by Add Date each semester: Add Date is the end of the 5th week of the semester. This summary will then be distributed to both the internal faculty advisor as well as the Chairperson of the Applied Mathematics Committee (for students in Applied Math) or the Chairman of the Graduate Program (for students in Pure Math). The summary should clearly state the name, title, department, school affiliation, email address and phone number of the external advisor. The length of the report is left up to the discretion of the students and the internal MIT Math Department advisors. A formal written report, with an attached signed cover sheet, must be submitted by the student and received in the Graduate Mathematics Office by Drop Date each semester. Drop Date is the end of the 10th week of the semester. Copies of the cover sheet will be distributed to each student with an external advisor. The external and internal advisors as well as the appropriate committee chairperson will be required to sign the cover sheet, indicating their evaluation of the attached summary of work in progress. In order for a satisfactory grade to be assigned at the end of the semester, all faculty must have indicated their approval of the student's research. Students who do not submit this report and signed cover sheet or whose advisors do not believe adequate progress has been made will receive an unsatisfactory grade in Thesis and may either subsequently be placed on warning or denied further registration by action of the Committee on Graduate School Policy (CGSP). The oral Qualifying Examination covers three distinct reasonably broad areas of mathematics. One is treated in greater depth than the other two. It normally becomes the student's area of specialization and the examiner in that area normally becomes the student's thesis advisor. The student is, however, not under any obligation to remain with that advisor or that area. The other two areas are examined roughly at the depth of a first year graduate course with perhaps some additional independent study. The exam is taken as soon as the student feels ready; it is strongly recommended to take the exam not later than 1.5 years after entering. In case of failure, another try is possible at a later date. In any case, the oral Qualifying Examination must be taken and passed by the last day of classes of the spring term of the second year. In order to schedule Qualifying Examinations, students must obtain preliminary approval of committee composition, examination topics, and tentative exam date. Students are requested to send email with these details to David Jerison (Pure Math) or Alar Toomre (Applied Math) and copy the following individuals in the same message: the registration advisor, the proposed thesis advisor, and the major examiner. Email approval should be sought at least one month prior to the examination. Once email approval is obtained, students should pick up two scheduling forms in the Graduate Mathematics Office: forms require faculty signatures. The Qualifying Examination typically takes place in the office of one of the examiners: students are responsible for making all scheduling arrangements. The length of the examination may differ from one program to another. Financial aid from MIT beyond the second year (as well as certification of "good standing" for external fellowships) is contingent on the oral Qualifying Examination being passed. In cases of marginal performance, the examination committee may insist on reexamining at a later date, or it may set further conditions such as readings or other studies in a specific area. A student who fails the Qualifying Examination outright will be separated from the program, though typically with the opportunity to obtain a Master's degree. After the oral Qualifying Examination is successfully completed, the student decides on the Thesis Topic and works with the chosen Thesis Advisor to master the field and write a thesis. Registration in 18.THG, Thesis, begins upon completion of the oral Qualifying Exam and continues each subsequent term. The Thesis must conform to MIT Specifications for Thesis Preparation. As the thesis approaches completion, a Thesis Examination Committee is formed, consisting of the Thesis Advisor and two additional faculty members in related fields. A form for the listing of this committee is available in the Graduate Mathematics Office. It should be returned to in the Graduate Mathematics Office early in the final thesis semester, before the thesis defense is scheduled. The members of the Thesis Examination Committee should have a copy of the thesis two weeks before the Thesis Defense. Announcements of the defense are posted on the web and department bulletin boards at least one week in advance of the defense. The student's successful defense of the thesis before the Examination Committee and submission of approved thesis texts to the Graduate Mathematics Office then completes the doctoral program. Ordinarily this should take place within four years of admission. While there is no Institute Language Requirement, doctoral candidates in the Department of Mathematics (both Pure Mathematics and Applied Mathematics) have to demonstrate a mathematical reading knowledge in at least one of the following languages: French, German, Italian, Russian, Spanish or Chinese. This proficiency can be demonstrated in any of the following ways:
PURE MATHEMATICS PROGRAM
The following are sample programs for the oral Qualifying Examination from recent oral exams; the main topic is listed first:
A Thesis Proposal, worked out in consultation with and
approved by the student's Thesis Advisor is to be
submitted to the Graduate Committee for approval. This proposal
should be about five pages, consisting of a preliminary thesis
title, background summary with relevant bibliography and a
description of the proposed research. The signature of the thesis
advisor is required on all thesis proposals. This proposal should
be submitted within a year after the orals are passed or at the
beginning of the 6th semester of graduate work whichever is
earlier. If a student's thesis plans change substantially, a
revised proposal should be submitted.
APPLIED MATHEMATICS PROGRAM
By the end of that first term, the student, in consultation with the advisor, should submit at least a tentative Plan of Study for approval by the Chairperson of the Applied Mathematics Committee, and before the end of the second term a firmer and more polished version of the same, for similar comment and approval. In addition to listing subjects to be taken (or already taken) in a major field, this plan should also include a few subjects that may seem less immediately relevant, simply to broaden one's familiarity with other areas of Applied Mathematics. For breadth in their studies, it is required that students complete at least one subject from four of these six areas:
The Applied Mathematics Committee will consider each student's proposed Plan of Study individually to insure maximum flexibility consistent with its general goals. Applied Mathematics students satisfy their distribution requirements through Coursework rather than through their Qualifying Examination. The purpose of the latter is instead to convince the examining committee of the student's readiness to pursue research in his/her chosen area. To this end, the examining committee should include the student's prospective Thesis Advisor and two other faculty members whose interests are closest to his or her field of interest. At least two of the members of this committee must be Applied Mathematics faculty members. The proposed composition of the committee is subject to approval by the Chairperson of the Applied Mathematics Committee. The Qualifying Examination should be taken during (or shortly after) the third semester of enrollment. Delay beyond this requires approval of the Chairperson of the Applied Mathematics Committee and should be justified by exceptional circumstances. Applied Mathematics graduate students are expected to have approached a prospective Thesis Advisor (and initiated some work with him or her) prior to the qualifying examination. Upon passing this examination, the student is expected to choose a thesis advisor. Students may change thesis advisors with the approval of the Chairperson of the Applied Mathematics Committee and the new advisor. Normally the Applied Mathematics Committee does not even insist on any formal Thesis Proposal from either the student or his/her thesis advisor. All it requires in most situations is that it be informed promptly by both parties as to the identity of this would-be supervisor, and it reserves an infrequently used right to disapprove, if that proposed thesis advisor happens to be unduly transient or from outside this Department. However, should any major change of thesis direction be contemplated, or should there be a wish to change from one thesis advisor to another, the Applied Mathematics Committee again insists that it be consulted in a timely fashion. It may at that point even require a formal thesis proposal that it had waived earlier. In any event, continued financial support from MIT will be contingent not only on the oral Qualifying Examination, but also on advisor reports or other evidence of reasonable progress on the thesis. The three-member Thesis Examination Committee must include the thesis advisor. At least two of the members of this committee must belong to the Applied Math faculty. SPECIFIC REGULATIONS FOR APPLIED MATHEMATICS GRADUATE STUDENTS WHOSE MAIN RESEARCH ADVISOR IS NOT A MEMBER OF THE FACULTY IN THE DEPARTMENT OF MATHEMATICS In the case of students whose main research advisor is from outside the Department of Mathematics, an Applied Mathematics faculty member (familiar with the area of research) is expected to act as formal (internal) advisor within Applied Mathematics. This person will also be the chairperson of the qualifying examination committee. Upon passing the qualifying examination, the student is expected to select a thesis advisor. If this advisor is not a member of the mathematics faculty, the student must continue to have an Internal Advisor within the Applied Mathematics faculty. This advisor should be knowledgeable in the subject area of the student's thesis research, must be kept abreast of the student's research progress on a regular basis, and must approve of the same. All students with advisors outside the department must submit a short written research progress summary each semester to his/her internal advisor. Such reports require approval of the internal advisor and the Chairperson of the Applied Mathematics Committee. However, it is expected that the internal advisor will be kept up-to-date on research progress informally in a more active and current way. Students may change thesis advisors with the approval of the Chairperson of the Applied Mathematics Committee and the new advisor. If the new advisor is outside the Applied Mathematics faculty, approval from the internal advisor is also required. Continuation of financial aid from the department is contingent upon the student maintaining good academic standing and obtaining approval of satisfactory research progress by the student's internal advisor. The student should attempt to arrange financial support from the external advisor. Students with an outside research advisor are expected to submit a tentative and informal thesis research proposal to their internal advisors no later than a year after having completed their qualifying examination. If such expectations are not met, it is the responsibility of the internal advisor to discuss the student's research plans and to report on them to the Chairperson of the Applied Mathematics Committee at least once each term until they are met. Consistent failure to comply may result in withdrawal of financial support to the student. The doctoral thesis must be approved by all members of the thesis examination committee and by the Chairperson of Applied Mathematics (if not a member of the thesis committee). In the case of students with an external thesis advisor, the three-member thesis examination committee must include the thesis advisor, the internal advisor, and another member of the Applied Mathematics Faculty. INFORMATION FOR MATH - HST/MEMP STUDENTS PURSUING DUAL THESIS FIELDS Background
Admission options
Funding
Registration Academic Requirements
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