Tufts University
Department of Mathematics

Requirements for the Ph.D.

A student may be admitted to the Ph.D. program either upon admission to the graduate program or later upon the recommendation of the graduate committee. When a student in the master's program fulfills the core requirement, the committee will vote whether to make such a recommendation, after considering the student's course work and performance in the core exams and assessing the student's potential of earning a Ph.D. under the direction of some member of the department. The department does not guarantee a dissertation advisor for every student, but recognizes its responsibility to help the student find a satisfactory match. The actual admission to the Ph.D. program is made by the Graduate School.

Students transferred to the doctoral program will normally receive a master's degree in the course of their studies.

To earn the Ph.D. degree, a student must fulfill the following requirements:

  • The residence requirement.
  • The foundation requirement.
  • The language requirement.
  • The candidacy examination.
  • The dissertation.
  • Teaching experience.
    • These requirements, including deadlines, apply to students in the master's program who may in the future be transferred to the Ph.D. program as well as to students who are already in the Ph.D. program.

    The residence requirement

    This requirement is described in the Bulletin.

    The foundation requirement

    The foundation requirement consists of passing a series of examinations testing the student's understanding of the fundamental ideas and tools for further mathematical study.

    Each student will take three oral examinations, each of length about 90 minutes or less, chosen from among the four subjects of analysis, algebra, geometry, and applied mathematics. Each examination will be administered by at least two faculty members appointed by the graduate committee. In special circumstances the committee may allow any of these examinations to be taken in written form. From time to time the graduate committee will publish a list of topics for each subject. It is intended that most of the topics for each examination can be covered in one graduate course, given sufficient undergraduate preparation; however, the examination need not be restricted to the material covered in a specific course.

    Each examination will be offered every September, January and May, if requested by some student. Students are encouraged to take each of these examinations as soon as possible, not necessarily all the same semester. They are required to pass all three examinations by the end of their fourth semester (term) of graduate study at Tufts unless special exemption of the deadline is granted by both the chair of the department and the graduate committee. Each of these examinations may be taken up to three times; a third failure leads to dismissal from the Ph.D. program or prevents admission to that program.

    It is recommended that at least two of the three examinations be taken by the end of the student's second semester of graduate study at Tufts. All students receiving financial assistance must pass all three examinations by the end of January in their second year of graduate study at Tufts in order for the assistance to be renewed.

    The student must inform the chair of the graduate committee of his or her intention to take any of these examinations at least one month before the last day of classes of the semester in question.

    The language requirement

    A student who is a native speaker of English must demonstrate adequate proficiency in reading mathematics that has been written in one of the languages French, German, and Russian. This proficiency is normally tested by an examination that consists of translating passages of mathematical writing with the use of a dictionary. The method of arranging the examination varies according to the language; the student should consult his or her advisor or the chair of the graduate committee.

    A student who is not a native speaker of English must demonstrate proficiency in one of the three languages listed above as in the preceding paragraph. Such a student must also demonstrate adequate proficiency in oral and written mathematical communication in English. This proficiency will be tested by judging the student's use of English in the core requirement examinations. If this is not judged satisfactory, the student will be required to pass an oral English examination within a year after fulfilling the core requirement.

    Students are advised to fulfill the language requirement as soon as possible. In accordance with the rules of the Graduate School, it must be fulfilled before taking the candidacy examination.

    The candidacy examination

    Before writing a dissertation and within a year after fulfilling the core requirement, a student must pass the candidacy examination. The purpose of this examination is to provide convincing evidence of the student's aptitude and preparation to do research in his or her chosen field of mathematics.

    Before taking this examination, the student must have fulfilled the core requirement and the language requirement. The student must register for guided individual study (Mathematics 293 or 294), specifically aimed towards the examination, with a member of the Mathematics Department who has agreed to be chair of the student's candidacy committee. The material studied will be in preparation for work on a dissertation. The candidacy examination should be taken as soon as the department member judges that the student is ready; it must be taken within a year after fulfilling the core requirement. It is recommended that it be taken by the end of the fourth semester of graduate study at Tufts.

    The candidacy examination is an oral examination given by a committee appointed by the graduate committee. The candidacy examination committee will normally be chaired by the department member who has directed the individual study, and also contain at least one department member from the field of mathematics of that study and at least one from a different field. The student must give a presentation of the material of the individual study, and must reply to questions deemed relevant by the committee. The student may

  • pass the examination,
  • be given a second chance, or
  • fail the examination.
    • In the second case the student must retake the examination within six months. The second examination may be based on individual study with a different faculty member who has agreed to chair a new candidacy examination committee. The second examination must be passed or failed; there can be no third chance.

    A student who fails the candidacy examination, or who does not pass it by the end of the sixth semester of graduate study at Tufts, will be dismissed from the Ph.D. program. In addition, students receiving financial aid should pass it by the end of their fifth semester of study in order for the aid to be renewed.

    The dissertation

    The major task of a doctoral student is to write a dissertation under the direction of a department member who has agreed to be the student's dissertation advisor. The dissertation must be a substantial original contribution to the field of the student's specialty and must meet standards of quality as exemplified by current mathematical research journals.

    The dissertation must be accepted by a committee appointed by the graduate committee. This committee will normally consist of the dissertation advisor, at least one other member of the department, and at least one expert from outside Tufts. The committee will conduct an oral examination of the student on the dissertation and its background, known as the ``defense''. Each member of the committee must be given a copy of the dissertation at least ten days before the defense.

    Teaching experience

    A doctoral student is required to have at least one semester's teaching experience at Tufts. This requirement can be fulfilled by teaching a section of a mathematics course, by running a tutorial room, or by giving review sessions. The way for each student to fulfill the teaching requirement will be determined by the graduate committee, the departmental curriculum committee, and the chair of the department.