Degrees and Requirements

Degrees and Requirements

It is the student’s responsibility to be familiar with the requirements and policies of the University and the Department, as stated in the Graduate School Bulletin and this handbook respectively. If a student is in doubt about the application of these policies to their own case, the matter should be brought to the attention of the student’s academic advisor.

The student should be aware of the general structure of the program as explained below, including the required coursework and the system of qualifying examinations. It is the student’s responsibility to initiate each step in their degree program. Students must also be aware of the statute of limitations, as explained below and in the Graduate School Bulletin.

Degree Options

The Department of Mathematics and Statistics offers PhD programs in Mathematics and Statistics and MS programs in Applied Mathematics and Statistics. It also grants an MS degree in Mathematics but this is usually only awarded as a step towards the PhD degree. Note that neither of the MS programs are primarily meant as preparation for a PhD program; a student who wishes to do a PhD after an MS in Applied Mathematics or Statistics must apply and be accepted to the PhD program like any other student. There is no formal distinction between pure and applied mathematics within the Mathematics PhD program.

A student who wishes to transfer from one degree option to another should notify the GPD as early as possible. Such a transfer requires the approval of the Graduate Admissions Committee, just as in the case of a new applicant, and will usually involve adjustments in the amount and/or duration of financial support as well as, in some cases, a formal application to the new program.

Degree Requirements

Formal degree requirements are given below. Coursework requirements may be waived by the GPD if in their judgment the student has taken acceptable equivalents elsewhere. In some cases, strong performance on one of the written exams can be accepted as a substitute for taking a course. In other cases it may be possible to substitute an alternative course for a required course. To request a waiver of a course requirement, students should contact the GPD directly, explaining the course to be waived, the alternative course to be taken, if any, and the justification for the request. The GPD will return a decision granting or denying the waiver, and a copy will be placed in the student’s file.

Students are reminded that in addition to Department requirements they must complete all degree requirements established by the Graduate School, as described in the Graduate School Handbook. Degree application forms for an MS or PhD can be found on the Graduate School website as well. The student must fill out the form and return it to the GPM for verification and signatures of the GPD and the Department Head. The GPM will then submit the form and a cover letter to the Office of Degree Requirements.

Follow the links below or use the menu for requirements specific to each degree.

Requirements for MS in Mathematics, Applied Mathematics or Statistics

 

Requirements for the PhD in Mathematics or Statistics

Statute of Limitations

This is the maximum time allowed for completion of a degree. A PhD student has six calendar years from acceptance into the graduate program, and a MS student four calendar years, to earn the degree. In exceptional circumstances, these limits may be extended with the approval of the GPD and the Dean of the Graduate School. Please note that these time limits are completely independent of any funding decisions.

All PhD students must

  • Choose an official dissertation advisor (and notify the GPM about the choice) within one year after the completion of all exam requirements, or the start of the sixth semester, whichever comes last.
  • Form a dissertation committee and submit a dissertation proposal (prospectus) to the Graduate School within 18 months after the completion of all exam requirements, or the start of the seventh semester, whichever comes last.
  • If a student fails to satisfy either one of these conditions, at the discretion of the GPD the student could be granted an extra semester to satisfy these requirements.
  • If a student fails to satisfy these requirements within the prescribed time period, the GAC in conjunction with the Department Head will review the student’s status and future financial support.

MS requirements

MS requirements

MS in Mathematics

Please note that the MS in Mathematics is usually only obtained by students within the Mathematics PhD program; there is no separate program awarding it.

  1. The student must complete 30 hours of coursework with grades of C or better, including at least 24 hours with grades of B or better. In addition, the student must have at least an overall B average.
  2. Any course outside the Department or numbered less than 600 must have the GPD’s approval to be counted toward the 30 hours. No more than four courses below the 600 level may be counted, and no more than 3 hours per course may be counted toward the 30 hours.
  3. The required 30 hours must include 21 hours of Mathematics and Statistics courses (at least 18 hours numbered above 600), normally including at least four of the courses: Math 605, 611, 621, 623, 645, 651, 671, Stat 607.

MS in Applied Mathematics

  1. The student must complete 30 hours of coursework with grades of C or better, including at least 24 hours with grades of B or better. In addition, the student must have at least an overall B average. (Note: Pass or fail courses cannot be used to satisfy this requirement.)
  2. Any course outside the Department or numbered less than 600 must have the AMD’s approval to be counted toward the 30 hours. No more than four courses below the 600 level may be counted, and no more than 3 hours per course may be counted toward the 30 hours.

  3. The required 30 hours must include at least 18 hours of Mathematics and Statistics courses, and must include:

    1. Math 532H: Nonlinear Dynamics or Math 645: Differential Equations and Dynamical Systems;
    2. Math 534H: Introduction to Partial Differential Equations;
    3. Math 651: Numerical Analysis I;
    4. Stat 607: Mathematical Statistics I or Math 605: Probability Theory I.

    Each of the four courses can be replaced by an elective course with the approval of the AMD, if a student has taken an equivalent course before entering the program. 

MS in Statistics

  1. The student must complete 30 hours of coursework, with grades of C or better, including at least 24 hours with grades of B or better. In addition, the student must have at least an overall B average.
  2. Any course outside the Department or numbered less than 600 must have the approval of the student’s Statistics Coordinator to be counted toward the 30 hours. No more than 3 hours per course may be counted toward the 30 hours.

  3. The required 30 hours must include:

    1. Stat 625 (Regression Analysis);
    2. Stat 607–608 (Mathematical Statistics I, II);
    3. Stat 535 (Statistical Computing);
    4. At least five other courses which are either Statistics courses numbered 526 or above, or some courses outside statistics numbered 500 and above subject to prior approval by the student’s Statistics Coordinator.  At least 12 credits toward the MS must be at the level 600 or higher.  A list of pre-approved courses outside of statistics is available here.

    Students are expected to have a background in advanced calculus and in linear algebra. Students with weak background in these areas will be required to take appropriate courses at an early stage of their graduate study here.

  4. The student must complete a project in statistics under the guidance of a faculty member. The project requirement can be satisfied in several ways:
    1. An external internship related to statistics or data science of sufficient scope;
    2. A written individual final project from a graduate statistics course numbered 526 or above or a 3-credit independent study that includes, at a minimum, an examination of methods through simulations and/or a detailed statistical analysis of real data;

    3. Successful completion of the project seminar course Stat 691P (which can then also count toward the 30 hour coursework requirement). 

      The project used to satisfy this requirement must receive approval from the Statistics Coordinator or Charles River Campus Director.

  5. The student must either complete at least one credit of statistical consulting (typically STAT 598C) or pass two of the three Basic exams in Applied Statistics, Probability, and Statistics.

PhD requirements

PhD requirements

PhD in Mathematics

  1. The student must complete successfully 36 credit hours of coursework, including:

    1. At least three of the full year sequences:
         Math 605–606, 611–612, 623–624, 645–646, 651–652, 671–672, Stat 607–608;
    2. At least one of Math 611, Math 623, Math 671;
    3. At least one of Math 645, Math 646, Math 651;
    4. At least one of Math 605, Math 606, Stat 607;
    5. At least one of Math 621, Math 706, Math 725, Math 731.

    A student can satisfy the requirement for a full year sequence in (a) by obtaining a passing score on the corresponding qualifying exam (except for 651–652, which does not correspond to a qualifying exam). Note that this does not count against the number of credit hours that must be completed. Any other changes or substitutions to these requirements must be approved by the GAC. The requirements in (b), (c), and (d) will not generally be waived, but in some cases the GAC may approve substituting a more advanced class in the area.

  2. The student must pass the Advanced Calculus/Linear Algebra exam.
  3. The student must pass two written exams chosen among Algebra, Analysis, Applied Mathematics, Stochastics and Topology.  (The advanced Statistics exam can also count for one of these exams, but this option should be used with caution and in consultation with the GPD).
  4. The student must form an oral exam committee and pass the oral exam as described below.
  5. The student must write a satisfactory dissertation and pass a final oral examination (primarily a defense of the dissertation), and must satisfy all other requirements of their dissertation committee. The student is required to register for a minimum of 18 dissertation credits.

PhD in Statistics

  1. The student must complete successfully 36 hours of coursework, including Math 523H (or Math 623, or Math 605), Stat 535, Stat 607, Stat 608, Stat 625, Stat 705, and Stat 725.
  2. The student must also complete five elective courses, including two 600 level statistics courses, and 3 courses of the student’s choice, which require prior approval by the statistics coordinator.
  3. The student must pass three Basic Exams at the PhD level in Applied Statistics, Probability and Statistics. (These cover the material from Stat 535 and Stat 625, Stat 607 and Stat 608 respectively.)
  4. The student must pass the advanced statistics exam and the oral literature-based exam. These exams are described below.
  5. The student must write a satisfactory dissertation and pass a final oral examination (primarily a defense of the dissertation), and must satisfy all other requirements of their dissertation committee. The student is required to register for a minimum of 18 dissertation credits.

Dissertation Committee, Prospectus, Dissertation Credits

This section applies to all PhD students.

Upon completion of all course and exam requirements for their program, the graduate student should select a dissertation advisor from the faculty in the Department as soon as practical. Most often the advisor will have been the chair of the oral exam committee, but this is not required. Upon selecting a dissertation advisor and confirming this choice with the advisor, the student should notify the GPM, who will in turn send a confirmation notice to the student, advisor, GPD and Director of Administration and Staff.

The PhD candidate must form a Dissertation Committee, consisting of a dissertation advisor together with three other graduate faculty members (one of whom must be from another department). The Department requires that the chair of the dissertation committee be graduate faculty in the Department of Mathematics and Statistics. Students are encouraged to form their dissertation committee as soon as possible after selecting their dissertation advisor.

The committee should advise the student about any expected need (in dissertation research or later) for reading material in a foreign language such as French or German.

A written prospectus of the proposed dissertation research must be drawn up with the advisor’s input and signed by all committee members. This prospectus must be submitted to the Graduate School and the dissertation defense must be scheduled at least one month before the actual date of the dissertation defense. A LaTeX form for this purpose may be obtained from the GPM.

After passing all exams and choosing an advisor the student may enroll for dissertation credits: a minimum of 18 such credits are required for graduation.