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New Graduate Curriculum, Ph.D. Qualifying Exams, and Ph.D. Comprehensive Exam (Effective Summer 2004)

New courses/course-descriptions

These courses should be accessible to students who have completed the equivalent of 22M:25, 26, 27, 28, 50 and 55.

Each student in the Ph.D. program is required to demonstrate competence in each of the four core course areas within the first two years of graduate study in our Department, either by passing the 100-level core course sequence above, or by passing the relevant portion of the Ph.D. Qualifying Exam (see below for procedure).

To help ensure that students plan appropriately, each (pre-comp) student will have his/her own individual plan of study, reviewed and approved by the DGS and by the Graduate Committee.

Each student in the Ph.D. program is required to pass a Ph.D. qualifying exam.

  • The Qualifying Exam must be passed within two and a half years of beginning graduate study in our Department.
  • The Qualifying Exam consists of subject exams in three of the core course areas, taken in the same exam period.
  • The area exams are based on the 100- level core course sequences listed above.
  • Each area exam is three hours long.
  • A student may take the Qualifying Exam at most twice.
  • For each area exam, a student will receive a grade of Ph.D. qualifying level pass, Master's level pass or not pass.
  • The definition of "pass the Ph.D. qualifying exam" is: Pass at least two area exams with "Ph.D. qualifying level pass" and a third with at least "Master's level pass".
  • If a student needs to take the Qualifying Exam a second time, then the student may choose to carry forward area exam score(s) of "Ph.D. qualifying level pass".
  • A student must register for the exam by the announced deadline, usually about a month before the start of the semester. A student cancelling the exam registration must do so at least one week prior to the exam. After this date, an exam not taken will be counted as a not pass.Using Qualifying Exam to satisfy core course requirements: A student may satisfy one or more of the core course requirements via the Qualifying Exam, in three ways:
  • A student who takes the Qualifying Exam will be exempted from the core course requirements in each of the three areas of his/her Qualifying Exam in which the score was Ph.D. qualifying level pass.
  • A student may choose to take all four area exams during one exam period, having registered for three as the Ph.D. Qualifying Exam, and designating the fourth to satisfy the core course requirements of the fourth area. A mark of Ph.D. qualifying level pass is necessary to satisfy the course requirement in this manner.
  • A student who has already passed the Ph.D. Qualifying Exam may take an individual area exam in a subsequent administration of the Ph.D. Qualifying Exam. A mark of Ph.D. qualifying level pass is necessary to satisfy the course requirement in this manner. This option may be exercised at most one time.

Graduate courses transferred from other universities may be used to satisfy the course/breadth requirements, subject to approval of the DGS and the graduate committee.

The Qualifying Exam will be given in all areas (as needed by student registration) at the beginning of each fall and spring semester.

This core course and qualifying exam system allows for example (see table below as well):

      1) Entering students with excellent preparation the opportunity to pass the Ph.D. Qualifying Exam in August of their beginning year, and move directly to research related activities, finish both Core Course Requirements and Comp by the beginning of their second year;

      2) Entering students with very strong preparation the opportunity to pass some of the area exams in August of their beginning year, and concentrate on the remaining areas, and possibly pass the Ph.D. Qualifying Exam in August of the beginning of their second year and thus again move quickly to research related activities as soon as their second, finish both Core Course Requirements and Comp by the end of their second year;

      3) Entering students with good preparation the opportunity to start three core sequences in the first year and possibly pass the Ph.D. Qualifying Exam in August of the beginning of their second year and thus again move quickly to research related activities as soon as their second, finish both Core Course Requirements and Comp by the end of their second year;

      4) Entering students with weaker preparation the opportunity to start two core sequences in the first year and another two the second year, possibly pass the Ph.D. Qualifying Exam in August of the beginning of their third year or latest the beginning of the spring of their third year, while in their third year they start on comp preparation, finish both Core Course Requirements and Comp by the end of their third year.

This two and a half years time frame also allows the flexibility for any student to switch the areas of the Qualifying Exams during their first two years here.

(One reason to keep the "Masters" mark for the Qual Exam is for the student, who fails the Ph.D. Qual Exam but his/her performance reaches the level of M.S., will not have to take another Master Comp exam.

It is required that every Ph.D. candidate must pass an oral  Ph.D. comp exam in his/her chosen area within three and a half years of beginning graduate study in our Department. Each student must submit a Ph.D. comp proposal to the graduate committee for approval prior to the comp preparation. The proposal must list the examining committee (at least five people including the chair of the committee) and be signed by the chair of the examining committee. Typically the comp preparation would build on one of the 200 level sequences with additional readings from books and research papers. The student would give an oral presentation of the material (usually about one hour) and be questioned over the material by the committee. Note that the comp is not open to the public.

Waivers, or modifications of rules, for students with weak backgrounds, or other special circumstances may deal with time restrictions, not weakening content requirements.

For the limited number of graduate students entering in the spring, individual plans of study, reviewed and approved by the DGS and by the graduate committee, will be adjusted to reflect the fact that most of our 100/200 level courses are offered as sequences.
 

Breadth Requirements for Ph.D. in Mathematics

There are two versions of this requirement. #1 is effective summer 1999, #2 is effective summer 2004. Students entering the doctoral program before the summer of 1999 should consult the Director of Graduate Studies.

#1 - 18-Hour Breadth Requirement (Effective summer 1999)

These requirements apply to students entering the doctoral program in or after summer 1999. Doctoral students already in the program have the option of using the version in effect when they were admitted or any revision since.

Of the required 72 hours of graduate credit, at least 18 hours must be in courses numbered from 200 to 371 with the exception of 224 and 225, subject to the following conditions:

i) The courses designated as preparatory for the Ph.D. comprehensive exam (currently 200-201, 205-206, 210-211, 216-217, 220-221) may be counted in this 18 hours only if the corresponding area is not one of the areas used by the student to pass the comprehensive exam.

ii) If the three areas used to pass the comprehensive exam are not Algebra, Analysis and Topology, then the student must pass with a grade of at least a B- at least one of the corresponding preparatory courses listed above in each of these three areas not used to pass the comprehensive exam.

#2 - 18-Hour Breadth Requirement (Effective summer 2004)

These requirements apply to students entering the doctoral program in or after summer 2004. Doctoral students already in the program have the option of using the version in effect when they were admitted or any revision since.

Every student in the Ph.D. program must pass at least 33 credit hours of graduate math courses
numbered from 22M:200 to 22M:371 with the exception of 224 and 225, such that at least 18
credit hours must be from 200 level courses.

Among the 200-level math courses, a student must

  • Choose three areas from the following areas:
    • Algebra (22M:205-206), Logic (22M:220-221)
    • Analysis (22M:210-211), Numerical Analysis (22M:270-271);
    • Differential Geometry (22M:260-261), Topology (22M:201-200);
    • Ordinary Differential Equations (22M:213-214), Partial Differential Equations (22M:216-217);
  • Pass at least two courses in each of the three chosen areas.

Updated on 10/6/08 by K. Voss