The Ph.D. Qualifying Examination is described in the Graduate Studies and Research Calendar as follows:

Preliminary or Qualifying Examination

Students must satisfy the department by written or oral examination, or by both, that they have the potential to obtain sufficient knowledge of their general field of study to proceed toward candidacy for the Ph.D. degree. Responsibility for this examination may be assigned to the Advisory Committee in cases where several departments are involved. Normally this examination is administered within the first year, preferably within the first four months, of the student's program. The results of this examination are likely to have a significant impact on the program of study developed for the student. The standard which a student must obtain to pass the qualifying examination is at the discretion of the department or the Advisory Committee, as the case may be. A student failing an examination for the first time is permitted a second qualifying examination. A second failure automatically disqualifies the student from further work for the Ph.D. degree. The results of all qualifying examinations must be reported to the Dean's Office.

Students recommended for transfer from a Master's to a Ph.D. program, must pass a Ph.D. qualifying examination before the transfer will be permitted

The Ph.D. Comprehensive Examination is described as follows:

Comprehensive Examination and Candidacy

The comprehensive examination covers a broad aspect of the appropriate discipline and may be in written and/or oral form. This examination is usually on topics cognate to the candidate's field of research, and is used as a means of judging whether the individual has a mature and substantive grasp of the discipline as a whole. A comprehensive knowledge of the subject will not only help to validate the Ph.D. student as an expert in the general field of choice, but will also complement research activity in the specific area under investigation. Normally this examination is scheduled after the student has completed all requirements except the doctoral thesis.

Only upon successful completion of the comprehensive examination at an appropriate time during the program is a student permitted to continue scholarly activity towards the Ph.D. degree. The comprehensive may be repeated once with the permission of the appropriate Academic Committee of the College. The results of all Comprehensive examinations must be reported to the Dean's Office.

 

DEPARTMENT REGULATIONS

Qualifying Examination

The examination normally consists of three written papers (of 3 hours each). Within one month of arrival at the U of S a student with an exceptionally strong background may apply to the advisory committee to substitute an oral examination for the written paper in any of the three chosen topics. If granted, the oral examination(s) will take place as early as possible during the first term of the student's program, in a meeting of the advisory committee with the student and the faculty members who are usually in charge of the written Qualifying exams in the chosen topic. The written papers have to be in topics chosen from the following lists, depending on the specialization of the candidate's program:

Specialization in Mathematics:

1) Algebra / Number Theory
2) Analysis
3) Topology
4) Mathematical Logic
5) Differential Geometry
6) Differential Equations
7) any one of the Qualifying Examination topics 1)-4) offered by the Statistics group

where at least two of the three topics must be chosen from 1)-4). In these topics, the students will be tested on the material of corresponding senior upper year honours classes.

 

Specialization in Statistics:

1) Mathematical Statistics
2) Applied Statistics I
3) Stochastic Processes
4) Applied Statistics II
5) any one of the Qualifying Examination topics 1)-6) offered by the Mathematics group.

Specialization in Applied Mathematics:

one of 1) - 4) from the Specialization in Mathematics, and two of:

1) Numerical analysis. In consultation with the advisory committee the student may substitute a project for the written exam.
2) Methods of Applied Mathematics. One of basic ODE's and linear PDE's, or applied group theory, or variational principles and integral equations.
3) In consultation with the advisory committee, any application area with significant mathematical content, such as but not exclusively one of quantum mechanics, classical mechanics, fluid mechanics, continuum mechanics, electromagnetism, special and general relativity.

The examination will be scheduled twice yearly: Spring (first 2 weeks in May) and late Summer (last week in August and first week in September), and will be completed over a two week period.

Each student will have two opportunities to write and pass the examination. A failure on the second attempt will result in the student being asked to discontinue.

In order to pass the examination, a student must pass all three papers. If a student passes two of the three papers then the student may, at the discretion of the Graduate Committee, be required to rewrite the single failed paper at the next scheduled examination period. It should not be presumed however that the student will not be required to write all three papers in the event that only one paper is failed on the first attempt. If two or more papers are failed on the first attempt then the student must write and pass three papers in the second attempt.

A student registering in the Ph.D. program in September (resp. in January), must pass the examination within 13 months (resp. 17 months). A student who has earned a M.Sc. degree in the Department and who continues with the intention of obtaining a Ph.D. degree must pass the examination within 13 months of the successful M.Sc. defence.

Comprehensive Examination

The Ph.D. Comprehensive Examination is to be interpreted as follows: The student should have completed almost all courses required for the Ph.D. degree and made considerable progress on acquiring the necessary background to the thesis research. The examination will be conducted by the student's Advisory Committee and will normally be an oral examination taking the form of a talk by the student outlining the thesis problems, an outline of an approach to them and results obtained to that time and followed by a period of questions by members of the Advisory Committee. The purpose of the examination is to satisfy the Graduate Committee, the student's Advisory Committee, and the student that his or her progress toward the thesis is adequate, or, if it is not found to be adequate, to permit the Advisory Committee to offer constructive criticism to assist the student in achieving the desired end. It is a possible, but not expected, outcome of the examination that the student will be asked to discontinue. The Examining Committee will submit a report on the Comprehensive Examination to the Graduate Committee, which will in turn report the result to the College of Graduate Studies and Research. The Comprehensive examination should be passed no later than 36 months after first registration as a Ph.D. student. Extensions to this deadline are to be made only by the Graduate Committee.

updated: May 31 2005