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20.2.1 THE DOCTOR OF PHILOSOPHY DEGREE 

Admission Requirements 

For admission requirements and period of study, the general regulations of the College of Graduate Studies and Research should be consulted (see 1.5). Qualifying examinations will not normally be required. 

Candidacy 

Students will be recommended for candidacy (see 1.5.1) only after successful completion of the Comprehensive Examinations and course work. 

Program Requirements for the Ph.D. (Mathematics) 

1) Course Work: Students admitted with an M.Sc. or equivalent must successfully complete at least four graduate courses numbered with the prefix 62-; further graduate courses may be assigned by the Graduate Studies Committee in consultation with the advisor. Transfer credits will not be allowed. In addition, graduate courses completed at this institution must include two of the following: Real Analysis (62-510), Functional Analysis (62-512), or Partial Differential Equations (62-561). 

Students admitted with an Honours B.Sc., or equivalent, which is done only in exceptional cases, must successfully complete at least twelve graduate courses, eight of which must be numbered with the prefix 62-; further graduate courses may be assigned by the Graduate Studies Committee in consultation with the advisor. Transfer credits will not be allowed. 

2) Doctoral Committee: Within the student's first term of study at the doctoral level, a doctoral committee will be appointed by the Head of the Department upon the advice of the Graduate Studies Committee. The doctoral committee must be approved by the Executive Committee of the College of Graduate Studies and Research. The doctoral committee shall include the student's advisor as chairperson, at least two other members of the Department, one faculty member from outside the Department, and an external examiner, who shall not be involved in the preparation of the dissertation. The selection of the external examiner is subject to the approval of the Dean of Graduate Studies and Research. Members of other departments may also be invited to join the committee (see also 1.5.2). 

3) Dissertation: The dissertation shall be defended at an oral examination (see also 1.5.2). 

4) Comprehensive Examinations: Each student will be required to pass a series of three written comprehensive examinations. These will test the student's background knowledge and preparedness for research in a particular area of mathematics. If a student fails an examination, it may be repeated once, but if the examination is failed a second time, the student must withdraw from the program (see also 1.5.3). In any case, these examinations must be successfully completed within twenty-five months of registration in the doctoral program. If this deadline is not met, the student must withdraw from the program. 

Program Requirements for the Ph.D. (Statistics) 

1) Course Work: Students admitted with an M.Sc. or equivalent must successfully complete at least four graduate courses numbered with the prefix 65-; further graduate courses may be assigned by the Graduate Studies Committee in consultation with the advisor. Transfer credits will not be allowed. (Up to two courses prefixed 65- may be replaced by 62-510 and/or 62-511.) 
Students admitted with an Honours B.Sc., or equivalent, which is done only in exceptional cases, must successfully complete at least twelve graduate courses, eight of which must be numbered with the prefix 65-; further graduate courses may be assigned by the Graduate Studies Committee in consultation with the advisor. Transfer credits will not be allowed. 

It is strongly recommended that all Ph.D. students in Statistics take a measure theoretic probability course. 

2) Doctoral Committee: within the student's first term of study at the doctoral level, a doctoral committee will be appointed by the Head of the Department upon the advice of the Graduate Studies Committee. The doctoral committee must be approved by the Executive Committee of the College of Graduate Studies and Research. The doctoral committee shall include the student's advisor as chairperson, at least two other members of the Department, one faculty member from outside the Department, and an external examiner, who shall not be involved in the preparation of the dissertation. The selection of the external examiner is subject to the approval of the Dean of Graduate Studies and Research. Members of other departments may also be invited to join the committee (see also 1.5.2). 

3) Dissertation: The dissertation shall be defended at an oral examination (see also 1.5.2). 

4) Comprehensive Examinations: A student must pass a series of three written comprehensive examinations as follows: 

(i) Paper I—Mathematical Statistics and Probability 
(ii) Paper II—Statistics OR Probability 
(iii) Paper III—Topics (two topics mutually agreed upon by the advisor and student). 
 
If a student fails an examination, it may be repeated once, but if the examination is failed a second time, the student must withdraw from the program (see also 1.5.3). In any case, these examinations must be successfully completed within twenty-five months of registration in the doctoral program. If this deadline is not met, the student must withdraw from the program. 

20.2.2 THE MASTER OF SCIENCE DEGREE 

Program Requirements for the M.Sc. (Mathematics) 

The candidate must complete six graduate courses, and a thesis, where the originality of a Master's thesis may lie in the organization, exhibition, and scholarly evaluation, rather than in the result. 

In addition, graduate courses completed at this institution must include two of the following: Real Analysis (62-510), Functional Analysis (62-512), or Partial Differential Equations (62-561). 
 
Program Requirements for the M.Sc. (Statistics) 

The candidate must complete six graduate courses, of which at least four must be numbered with the prefix 65-, and a thesis, where the originality of a Master's thesis may lie in the organization, exhibition, and scholarly evaluation, rather than in the result. 

Master's Committee 

A Master's committee must be appointed within the student's first term of study at the II Master's (Candidate) level. The Master's committee must be approved by the Executive Committee of the College of Graduate Studies and Research. The Master's committee shall include the student's supervisor as chairperson, one other member of the Department, and one faculty member from outside the Department.