MATHEMATICS AND STATISTICS: PROGRAMS OF STUDY Mathematics (MSc) Statistics (MSc) Statistics (PhD) THE DOCTOR OF PHILOSOPHY DEGREE Admission Requirements For admission requirements and period of study, the general regulations of the Faculty 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. (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 Faculty 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. THE MASTER OF SCIENCE DEGREE Program Requirements for the M.Sc. (Mathematics) The candidate shall successfully complete one of the following courses of study: (a) seven graduate courses and a major paper; (b) six graduate courses and a thesis. The originality of a Master's thesis may lie in the organization, presentation, 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 shall successfully complete one of the following courses of study: (a) seven graduate courses, of which at least five must be numbered with the prefix 65-, and a major paper; (b) six graduate courses, of which at least four must be numbered with the prefix 65-, and a thesis. The originality of a Master's thesis may lie in the organization, presentation, and scholarly evaluation, rather than in the result. In both M.Sc. (Statistics) programs, up to two courses prefixed 65- may be replaced by 62-510 and/or 62-511. Master's Committee If the Thesis option is taken for either the M.Sc. (Mathematics) or the M.Sc. (Statistics), a Masters 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 Faculty 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.