Combinatorics & Optimization

Admission Requirements

The minimum requirements for admission to the MMath program normally include:

• a four-year honour's bachelor's degree or its equivalent in mathematics or in a closely related field; an overall B+ average or its equivalent for undergraduate work;
• three letters of reference, normally from academic sources; proof of competency in English (if applicable). A score of at least 580 (paper-based total) or 237 (computer-based total) is required in the Test of English as a Foreign Language (TOEFL). (See Academic Regulations - English Language Proficiency Certification for other acceptable tests of English.)
• Applicants from foreign countries must normally take the Graduate Record Examinations (GRE) General Test and Subject Tests.

A graduate student without the required prerequisite knowledge may find it necessary to complete some courses at the 3rd or 4th year undergraduate level before proceeding to the core courses. The core courses may be replaced with other courses provided the Department Graduate Committee agrees that they are equivalent. The choice of the precise set of core courses is left to the student and the student's supervisor.

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Degree Requirements

The regular MMath degree can be taken in either of two forms - as a course work degree, or a thesis degree. Each requires at least two terms of full-time registration. (See Academic Regulations - Residence Requirements.) Students should normally complete the MMath degree in one year (three semesters).

Course Requirements

All MMath students must satisfactorily complete one of four core programs, outlined below. If students have credit for a course deemed equivalent to a particular required course by the Department Graduate Committee, then that part of the core requirement may be waived. An overall average of at least a B (75%) must be maintained.

A student may obtain credit for one graduate term course by completing two undergraduate term courses; however, any student wishing to exercise this option must seek the approval of the Departmental Graduate Committee.

Unsatisfactory academic performance in any one course will result in a review of the candidate's status by the Departmental Graduate Committee. If a student with a failed course is permitted to continue, additional work may be required to clear the failure in that course, or by replacement of the failed course; alternatively, the student may be required to repeat part or all of the program.

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Combinatorics & Optimization (C&O) Core

Course Work Degree:
Course Requirement: eight courses, including

• 2 of CO 630, CO 634, CO 642, CO 644
• 1 of CO 650, CO 652
• 1 of CO 663, CO 666

At least 5 of the 8 courses taken for credit toward the degree must be C&O courses.

Thesis Degree:
Course Requirement: four courses, including

• 1 of CO 630, CO 642
• 1 of CO 650, CO 666
• 1 additional course from CO 630, CO 634, CO 642, CO 644, CO 650, CO 652, CO 663, CO 666, CO 671, CO 681, CO 685

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Cryptography Core

Course Work Degree:
Course Requirement: eight courses, including

• CO 685
• a second C&O graduate course in cryptography
• 1 of CO 630, CO 634, CO 642, CO 644
• 1 of CO 650, CO 652, CO 663, CO 666
• 1 additional course from CO 630, CO 634, CO 642, CO 644, CO 650, CO 652, CO 663, CO 666, CO 671, CO 681, CS 666, CS 687, CS 764, PMATH 640, PMATH 641

Thesis Degree:
Course Requirement:

• CO 685
• a second C&O graduate course in cryptography
• 1 of CO 630, CO 642, CO 650, CO 652, CO 666
• 1 additional course from CO 630, CO 634, CO 642, CO 644, CO 650, CO 652, CO 663, CO 666, CO 671, CO 681, CS 666, CS 687, CS 764, PMATH 640, PMATH 641

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Mathematics of Operations Research (MOR) Core

Course Work Degree:
Course Requirement: eight courses, including

• CO 650, CO 666
• 2 of CO 652, CO 663, CO 671, CS 672, MSCI 631, MSCI 632, STAT 833, STAT 835

It is recommended that the four additional courses needed to complete the course requirement be selected from CO 652, CO 663, CO 664, CO 671, CS 657, STAT 833 and STAT 909. Students may choose some of the four non-core courses from other departments. For example, many students choose courses offered by the Pure Mathematics Department.

Thesis Degree:
Course Requirement:

• CO 650, CO 666
• 2 of CO 652, CO 663, CO 671, CS 672, MSCI 631, MSCI 632, STAT 833, STAT 835

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Quantum Information Core

Course Work Degree:
Course Requirement: eight courses, including

• CO 681
• a second C&O graduate course in quantum computing
• 1 of CO 630, CO 634, CO 642, CO 644
• 1 of CO 650, CO 652, CO 663, CO 666
• 1 additional course from CO 630, CO 634, CO 642, CO 644, CO 650, CO 652, CO 663, CO 666, CO 671, CO 685, AM 673, CS 662, CS 666, CS 764, PHYS 701

Thesis Degree:
Course Requirement:

• CO 681
• a second C&O graduate course in quantum computing
• 1 of CO 630, CO 642, CO 650, CO 666, CO 671
• 1 additional course from CO 630, CO 634, CO 642, CO 644, CO 650, CO 652, CO 663, CO 666, CO 671, CO 685, AM 673, CS 662, CS 666, CS 764, PHYS 701

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Additional Requirements

Research Skills Seminar: Required for all graduate students in C&O.

Course Work Option - Research Paper Requirement

This requirement consists of two parts: the writing of a research paper, and the presentation of it in an appropriate seminar or class. The topic is arranged with the student's supervisor. The research paper requirement is met, and credit assigned, when the supervisor and reader returns a signed Accreditation form to the Department Graduate Officer, approving the written document and the research paper presentation.

Thesis Option

The thesis requirement consists of the writing of an expository or research thesis. The thesis topic is to be arranged with a faculty member who serves as the Thesis Supervisor. This requirement is met, and credit assigned, when the Thesis Supervisor and two additional readers approve the thesis. In addition to distributing a copy of the MMath thesis to the supervisor and readers, the thesis should also be deposited in the Mathematics Graduate Office for display for a period of three weeks.