Master of Mathematics (MMath) in Combinatorics and Optimization

The program information below was valid for the spring 2023 term (May 1, 2023 - August 31, 2023). This is the archived version; the most up-to-date program information is available through the current Graduate Studies Academic Calendar.

The Graduate Studies Academic Calendar is updated 3 times per year, at the start of each academic term (January 1, May 1, September 1). Graduate Studies Academic Calendars from previous terms can be found in the archives.

• Admit term(s) 
  • Fall
  • Winter
  • Spring
• Delivery mode 
  • On-campus
• Length of program 
  • Students are required to complete the program in accordance with the University program time limits.
• Program type 
  • Master's
  • Research
• Registration option(s) 
  • Full-time
  • Part-time
• Study option(s) 
  • Thesis
  • Master's Research Paper

• Minimum requirements 
  • A four-year Honours Bachelor degree or its equivalent in mathematics or in a closely related field with a 78% overall average or its equivalent for undergraduate work.
  • Applicants educated outside of Canada, including those from the United States, are recommended to submit scores from the Graduate Record Examinations (GRE) subject test in mathematics. Neither the GRE general test nor the GRE subject test is required.
• Application materials 
  • Supplementary information form
  • Transcript(s)
• References 
  • Number of references:  3
  • Type of references: 

    normally from academic sources.

• English language proficiency (ELP) (if applicable)

Thesis option:

Graduate Academic Integrity Module (Graduate AIM)

Courses 


Combinatorics and Optimization (C&O) core option

• Students must complete 4 courses, including 2 core courses and at least 1 other CO course. The 4th required course must be a graduate course in the Faculty of Mathematics, or a course approved by the CO Graduate Committee.
• Core courses:
  • CO 630 Algebraic Enumeration
  • CO 642 Graph Theory
  • CO 650 Combinatorial Optimization
  • CO 663 Convex Optimization and Analysis
  • CO 681 Quantum Information Processing
  • CO 685 The Mathematics of Public-Key Cryptography
• 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 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 Department Graduate Committee.
• Unsatisfactory academic performance in any one course will result in a review of the student's status by the Department 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.
• Students 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.
   

Mathematics of Operations Research (MOR) core option

• Students must complete 4 courses, including CO 650 Combinatorial Optimization, CO 666 Continuous Optimization, and 2 core courses.
• Core courses:
  • CO 652 Integer Programming
  • CO 663 Convex Optimization and Analysis
  • CO 671 Semidefinite Optimization
  • MSCI 631 Probabilistic Models in Operations Research
  • MSCI 632 Discrete Event Simulation
  • STAT 833 Stochastic Processes
  • STAT 835 Statistical Methods for Process Improvement
• 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 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 Department Graduate Committee.
• Unsatisfactory academic performance in any one course will result in a review of the student's status by the Department 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.
• Students 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.

Link(s) to courses

• Combinatorics and Optimization (CO) courses

Graduate Studies Research Skills Seminar

Master’s Thesis

• 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.

Master's Research Paper option:

Graduate Academic Integrity Module (Graduate AIM)

Courses 


Combinatorics and Optimization (C&O) core option

• Students must complete 7 courses, including 3 core courses and at least 1 other CO course. The remaining 3 courses must be graduate courses in the Faculty of Mathematics, or courses approved by the CO Graduate Committee.
• Core courses:
  • CO 630 Algebraic Enumeration
  • CO 642 Graph Theory
  • CO 650 Combinatorial Optimization
  • CO 663 Convex Optimization and Analysis
  • CO 681 Quantum Information Processing
  • CO 685 The Mathematics of Public-Key Cryptography
• 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 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 Department Graduate Committee.
• Unsatisfactory academic performance in any one course will result in a review of the student's status by the Department 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.
• Students 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.
   

Mathematics of Operations Research (MOR) core option

• Students must complete 7 courses, including CO 650 Combinatorial Optimization, CO 666 Continuous Optimization, 2 core courses and at least 3 other courses.
• Core courses:
  • CO 652 Integer Programming
  • CO 663 Convex Optimization and Analysis
  • CO 671 Semidefinite Optimization
  • MSCI 631 Probabilistic Models in Operations Research
  • MSCI 632 Discrete Event Simulation
  • STAT 833 Stochastic Processes
  • STAT 835 Statistical Methods for Process Improvement
• The remaining 3 courses must be graduate courses in the Faculty of Mathematics, or courses approved by the CO Graduate Committee. It is recommended that they be selected from CO 652, CO 663, CO 664, CO 671, CS 657, and STAT 833.
• 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 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 Department Graduate Committee.
• Unsatisfactory academic performance in any one course will result in a review of the student's status by the Department 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.
• Students 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.

Link(s) to courses

• Combinatorics and Optimization (CO) courses

Graduate Studies Research Skills Seminar

Master’s Research Paper

• 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 return a signed Accreditation form to the Department Graduate Officer, approving the written document and the research paper presentation.