
Combinatorics and Optimization - Doctor of Philosophy (PhD)
Course at a Glance
- PhDDegree level
- 4 yearsDuration
- Main Campus, Waterloo, CanadaLocation
- Faculty of MathematicsField of study
- EnglishLanguage of instruction
- Main Campus, WaterlooCampus
- Doctor of Philosophy (PhD)Awards
- $22,188Fees
- AvailableScholarship
About this programme
Whether your interests lie in the study of discrete structures and related algorithms through combinatorics, or their applications to real world problems, the PhD in Combinatorics and Optimization program seamlessly integrates both. Research in this department emphasizes six fields: algebraic combinatorics, combinatorial/discrete optimization, continuous optimization, cryptography, graph theory, and quantum computing.
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Here at Waterloo, we understand the interconnectedness of these fields – you’ll have the chance to use tools and ideas from other areas to further your own work. Get solid academic experience with a variety of courses that span the discipline and conduct independent research that generates new knowledge. You’ll be prepared to pursue a career in academia or across industries ranging from finance and banking to national defence and government services, to insurance, software and hardware.
Is this course right for you?
Our counsellors check your profile against this programme's entry criteria and tell you where you stand — before you pay anything.
What we look at
- Your subject background and grades
- Your English score, or how to get one
- Budget, including living costs
University & programme
- Listed from the catalogueNot yet staff-verified — ask us to confirm the details.
- English requirementIELTS Overall 7.0
- Study modeFull-time, Part-time
Admissions checklist
Entry requirements
• A master's degree in combinatorics and optimization, or in a closely related field, with a minimum 89% average in master's level coursework. || • Completion of a master's thesis. || • It is essential that the application for admission into the PhD program contains evidence of research ability or potential. || • Students in the PhD program are regarded as being on probation during their first year in the department, and their performance during this first year determines whether they are allowed to continue in the program. In particular, failure in any one course, or an unsatisfactory performance in the comprehensive examination, automatically results in a review of the student's progress by the Department Graduate Committee. PhD students' progress will be reviewed at least once per year. || • A student who is enrolled in the Master of Mathematics (MMath) program in the Department of Combinatorics and Optimization and wishes to continue in the PhD program has to apply for admission into the program. In exceptional cases, a graduate student enrolled in a MMath (Thesis) program in the Department of Combinatorics and Optimization may, through the Graduate Officer and with the consent of the Supervisor, petition the Graduate Committee to be transferred into a PhD program. The guidelines for such a transfer are as follows: || • The student has been enrolled in the MMath (Thesis) program for at least two terms. || • The student has made considerable progress in the research project (of the type that would warrant the MMath degree) and is committed to carrying the project to completion in a PhD program. || • The student gives a seminar presentation of the work carried out so far, and answers related questions to the satisfaction of an examining committee consisting of the supervisor and two other faculty members. || • Students applying to the PhD program who hold a master's degree from another university may, in some cases, be admitted initially into the MMath program. In such cases the Graduate Committee will decide, within three terms, whether to transfer the student into the PhD program. || • 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. || • Statement of interest || • Uploaded as a supporting document in the online application. Review the writing your personal statement resources for helpful tips and tricks on completion. || • Provide a short statement (max. 500 words) outlining your interest in the C&O grad program. The statement may address the following: || • Describe your reasons for pursuing this grad program, and previous experiences that have prepared you for graduate study in mathematics; the areas of research that interest you the most. The department has active research programs in the areas of Algebraic Combinatorics, Continuous Optimization, Cryptography, Discrete Optimization, Graph Theory, and Quantum Computing. || If you have an interest in multiple areas, please describe them all as this may help in matching you with a potential supervisor; your long-term career goals, and the relevance of the C&O grad program to those goals. || • Program-specific questions (PSQ) || • These are questions specific to the program you’re applying to. They can be viewed once you’ve started an application and are completed through a form in t · English: IELTS 7.0 (no band below 6.5) · English test waiver: Exempt from submitting an ELP test score if any one applies: three or more years of post-secondary education at a Canadian institution or university; a completed graduate degree at a Canadian university; three or more years of post-secondary education or a completed graduate degree in an exempt country (list includes Australia, Ireland, New Zealand, Nigeria, Singapore, South Africa, UK, USA and others); at least three years' employment in a position where English was the language of business in a listed country; or three or more years of post-secondary education / a graduate degree at a university where English is the only language of instruction per the IAU WHED (this WHED exemption expires two years after graduation). Letters from a university stating the medium of instruction is English do NOT satisfy the requirement. Source: https://uwaterloo.ca/future-graduate-students/admissions/admission-and-english-language-proficiency-requirements · GRE/GMAT: 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 fee: CAD 150.00 per program, non-refundable (Graduate Studies Applicant Portal)
The usual set for this level. Your counsellor confirms the exact list for this university.
- Academic transcripts
- English test score (IELTS/TOEFL)
- Passport copy
- Statement of purpose (optional)
- Recommendation letters (optional)
Cost & scholarships
- Tuition$22,188 CAD / year≈ $16,315 / year
- Application feeNo application fee for this programme
- Living costsVary by city — see the destination guide.
- ScholarshipsWaterloo publishes guaranteed minimum funding for research-based programs: full-time research-based master's students (domestic and international) often receive minimum funding of CAD 12,000 for one year; full-time doctoral students receive minimum funding of CAD 29,145 per year (effective 1 May 2026) for up to four years. Minimum funding can come from scholarships, awards and graduate teaching/research assistantships. SourceView scholarship page
Application timeline
Typical timings. Deadlines differ per university and intake.
- 1Prepare documents1–2 weeks
- 2Submit application1–3 weeks
- 3Receive offer letter2–6 weeks
- 4Apply for visa4–8 weeks
Application deadline: • January 15 (for admission in September) || • July 1 (for admission in January of the following year) || • October 1 (for admission in May of the following year)
Visa & support journey
- Offer letterFrom the university
- Visa guidanceExpert support
- Pre-departureAccommodation & travel
- Ongoing supportEven after you arrive
Student stories
Real students. Real results.
- Average rating
- 4.9
- Google reviews
- 360+
- Rated five stars
- 95%
Average rating
Google reviews
Rated five stars
“I would like to express my gratitude for the excellent assistance provided during my student visa process. The team was responsive, knowledgeable, and supportive at every stage, from document preparation to submission guidance. Their clear communication and professional approach made the process much easier and more efficient.”
1 / 8
Nihad K, 5 out of 5 stars
Every review below is a real Google review — see all of them
Frequently asked questions
How much does Combinatorics and Optimization - Doctor of Philosophy (PhD) cost?
CAD 22,188 / year.
What English score does it need?
IELTS 7.0 overall is the score listed for this programme.
How long is it?
4 years, as listed by the university.
What are the entry requirements?
• A master's degree in combinatorics and optimization, or in a closely related field, with a minimum 89% average in master's level coursework. || • Completion of a master's thesis. || • It is essential that the application for admission into the PhD program contains evidence of research ability or potential. || • Students in the PhD program are regarded as being on probation during their first year in the department, and their performance during this first year determines whether they are allowed to continue in the program. In particular, failure in any one course, or an unsatisfactory performance in the comprehensive examination, automatically results in a review of the student's progress by the Department Graduate Committee. PhD students' progress will be reviewed at least once per year. || • A student who is enrolled in the Master of Mathematics (MMath) program in the Department of Combinatorics and Optimization and wishes to continue in the PhD program has to apply for admission into the program. In exceptional cases, a graduate student enrolled in a MMath (Thesis) program in the Department of Combinatorics and Optimization may, through the Graduate Officer and with the consent of the Supervisor, petition the Graduate Committee to be transferred into a PhD program. The guidelines for such a transfer are as follows: || • The student has been enrolled in the MMath (Thesis) program for at least two terms. || • The student has made considerable progress in the research project (of the type that would warrant the MMath degree) and is committed to carrying the project to completion in a PhD program. || • The student gives a seminar presentation of the work carried out so far, and answers related questions to the satisfaction of an examining committee consisting of the supervisor and two other faculty members. || • Students applying to the PhD program who hold a master's degree from another university may, in some cases, be admitted initially into the MMath program. In such cases the Graduate Committee will decide, within three terms, whether to transfer the student into the PhD program. || • 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. || • Statement of interest || • Uploaded as a supporting document in the online application. Review the writing your personal statement resources for helpful tips and tricks on completion. || • Provide a short statement (max. 500 words) outlining your interest in the C&O grad program. The statement may address the following: || • Describe your reasons for pursuing this grad program, and previous experiences that have prepared you for graduate study in mathematics; the areas of research that interest you the most. The department has active research programs in the areas of Algebraic Combinatorics, Continuous Optimization, Cryptography, Discrete Optimization, Graph Theory, and Quantum Computing. || If you have an interest in multiple areas, please describe them all as this may help in matching you with a potential supervisor; your long-term career goals, and the relevance of the C&O grad program to those goals. || • Program-specific questions (PSQ) || • These are questions specific to the program you’re applying to. They can be viewed once you’ve started an application and are completed through a form in t · English: IELTS 7.0 (no band below 6.5) · English test waiver: Exempt from submitting an ELP test score if any one applies: three or more years of post-secondary education at a Canadian institution or university; a completed graduate degree at a Canadian university; three or more years of post-secondary education or a completed graduate degree in an exempt country (list includes Australia, Ireland, New Zealand, Nigeria, Singapore, South Africa, UK, USA and others); at least three years' employment in a position where English was the language of business in a listed country; or three or more years of post-secondary education / a graduate degree at a university where English is the only language of instruction per the IAU WHED (this WHED exemption expires two years after graduation). Letters from a university stating the medium of instruction is English do NOT satisfy the requirement. Source: https://uwaterloo.ca/future-graduate-students/admissions/admission-and-english-language-proficiency-requirements · GRE/GMAT: 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 fee: CAD 150.00 per program, non-refundable (Graduate Studies Applicant Portal)
Is there a scholarship?
Waterloo publishes guaranteed minimum funding for research-based programs: full-time research-based master's students (domestic and international) often receive minimum funding of CAD 12,000 for one year; full-time doctoral students receive minimum funding of CAD 29,145 per year (effective 1 May 2026) for up to four years. Minimum funding can come from scholarships, awards and graduate teaching/research assistantships. Source View scholarship page
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