- What is Combinatorics and Optimization (C&O)?
- What degrees are offered?
- Who will be my advisor?
- How will I be supported?
- What courses will I take?
- How do I apply?
- Where will I live?
Combinatorics is the study of discrete structures, and related algorithms. We might be interested in these things for their own sake, or because of potential applications to real world problems. Optimization deals with determining the values of variables that maximize or minimize an objective.
Research and teaching in our department emphasizes six areas: algebraic combinatorics, combinatorial/discrete optimization, continuous optimization, cryptography, graph theory, and quantum computing. At other universities, these subjects would lie in mathematics, computer science or operation research departments, but at Waterloo we find that they fit together very well, and cross fertilize each other in ways you might not at first expect. Thus students in quantum computing may use tools from continuous optimization, while effective algorithms for combinatorial optimization can depend on sophisticated ideas from graph theory.
More information can be found at our Why C&O page for Undergraduates.
Graduate degrees offered are MMath and PhD. The MMath (Master's) degree involves about a year of graduate courses and either a research report or thesis supervised by a faculty member. The department offers the MMath degree in Combinatorics & Optimization and in three specializations: Cryptography, Operations Research and Quantum Information. The PhD involves about two years of graduate courses followed by research and a dissertation, and typically lasts four years. More details are available on MMath requirements and PhD requirements. Most applicants are admitted to the MMath program and often continue onto the PhD.
Back to top
The department boasts 27 faculty members with international leadership in their subjects. Among the faculty are two Fulkerson Prize winners, two Fellows of the Royal Society of Canada, a Sloan Fellow, a Guggenheim Fellow, a Hall medalist, an Euler medalist, and four Canada Research Chairs. Members of the faculty have collectively authored many well-known books in their subjects. If you are admitted, the department will match you up with an advisor based on the interests expressed in your application, although some students change advisors as their interests change.
All incoming graduate students are offered a full support package that includes a living stipend and tuition. Students are sometimes supported by teaching assistantships (TAs), but it is important to note that TAships at Waterloo entail a five hour/week commitment, in contrast to the typical 15 hour/week commitment at many other North American universities.
Canadian citizens and permanent residents are normally promised a minimum of $27,000 (before tuition fees and taxes) per year. This includes scholarships or awards held by the student, although students holding external awards typically receive considerably more. The promised funding is guaranteed throughout the program, while the student is deemed in good standing by the Department Graduate Committee. Students are expected to earn part of their funding through TAs. This normally amounts to five hours per week of work (that is, one TA unit per term).
Students are encouraged to apply for external scholarships. The two main sources of funding for Canadians are the Natural Sciences and Engineering Research Council of Canada (NSERC) Postgraduate Scholarship Program and the Ontario Graduate Scholarship (OGS) Program. NSERC and OGS award holders will automatically receive an additional $10,000 President's Graduate Scholarship from the University of Waterloo. Applications for NSERC and OGS awards are made in the Fall term. Undergraduate students are advised to apply in the Fall term prior to the completion of their program.
International Students are normally promised $41,000 (before tuition fees and taxes) per year, including awards held by the student. This amount is guaranteed throughout the program, while the student is deemed in good standing by the Department Graduate Committee. International students not receiving full external funding, will automatically receive an International Graduate Student Award (Master's/Doctoral) from the university. Students are expected to earn part of their funding through TAs. This normally amounts to five hours per week of work (that is, one TA unit per term).
The department offers a rich set of courses spanning the discipline. In addition, students often take a few courses outside the department, e.g., a computer science class in cryptology. Please visit our list of graduate courses. Not all courses are offered every term: please refer to the list of term-by-term course offerings.
Go to our General Requirements page for all the information.
You will probably live in Waterloo, which was recently voted one of the seven most intelligent cities in the world. Waterloo and its twin city Kitchener are located in southern Ontario, Canada. This thriving area, notable for its technology industry, has the advantages of city living and yet is conveniently close to natural attractions such as camping, biking or hiking along the Grand River and the world-famous "Journey Behind the Falls" and "Maid of the Mist" in Niagara Falls, Ontario (2 hours away). Waterloo is an easy 90-minute drive or bus-ride to downtown Toronto, Canada's largest city. UWaterloo's housing office has information on locating housing.