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Combinatorics and Optimization - Doctor of Philosophy (PhD) at University of Waterloo

University of Waterloo, Canada

Programme overview

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. Unlike other universities, where these subjects would lie in mathematics, computer science or operation research departments, 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.

Faculty: Faculty of Mathematics  |  Department: Combinatorics and Optimization  |  Duration: 48 months (full-time)  |  Study mode: full-time  |  Intake: Fall (September - December), Winter (January - April), Spring (May - August); application deadlines: 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)  |  Location: Waterloo, Ontario, Canada

What you will study

Research fields: Algebraic and Enumerative Combinatorics, Continuous Optimization, Cryptography, Discrete Optimization, Graph Theory, Quantum Computing. Study option(s): Thesis.

Career pathways

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.

Official programme page

Application information

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.

Tuition is charged per credit, so the total depends on the courses you register for each year. Current fees are listed in the official fee schedule.

Graduate applications are made online through the Graduate Studies Application and the non-refundable application fee is $150 CAD per program. Deadlines are set by each programme.

Apply through the official page: https://grad.apply.uwaterloo.ca/apply/

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