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Combinatorics and Optimization - MMath

Discrete or combinatorial optimization embodies a vast and significant area of combinatorics that interfaces many related subjects. Included among these are linear programming, operations research, theory of algorithms and computational complexity.

Much of combinatorial optimization is motivated by very simple and natural problems such as routing problems in networks, packing and covering problems in graph theory, scheduling problems, and sorting problems. But the methodology of the subject encompasses a variety of techniques ranging from elementary tree-growing procedures to constructions of Hilbert bases of integer lattices.

The growth of this area has been linked with the development of linear programming and of graph theory over the last forty years. It also has close connections with the theoretical computer science, in particular, the analysis of algorithms. Generally the problems are to find efficient methods of constructing good solutions and to find methods of measuring the solution quality. That is, we wish to be able to produce bounds on the optimum solution which enable us to assert that the error of the solution in hand is no worse than, say, 2%.

The C&O department has played a major role in the development of this area. During the seventies and eighties department members have made contributions to matching theory, polyhedral theory, combinatorial decomposition theory, minimax theorems for directed graphs, and oriented matroids. Currently, active work is being done on polyhedral combinatorics, approximation algorithms for NP-hard problems, semi-definite relaxations, extensions of matching and network flow theory, matroids and generalizations as well as on algorithmic game theory.

Intakes

Application Processing Time in Days: 30

Minimum English Language Requirements

English Level Description	IELTS (1.0 -9.0)	TOEFL IBT (0-120)	TOEFL CBT (0-300)	PTE (10-90)
Expert	9	120	297-300	86-90
Very Good	8.5	115-119	280-293	83-86
Very Good	8	110-114	270-280	79-83
Good	7.5	102-109	253-267	73-79
Good	7	94-101	240-253	65-73
Competent	6.5	79-93	213-233	58-65
Competent	6	60-78	170-210	50-58
Modest	5.5	46-59	133-210	43-50
Modest	5	35-45	107-133	36-43
Limited	4	32-34	97-103	30-36
Extremely Limited	< 4	< 31	< 93	< 30

Job Opportunity Potential

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Learn about industry trends, what careers in these industries might look like in the future, and university programs that will help you get there.

Careers in business
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Careers in math, coding, and data
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PSW Opportunity

Eligibility for Post-Graduation Work Permit (PGWP):
Graduated from a designated learning institution (DLI) in Canada.
Desire to stay in Canada temporarily for work.

Important Note:
Graduating from a DLI doesn't automatically qualify you for a PGWP.

Validity of PGWP:
Depends on the length of the study program or the expiry date of your passport, whichever comes first.

Duration of PGWP Based on Study Program Length:
Less than 8 months (or 900 hours for Quebec credentials): Not eligible for PGWP.
At least 8 months (or 900 hours for Quebec credentials), but less than 2 years: PGWP may be granted for the same length as the study program (e.g., a 9-month program results in a 9-month PGWP).
2 years or more: PGWP may be valid for 3 years.

Completion of Multiple Programs:
PGWP may combine the lengths of each program if:
Each program is PGWP eligible.
Each program is at least 8 months (or 900 hours for Quebec credentials) in length.

Important Restriction:
You cannot obtain a PGWP if you already had one after completing an earlier program of study.

Admission Requirement / Eligibility Criteria

Master's program and Graduate Diploma admissions
Applying with domestic credentials:

Have at least a 75% overall standing in the last two years of a four-year Honours Bachelor's degree or equivalent
Applying with international credentials:

Have at least a 75% overall standing in a four-year Honours Bachelor's degree or equivalent
Application materials
Resume

Supplementary information form (SIF)
The SIF contains questions specific to your program, typically about why you want to enrol and your experience in that field. Review the application documents web page for more information about this requirement
If a statement or letter is required by your program, review the writing your personal statement resources for helpful tips and tricks on completion
Transcript(s)

References
Three references are required; academic or professional sources
Proof of English language proficiency, if applicable
TOEFL 90 (writing 25, speaking 25), IELTS 7.0 (writing 6.5, speaking 6.5)

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University of Waterloo

Waterloo, Ontario, Canada