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Combinatorics and Optimization

Master two of math’s most powerful techniques.

Hone the skills you need to solve problems in computer science, business, communications, and more.

Combinatorics looks at permutations and combinations. Optimization explores ways to make any operation work more efficiently within given constraints. Together, they provide powerful methods for modelling and solving large management problems, from optimizing flight schedules to making a factory’s layout as efficient as possible.

In Combinatorics and Optimization at Waterloo, you’ll learn concepts such as enumeration, combinatorical designs, graph theory, linear programming, nonlinear optimization, operations research, and combinatorical optimization, and how to use them in real-world applications.

When you graduate, you can put your skills to work in areas as diverse as cryptography, electronic security, software development, social media, and risk analysis.

Add research to your résumé

As an undergraduate research assistant, you could spend a term working on a research problem with one of our award-winning professors.

Have fun with other mathies

Take a break from your studies. The student-run Pure Math, Applied Math, Combinatorics and Optimization Club offers talks, food, board games, and more.


Student writing equations on whiteboard

The Department of Combinatorics and Optimization at Waterloo was the first of its kind in the world and houses the largest concentration of faculty and researchers in the field.

About the Combinatorics and Optimization program

briefcase Available as a co-op and regular program

Arrow pointing up and clickingApply to Mathematics and choose Combinatorics and Optimization as your major

Graduation cap Earn a Bachelor of Mathematics degree


    #11st Faculty of Mathematics in North America

    math tieOffered by the Faculty of Mathematics

    book iconAvailable as a major and minor


    Combinatorics and Optimization admission requirements

    We strongly encourage you to participate in the Canadian Senior Mathematics Contest and/or the Euclid Mathematics Contest to enhance your admissions status.  

    To be considered for entrance scholarships in the Faculty of Mathematics, you must write one or both of the contests. If you complete both contests, we'll use the results of the contest in which you performed best.

    First-year Combinatorics and Optimization courses

    You may select advanced-stream courses for algebra, calculus, and computer science if you meet the requirements. 

    September to December

    MATH 135 - Algebra 
    MATH 137 - Calculus 1
    Choose one of:
     • CS 115 - Introduction to Computer Science
     • CS 135 - Designing Functional Programs
    1 communication skills course
    1 elective

    January to April

    MATH 136 - Linear Algebra 1 
    MATH 138 - Calculus 2 
    Choose one of:
     • CS 116 - Introduction to Computer Science 2
     • CS 136 - Elementary Algorithm Design and Data Abstraction
    2 electives


    After first year

    You’ll take upper-year courses in combinatorics and optimization and other areas in the Faculty of Mathematics. With your remaining classes, you can choose electives from many of the 100 subject areas at Waterloo.

    View a list of all the courses required for your degree.

    Sample upper-year courses

    CO 331 - Coding Theory
    CO 380 - Mathematical Discovery and Invention
    CO 450 - Combinatorial Optimization
    CO 471 - Semidefinite Optimization


    Customize your degree in Combinatorics and Optimization

    You can add additional areas of interest and expertise by including a minor (or minors) as part of your degree.

    Gain relevant work experience through co-op

    By alternating school terms and paid co-op work terms throughout your degree, you can explore new career areas and types of employers as your career interests evolve.

    Sample co-op job titles

    • Business technology analyst
    • Data analyst
    • Full stack developer
    • Quantitative trading associate
    • Software developer
    • Software QA specialist
    • Web interface developer

    Sample co-op employers

    • Facebook
    • Deloitte
    • Sybase Canada
    • Ontario Ministry of Government and Community Services
    • Department of National Defence
    • OpenText Corporation
    • Cisco Systems Canada

    Careers in Combinatorics and Optimization

    • Catastrophe Analyst, Validus Research 
    • Analytics Team Member, Maple Leaf Sports & Entertainment
    • Manager, Precision Health Data Institute, Everyday Health
    • Project Manager, Allegro Mobile Solutions
    • Risk Modelling Manager, TD Canada Trust
    • Software Developer, BlackBerry 
    • System Analyst, Rogers Communications
    • Treasurer, Shinhan Bank Canada
    • Application Developer, Oracle Corporation Canada 

    Learn more about Combinatorics and Optimization