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. Plus, you'll have the opportunity to gain paid work experience through the co-op program.

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.

Combinatorics and Optimization admission requirements

Apply to Mathematics and choose Combinatorics and Optimization as your major at the end of first year. Once you've applied, you'll need to complete the Admission Information Form as part of the application process.

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
  • One communication skills course
  • One 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
  • Two 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


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.

briefcaseAvailable as a co-op and regular program

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

Graduation capEarn a Bachelor of Mathematics degree


Co-op = relevant paid work experience

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

#1First faculty of mathematics in North America

math tieOffered by the Faculty of Mathematics

book iconAvailable as a major and minor


Customize your degree in Combinatorics and Optimization

You can add additional areas of expertise to your degree by including one or more of the minors available to all Waterloo students.

What can you do with a degree in Combinatorics and Optimization?

Waterloo Combinatorics and Optimization graduates often pursue careers in software development, data analysis, and more. They often work for entertainment companies, financial institutions, and software companies. 

Recent graduates

  • Junior Quantitative Analyst – Green Brick Labs
  • Risk Analyst – Rogers Bank
  • Actuary – Sun Life Financial 
  • Software Engineer – Amazon Canada
  • Statistical Analyst – Ministry of the Attorney General
  • Platform Developer – IGLOO 
  • Engineer, Software Development - Microsoft Canada

For more information on potential careers, check out our page on careers in business.

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.


Ready to learn more?