Pure Mathematics

Pure Math Alex

“The satisfaction from understanding an idea at a deeper level and tying together unrelated branches of mathematics or physics for the first time is the most rewarding part of learning and understanding mathematics. What I really enjoy is developing a deep understanding of a mathematical concept from many different perspectives.”

What is Pure Mathematics?

Go beyond the basics and find the answers to the “how” and “why” behind the mathematics. If first-year calculus teaches you how to drive the car, Pure Mathematics teaches you how to build one. Mathematicians know that there could be no general relativity without differential geometry, and no computer security without advanced number theory.

Pure Mathematics at Waterloo is a small, cohesive, and challenging program that will open countless doors for you. You can use this program as a springboard into careers in information technology, finance, business, science, education, insurance, or go on to graduate studies at some of the world’s most prestigious institutions.

  • Available as a co-op or regular program
  • There are 40 courses for this degree
  • Graduate with a Bachelor of Mathematics, major in Pure Mathematics

First-year courses

  • MATH 135/145 - Classical Algebra
  • MATH 137/147 - Calculus 1
  • CS 115/135/145 - Computer Science
  • A communications course
  • One non-math elective

See full courses in our undergraduate calendar.

Upper-year courses

  • MATH 239 - Introduction to Combinatorics
  • PMATH 347 - Groups and Rings
  • PMATH 352 - Complex Analysis
  • PMATH 441 - Algebraic Number Theory
  • PMATH 465 - Smooth Manifolds

Sample courses

  • PMATH 320 - Euclidean Geometry
  • PMATH 351 - Real Analysis
  • PMATH 343 - Introduction to the mathematics of quantum information
  • PMATH 465 - Smooth Manifolds


If you’re curious about the research that professors conduct, research opportunities are available for strong undergraduate students. You could be paid for a part-time opportunity, or a full-time position may substitute as a co-op term. It’s not uncommon for students to publish their work. You can find details about the application, deadlines, and examples of research conducted by previous undergraduates in the department and school websites. Successful applicants are then matched with a professor.


Pure Mathematics/Teaching (Co-op only) — Combine a major in Pure Mathematics with Mathematics/Teaching if you want to teach at the intermediate (grades 7 and 8) or senior (grades 9 to 12) level. You complete at least two of six work terms in the classroom, earning more experience than concurrent education programs provide. Math/Teaching guides you to complete a second teachable in subjects like chemistry, physics, French, or music. In fourth year, you apply to BEd programs to earn your professional teacher’s certificate.

Sample co-op jobs

  • Business Analyst Assistant, Department of National Defence
  • Data Quality Engineering, Imagine Communications Corp
  • Instructional Support Assistant, Korea Advanced Institute of Science and Technology
  • Policy and Research Assistant, Natural Resources Canada
  • QA Automation Developer, VersaCold Logistics Services
  • Research Assistant, Agriculture and Agri-Food Canada
  • Security & Distributed System Engineer, Centennial College of Applied Arts & Technology

Sample careers

  • Chief Software Modeller, RPM Technologies
  • Technology Development Fellow, Harvard School of Engineering and Applied Sciences
  • Research Assistant, Wyss Institute for Biologically Inspired Engineering
  • Field Applications Engineer, Nanometrics - Seismic Monitoring Solutions
  • Technical Program Manager, Google
  • Data Analyst, Real Matters
  • Business Analyst, Bank of America Canada
  • Manager, Liquidity and Interest Rate Risk, Scotiabank
  • Compensation Manager, BlackBerry

Student story

Meet Alex

Not only is Alex pursuing a double major in Pure Math and Combinatorics and Optimization, he’s also putting his love of math into action. He spent a hands-on summer as a National Sciences and Engineering Research Council (NSERC) undergraduate award winner, traveled to Budapest for a term abroad, and is an active participant in on-campus events like datathons and Hack the North.

Meet Josué

Josué is double majoring in Pure Math and Combinatorics and Optimization. He's been a member of the Math Ambassador Team for a number of years and is heavily involved at Waterloo working as a Faculty Orientation Coordinator (FOC) for Math Orientation and a MathSoc Councillor and Director. On co-op, he's worked as an Instructional Support Assistant and Undergraduate Research Assistant.

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How to apply

Apply to Mathematics for admissions consideration. If admitted, speak with an academic advisor after first year to declare Pure Mathematics as a major.

Find out more information on the steps to apply.