Bachelor of Mathematics in Combinatorics and Optimization

Canada

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What will I learn?

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 factorys layout as efficient as possible.In Combinatorics and Optimization at Waterloo, youll 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 is the study of discrete structures and their properties. It includes coding theory, combinatorial design, enumeration theory, graph theory, and polyhedral theory. Many modern scientific advances have employed combinatorial structures to model the physical world, and recent advances in computational technology have made such investigations feasible. In particular, since computers process discrete data, combinatorics has become indispensable to computer science. Optimization, or mathematical programming, is the study of maximizing and minimizing functions subject to specified boundary conditions or constraints. The functions to be optimized arise in engineering, the physical and management sciences, and in various branches of mathematics. With the emergence of computers, optimization experienced a dramatic growth as a mathematical theory, enhancing both combinatorics and classical analysis. In its applications to engineering and management sciences, optimization forms an important part of the discipline of operations research.

Which department am I in?

Faculty of Mathematics

Study options

Full Time (4 years)

Tuition fees
CAD$60,000.00 (36,38,789) per year
Start date

September 2025

Venue

Faculty of Mathematics

University of Waterloo,

WATERLOO,

Ontario (ON),

N2L 3G1, Canada

Entry requirements

For international students

Applicants have to complete ontario high school.

Ontario students: six Grade 12 U and/or M courses including

  • Advanced Functions
  • Calculus and Vectors
  • Any 4U English
  • One other 4U course

Recommended course: Grade 11 U Introduction to Computer Science

Admission averages: Individual selection from the high 80s

English language requirements:

  • Internet-based TOEFL (iBT) - Test Of English as a Foreign Language: 90 overall; 25 writing, 25 speaking.
  • IELTS Academic - International English Language Testing System: 6.5 overall; 6.5 writing, 6.5 speaking, 6.0 reading, 6.0 listening.
  • MELAB - Michigan English Language Assessment Battery: 85 overall; 80 per section; if you're applying to a co-op program: 3 speaking.
  • CAEL - Canadian Academic English Language Assessment: 70 overall 60 per band; 70 writing, 70 speaking.
  • PTE Academic - Pearson Test of English: 63 overall; 65 writing, 65 speaking.
  • EFAS - English for Academic Success: 75% overall in 400 levels; 75% in each of academic, oral, and writing.

*There may be different IELTS requirements depending on your chosen course.

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