Program Overview

Program Overview

The Department of Applied Mathematics at the University of Waterloo offers various programs for undergraduate and graduate students.

Undergraduate Programs

The department provides undergraduate programs in Applied Mathematics, including majors, minors, and specializations.

• Majors, minors and specializations
  • The Mathematical Physics Plan
• Courses
• Scholarships and awards
• Non-majors
• Transfer to Applied Mathematics
• Undergraduate research opportunities
  • Applying for a research award
  • Research topics
• Continuum and Fluid Mechanics students
  • AMATH 361
    • Deformation
    • Material characterization in a laboratory
    • Memory intergrals
  • AMATH 463
    • Geophysical Fluid Dynamics
    • Internal gravity waves
    • Laminar flow
    • Surface gravity waves
    • Vorticity
• Continuum and Fluid Mechanics Media
• First and second year students
  • Approximation
  • Computation
  • Differential equations and non-linearity
  • Wave motion
• Maple Worksheets
• Program Changes for Fall 2025

Future Undergraduates

For prospective students, the department offers information on what Applied Mathematics is, what can be learned in the program, and career opportunities.

• What is Applied Mathematics?
• What you can learn in Applied Mathematics
  • Continuum and Fluid Mechanics
    • Vortices
    • Internal gravity waves
    • Prospective students
  • Control Theory
    • Block diagram for cruise control
    • Control of man-made systems
    • Control in biological systems
  • Differential Equations
    • Ordinary Differential Equations
    • Partial Differential Equations
  • Dynamical Systems
    • Strange attractors
  • Quantum Theory
    • Failure of classical Physics
    • The Quantum world
    • Quantum Theory and technology
  • Relativity and Cosmology
    • Black holes
    • Gravitational lensing
    • Gravitational waves
    • Big-bang origin of the universe
    • Gravity affects clocks
  • Scientific Computing
    • Gas flow in nozzles
  • Waves
• Programs and courses
  • First-year courses
  • Focus your studies
• Careers in Applied Mathematics

Graduate Programs

The department offers graduate programs, including MMath and PhD programs.

• MMath programs
• PhD program
• Master's degree completion procedures
• Courses
  • Graduate courses
  • Courses and research topics
• Funding and awards
• Theses and Papers
  • PhD theses
  • Master's theses
  • Master’s research papers
• Graduate Student Profiles

Course Details

AMATH 442/CM 452: Computational Methods for Partial Differential Equations

• Offered every fall term.
• Brief description: Mathematical models based on Partial Differential Equations (PDEs) are ubiquitous these days, arising in all areas of science and engineering, and also in finance and economics. The goal of this course is threefold.
  • You will receive a solid introduction to the theory of numerical methods for partial differential equations (with derivations of the methods and some proofs).
  • You will learn to implement the computational methods efficiently in Matlab, and
  • You will apply the methods to problems in several fields, for example, fluid mechanics, diffusion processes, wave phenomena, and biomedicine.
• Prerequisites:
  • AMATH 342
• Intended audience: This course will be of interest to anyone who wants to be able to use computers to simulate mathematical models based on partial differential equations.

Research Areas

The department has various research areas, including:

• Climate Change
• Control and Dynamical Systems
• Fluid Mechanics
• Mathematical Medicine and Biology
• Mathematical Physics
• Mathematics of Data Science and Machine Learning
• Scientific Computing

Events

The department hosts various events, including:

• Applied Math distinguished lecture
• Applied Math Colloquium
• Applied Math seminar
• Control Theory seminar
• Mathematical Medicine and Biology seminar
• Numerical Analysis and Scientific Computing seminar
• Fluid Mechanics seminar
• Mathematical Physics seminar
• Physics of information seminar
• Graduate Student Seminar
• PhD Defences
• PhD Comprehensive Seminars
• PhD Comprehensive Exams
• PhD Transfer Exams
• Dean's distinguished women in mathematics, statistics, and computer science lecture series
• Master's Defences
• Applied Math Undergraduate Events

Equity, Diversity, and Inclusion

The department is committed to equity and inclusion principles.

• Equity and Inclusion Principles

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg, and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.