PhD in Applied Mathematics - Control and Dynamical Systems in Waterloo Canada | University of Waterloo

The interplay between Mathematics and the Sciences has profoundly influenced modern civilization through centuries of reciprocal inspiration. Within this framework, the Department of Applied Mathematics provides graduate students with specialized study options in Control Theory and Dynamical Systems, Fluid Mechanics, Mathematical Medicine and Biology, Mathematical Physics, and Scientific Computation. Student research initiatives employ advanced mathematical applications across diverse scientific disciplines, spanning from optimizing cancer treatments and manipulating shape memory alloys to processing fractal images, advancing quantum computing, and investigating climate patterns, cosmic inflation, and nanoscale technologies. As part of the University of Waterloo's Faculty of Mathematics - ranked 20th globally in the 2015 QS Mathematics Rankings - our department maintains strong collaborations with Science and Engineering faculties, along with numerous research centers including those focused on Mathematical Medicine, Theoretical Neuroscience, Quantum Computing, Theoretical Physics, Nanotechnology, Water Research, and Industrial Mathematics. We provide both Master's and doctoral programs: our thesis-based Master of Mathematics (MMath) typically requires two years, with graduates often continuing to PhD studies or securing prominent roles in industry and government. The PhD program generally spans four years, preparing most graduates for academic research careers, while others enter industrial, governmental, or commercial R&D sectors.

This discipline focuses fundamentally on differential equations, which form the mathematical foundation for modeling phenomena across physical sciences, engineering, life sciences, and economics. The scope encompasses classical ordinary and partial differential equations, as well as contemporary formulations like delay and stochastic differential equations. Our program emphasizes two key aspects: control theory and dynamical systems.
Control theory involves directing physical or biological systems toward specific objectives, primarily through feedback mechanisms, with system behaviors described by various differential equations. Dynamical systems theory examines the qualitative properties of solutions to both differential and difference equations - the latter constituting discrete dynamical systems with applications in fields like biology and signal analysis. An emerging concept is hybrid dynamical systems, which integrate discrete events with continuous processes, offering powerful frameworks for modeling complex reactive or intelligent systems where physical phenomena interact with automated environments.