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Our institution provides both Master's and doctoral programs. The thesis-focused Master's of Mathematics (MMath) typically spans two years. Graduates often continue to PhD studies or secure fulfilling roles in industry or government sectors. The PhD program usually requires four years, with most alumni securing academic research positions, while others enter industrial, governmental, or commercial R&D roles. Following this tradition, the Department of Applied Mathematics enables graduate studies in Control Theory and Dynamical Systems, Fluid Mechanics, Mathematical Medicine and Biology, Mathematical Physics, and Scientific Computation. Student research explores pioneering applications of mathematical theory across diverse scientific fields, such as optimizing cancer treatments, manipulating shape memory alloys, fractal-based image processing, quantum computing, and investigating climate patterns, cosmic inflation, and nanotechnology. As part of the University of Waterloo's Faculty of Mathematics—ranked 20th globally in the 2015 QS Mathematics Rankings—our department fosters strong collaborations with Science and Engineering faculties, the Centre for Mathematical Medicine, the Centre for Theoretical Neuroscience, the Institute for Quantum Computing, the Perimeter Institute for Theoretical Physics, the Waterloo Institute for Nanotechnology, the Water Institute, and the Centre for Computational Mathematics in Industry and Commerce.