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The interplay between Mathematics and the Sciences has profoundly influenced modern civilization through centuries of reciprocal inspiration. Within this legacy, 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, developing quantum computers, 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 specialized institutes focusing on mathematical medicine, theoretical neuroscience, quantum research, nanotechnology, water resources, and industrial mathematics. The department provides both Master's and doctoral programs, with the thesis-based Master of Mathematics (MMath) typically requiring two years of study. Graduates often progress to PhD programs or secure prominent roles in industry and government sectors. Our four-year PhD program primarily prepares students for academic research careers, though many graduates also excel in industrial, governmental, or commercial research and development positions.