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Contemporary civilization has been profoundly influenced by centuries of reciprocal stimulation and advancement between Mathematics and the Sciences. Following this legacy, the Department of Applied Mathematics provides graduate students with specialized programs in Control Theory and Dynamical Systems, Fluid Mechanics, Mathematical Medicine and Biology, Mathematical Physics, and Scientific Computation. Student research initiatives employ state-of-the-art mathematical applications across diverse scientific disciplines, both fundamental and applied. These encompass areas such as optimizing cancer treatments, manipulating shape memory alloys, processing fractal images, advancing quantum computing, and investigating climate patterns, cosmic inflation theories, and nanoscale technologies. As part of the University of Waterloo's Faculty of Mathematics - ranked 20th globally in the 2015 QS University Rankings for mathematics - our department maintains strong collaborations with Science and Engineering faculties, along with premier research centers including those focused on Mathematical Medicine, Theoretical Neuroscience, Quantum Computing, Theoretical Physics, Nanotechnology, Water Research, and Industrial Mathematics. The department provides both Master's and doctoral programs. Our research-intensive 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 assume influential positions in industrial, governmental, or commercial research and development sectors.