Applied and computational mathematics has a long and storied history in the Department of Chemical Engineering and Materials Science at the University of Minnesota. The University was among the first to establish its own supercomputing facility, the Minnesota Supercomputing Institute, and the Institute for Mathematics and its Applications has historically promoted broad activity in applied mathematics. On the Departmental level, former Professor and Department Head Neal Amundson is lauded as one of the giants of mathematical analysis applied to problems in chemical engineering and established a legacy for the important role that mathematics would play in the Department’s approach to research in materials science and engineering. Indeed, applied and computational mathematics provides a paradigm for understanding complicated physical and engineering systems while simultaneously enriching experimental research. CEMS faculty are developing and applying ever more powerful tools applied toward mathematical analysis and computational simulation in fields ranging from solid-state materials to chemical reactions to biological systems to fluid dynamics. Ongoing efforts in applied and computational mathematics range from analytical and numerical models to describe physical phenomena, from atomistic to continuum, to systems-level analysis, control, and optimization.