In the past decades, new problems, areas of application, and techiques appearing in modern dynamical processes in physics, chemistry, engineering and economics have come to light. In seeking better and better results from simulations, the computational mathematician or scientist needs not only capacity to carry out simulations, but also innovative ideas and foundational analysis for algorithms. Computational mathematics, science and engineering are rapidly growing multidisciplinary areas with connections to business, economics, engineering, mathematics and computer science through academia as well as industry. There is furthermore a constant need in these fields for the quick and efficient advancement of information exchange with an expert audience. Conferences are often organized within specialty disciplines, compartmentalizing information exchange by field of specialty. In the midst of these successful conferences there remains a niche for unifying, cross-cutting, interdisciplinary gatherings, where specialists can have exposure to diverse fields, a chance to meet new people in or near their individual areas of research, and participate in special sessions different from their own field. The proposed meeting, Computational and Mathematical Methods in Science and Engineering (CMMSE 2015), has this purpose, to serve as a catalyst for computational mathematics among cutting edge applications in science and engineering.