New Direction in Mathematics for Materials Science

This book is the 1st volume of the "SpringerBriefs in the Mathematics of Materials" and shows the overall introduction to the application of mathematics to materials science. In the anterior part of this book, the history of "materials science" is described as well as the interaction between mathematics and materials in history. The emergence of "materials science" was itself a result of interdisciplinary movement in 1950s and 60s. Materials science was formed by the integration of metallurgy, polymer science, solid state physics, and so on. We think that such historical background helps the readers to understand the importance of interdisciplinary interaction such as mathematics-materials science collaboration. In the main part, we describe some mathematical ideas and methods which can be applied to materials problems and introduce some examples of the specific studies, for example, computational homology applied to structure analysis of glassy materials, mathematical treatment of the dynamics of colloidal fluids, stochastic models for formation process of materials, compressed sensing for materials imaging, new geometric measures for finite carbon nanotubes, mathematical technique predicting molecular magnet, quantization of interface currents. The details of these works will be shown in the subsequent volumes of this "SpringerBriefs in the Mathematics of Materials" series by the individual authors. In the posterior part, we would like to present several activities to promote mathematics-science (not necessarily materials science but other fields) collaboration in Japan.