A New Direction in Mathematics for Materials Science

  • Susumu Ikeda
  • Motoko Kotani

Part of the SpringerBriefs in the Mathematics of Materials book series (BRIEFSMAMA, volume 1)

Table of contents

  1. Front Matter
    Pages i-x
  2. Susumu Ikeda, Motoko Kotani
    Pages 1-9
  3. Susumu Ikeda, Motoko Kotani
    Pages 11-50
  4. Susumu Ikeda, Motoko Kotani
    Pages 77-78
  5. Back Matter
    Pages 79-86

About this book


This book is the first volume of the SpringerBriefs in the Mathematics of Materials and provides a comprehensive guide to the interaction of mathematics with materials science. The anterior part of the book describes a selected history of materials science as well as the interaction between mathematics and materials in history. The emergence of materials science was itself a result of an interdisciplinary movement in the 1950s and 1960s. Materials science was formed by the integration of metallurgy, polymer science, ceramics, solid state physics, and related disciplines. We believe that such historical background helps readers to understand the importance of interdisciplinary interaction such as mathematics–materials science collaboration. 

The middle part of the book describes mathematical ideas and methods that can be applied to materials problems and introduces some examples of specific studies—for example, computational homology applied to structural analysis of glassy materials, stochastic models for the formation process of materials, new geometric measures for finite carbon nanotube molecules, mathematical technique predicting a molecular magnet, and network analysis of nanoporous materials. 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. 

The posterior section of the book presents how breakthroughs based on mathematics–materials science collaborations can emerge. The authors' argument is supported by the experiences at the Advanced Institute for Materials Research (AIMR), where many researchers from various fields gathered and tackled interdisciplinary research.


Topology hierarchical structure history and emergence of materials science mathematics-materials science collaboration non-equilibrium systems and dynamics

Authors and affiliations

  • Susumu Ikeda
    • 1
  • Motoko Kotani
    • 2
  1. 1.Advanced Institute for Materials ResearchTohoku UniversitySendaiJapan
  2. 2.MiyagiJapan

Bibliographic information