Topological Crystallography With a View Towards Discrete Geometric A
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Si
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Surveys and Tutorials in the Applied Mathematical Sciences Volume 6
The history of science, from its very beginnings, is replete with great achievements facilitated by innovative mathematical thinking. Unfortunately, it is increasingly common for mathematics to be only loosely linked to the science, by an online device called Supplementary Material. This practice is especially common in biology, the heroic science our age, but it also is present in other fields. The result is usually poorly coupled mathematics that is presented in a manner that fails to convey the central role that analytical thinking plays in achieving the full scientific understanding of a subject. With this in mind, the STAMS series of Springer-Verlag will take on the new goal of countering this tendency, while retaining its existing goal of providing short, up-to-date, readable tutorials and surveys, written in a style accessible to researchers, professionals and graduate students, which can serve as an introduction to recent and emerging subject areas. In future we therefore will strive to publish manuscripts that emphasize the dual roles of science and mathematics and which achieve the goal of scientific exposition that invites mathematical interest and vice versa.
Larry Sirovich Editor-in-Chief
Toshikazu Sunada
Topological Crystallography With a View Towards Discrete Geometric Analysis
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Toshikazu Sunada Professor School of Science and Technology Meiji University 1-1-1 Higashi-Mita Tama-ku, Kawasaki-shi Kanagawa, Japan
Editor-in-Chief: L. Sirovich Laboratory of Applied Mathematics Department of Bio-Mathematical Sciences Mount Sinai School of Medicine New York, NY, USA
ISBN 978-4-431-54176-9 ISBN 978-4-431-54177-6 (eBook) DOI 10.1007/978-4-431-54177-6 Springer Tokyo Heidelberg New York Dordrecht London Library of Congress Control Number: 2012953120 © Springer Japan 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general
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