Recurrences: Rendering Complex Structure Manageable
One of the intellectually most powerful strategies for all manner of human endeavor is to “learn from the past”—i.e., to re-use knowledge that one has acquired earlier in order to acquire new knowledge.
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nderstand Mathematics, Understand Computing Discrete Mathematics That All Computing Students Should Know
Understand Mathematics, Understand Computing
Arnold L. Rosenberg • Denis Trystram
Understand Mathematics, Understand Computing Discrete Mathematics That All Computing Students Should Know
Arnold L. Rosenberg College of Information and Computer Science University of Massachusetts Amherst, MA, USA
Denis Trystram Grenoble INP Université Grenoble Alpes Saint Martin d’Hères, France
ISBN 978-3-030-58375-0 ISBN 978-3-030-58376-7 (eBook) https://doi.org/10.1007/978-3-030-58376-7 © Springer Nature Switzerland AG 2020 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. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Addition
Roger Trystram, 1973
v
To my beloved wife, Susan, and my children Paul and Rachel for decades of patience during my extended episodes of “cerebral absence.” To Professor Oscar Zariski, who changed my life by introducing me to “real” mathematics. With love to my wife C´ecile and my children Alice and No´e who help me to stay connected to the “real” world. To all past students who inspired this book. To all future students who will read this book.
Contents
MANIFESTO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi x PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi 1
2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Why Is This Book Needed? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Why Is This Book Needed? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 T
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