A Brief Journey in Discrete Mathematics
The goal of this book is to showcase the beauty of mathematics as revealed in nine topics of discrete mathematics. In each chapter, properties are explored through a series of straightforward questions that terminate with results that lie at the doorstep
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A Brief Journey in Discrete Mathematics
A Brief Journey in Discrete Mathematics
Randolph Nelson
A Brief Journey in Discrete Mathematics
Randolph Nelson (Home address) Beverly, MA, USA
ISBN 978-3-030-37860-8 ISBN 978-3-030-37861-5 (eBook) https://doi.org/10.1007/978-3-030-37861-5 Mathematics Subject Classification: 97N70 © 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
Beauty is the first test: There is no permanent place in the world for ugly mathematics. G. H. Hardy (1877–1947)
Dedicated to my wife - Cynthia Nelson
Acknowledgments
I would like to thank several of my colleagues at work who shared their enthusiasm and interest for the book over the many years it took to write. Sean McNeill suffered through many monologues concerning mathematical relationships that I found particularly beautiful and I remember Rod Dodson having to undergo similar orations. Eric Norman was always receptive to the ideas in the book and even had his daughter read some chapters. Linda Wu, a fellow mathematician, shared her exuberant interest in the material and continually encouraged me towards publication. I have sat across a restaurant table literally hundreds of times with my business partner, Ira Leventhal. Frequently, during our conversations, the topic would veer away from business towards mathematics. Invariably, this led me to profit from Ira’s uncanny intuition regarding numerical relationships. I would be amiss without acknowledging two professors who have had a major influence on my research career. Rod Oldehoeft’s warm and enthusiastic reception of a new student who walked into his office one day started my career. Leonard Kleinrock, my doctorate thesis advisor,
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