An Excursion through Elementary Mathematics, Volume III Discrete Mat
This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester unde
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Antonio Caminha Muniz Neto
An Excursion through Elementary Mathematics, Volume III Discrete Mathematics and Polynomial Algebra
Problem Books in Mathematics Series Editor: Peter Winkler Department of Mathematics Dartmouth College Hanover, NH USA
More information about this series at http://www.springer.com/series/714
Antonio Caminha Muniz Neto
An Excursion through Elementary Mathematics, Volume III Discrete Mathematics and Polynomial Algebra
123
Antonio Caminha Muniz Neto Universidade Federal do Ceará Fortaleza, Ceará, Brazil
ISSN 0941-3502 ISSN 2197-8506 (electronic) Problem Books in Mathematics ISBN 978-3-319-77976-8 ISBN 978-3-319-77977-5 (eBook) https://doi.org/10.1007/978-3-319-77977-5 Library of Congress Control Number: 2017933290 © Springer International Publishing AG, part of Springer Nature 2018 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, express 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. Printed on acid-free paper This Springer imprint is published by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
E horas sem conta passo, mudo, O olhar atento, A trabalhar, longe de tudo O pensamento. Porque o escrever - tanta perícia, Tanta requer, Que ofício tal.., nem há notícia De outro qualquer. Profissão de Fé (excerto) Olavo Bilac
Preface
This is the final volume of a series of three volumes (the other ones being [9] and [8]) devoted to the mathematics of mathematical olympiads. Generally speaking, they are somewhat expanded versions of a collection of six volumes, first published in Portuguese by the Brazilian Mathematical Society in 2012 and currently in its second edition. The material collected here and in the other two volumes is based on course notes that evolved over the years since 1991, when I first began coaching students of Fortaleza to the Brazilian Mathematical Olym
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