Topics in Algebra and Analysis Preparing for the Mathematical Olympi
The techniques presented here are useful for solving mathematical contest problems in algebra and analysis. Most of the examples and exercises that appear in the book originate from mathematical Olympiad competitions around the world. In the first four ch
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Topics in Algebra and Analysis Preparing for the Mathematical Olympiad
Radmila Bulajich Manfrino José Antonio Gómez Ortega Rogelio Valdez Delgado
Topics in Algebra and Analysis Preparing for the Mathematical Olympiad
Radmila Bulajich Manfrino Facultad de Ciencias Universidad Autónoma del Estado de Morelos Cuernavaca, Morelos, México
José Antonio Gómez Ortega Facultad de Ciencias Universidad Nacional Autónoma de México Distrito Federal, México
Rogelio Valdez Delgado Facultad de Ciencias Universidad Autónoma del Estado de Morelos Cuernavaca, Morelos, México
ISBN 978-3-319-11945-8 ISBN 978-3-319-11946-5 DOI 10.1007/978-3-319-11946-5
(eBook)
Library of Congress Control Number: 2015930195 Mathematics Subject Classification (2010): 00A07, 11B25, 11B65, 11C08, 39B22, 40A05, 97Fxx Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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.
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Introduction Topics in algebra and analysis have become fundamental for the mathematical olympiad. Today, the problems in these topics that appear in the contests are frequent, and the problems from other areas that use algebra and analysis in their solutions are also frequent. In this book, we want to point out the principal algebra and analysis tools that a student must assimilate and learn to use gradually in training for mathematical contests and olympiads. Some of the topics that we study in the book are also part of the mathematical syllabus in high school courses, but there are other topics that are presented at the college level. That is, the book can be used as a reference text for undergraduates in the first year of college who will be facing algebra and analysis problems and will be interested in learning techniques to solve them. The book is divided in ten chapters. The first four correspond to topics
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