Exploring Mathematics Problem-Solving and Proof
Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers
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Daniel Grieser
Exploring Mathematics Problem-Solving and Proof
Springer Undergraduate Mathematics Series Advisory Board M. A. J. Chaplain, University of St. Andrews A. MacIntyre, Queen Mary University of London S. Scott, King’s College London N. Snashall, University of Leicester E. Süli, University of Oxford M. R. Tehranchi, University of Cambridge J. F. Toland, University of Bath
More information about this series at http://www.springer.com/series/3423
Daniel Grieser
Exploring Mathematics Problem-Solving and Proof
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Daniel Grieser Institut für Mathematik Carl von Ossietzky Universität Oldenburg Oldenburg Germany
ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISBN 978-3-319-90319-4 ISBN 978-3-319-90321-7 (eBook) https://doi.org/10.1007/978-3-319-90321-7 Library of Congress Control Number: 2018939472 Mathematics Subject Classification (2010): 00-01, 00A07, 00A09, 97D50 Translation from the German language edition: Mathematisches Problemlösen und Beweisen by Daniel Grieser, © Springer Fachmedien Wiesbaden 2013. All Rights Reserved. © 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
For Ricarda and Leonard
Preface to the English edition The classical curriculum for university mathematics education has emphasized calculation and – on a higher level – proofs and systematic development of mathematical theories. In recent years there has been a growing interest in supplementing this with a problem-solving approach. It has become clear that this is not only fun but also very useful as preparation for understanding the mathematical
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