Review Exercises
This section gives review exercises for each of the chapters.
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Norman Schofield
Mathematical Methods in Economics and Social Choice Second Edition
Springer Texts in Business and Economics
For further volumes: www.springer.com/series/10099
Norman Schofield
Mathematical Methods in Economics and Social Choice Second Edition
Norman Schofield Center in Political Economy Washington University in Saint Louis Saint Louis, MO, USA
ISSN 2192-4333 ISSN 2192-4341 (electronic) ISBN 978-3-642-39817-9 ISBN 978-3-642-39818-6 (eBook) DOI 10.1007/978-3-642-39818-6 Springer Heidelberg New York Dordrecht London © Springer-Verlag Berlin Heidelberg 2004, 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to the memory of Jeffrey Banks and Richard McKelvey
Foreword
The use of mathematics in the social sciences is expanding both in breadth and depth at an increasing rate. It has made its way from economics into the other social sciences, often accompanied by the same controversy that raged in economics in the 1950s. And its use has deepened from calculus to topology and measure theory to the methods of differential topology and functional analysis. The reasons for this expansion are several. First, and perhaps foremost, mathematics makes communication between researchers succinct and precise. Second, it helps make assumptions
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