Editorial Board Walter Craig Nikolai Ivanov Steven G. Krantz David Saltman (Chair) 2000 Mathematics Subject Classification. Primary 52–01, 52–02, 52B45, 52C07, 46A20, 46N10, 90C05, 90C08, 90C22, 49N15. Library of Congress Cataloging-in-Publication Data Barvinok, Alexander, 1963– A course in convexity / Alexander Barvinok. p. cm. (Graduate studies in mathematics, ISSN 1065-7339 v. 54) Includes bibliographical references and index. ISBN 0-8218-2968-8 (alk. paper) 1. Convex geometry. 2. Functional analysis. 3. Programming (Mathematics) I. Title. II. Series. QA639.5 .B37 2002 2002028208 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can also be made by e-mail to reprint-permission@ams.org. c 2002 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. Visit the AMS home page at http://www.ams.org/ 10 9 8 7 6 5 4 3 2 16 15 14 13 12 11
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