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Advances in computer technology have had a tremendous impact on mathematics in the last two decades. In June of 1989, an international conference was held at MIT, bringing together mathematicians and computer scientists, to survey the work that has been done in computational mathematics, to report recent results in this field, and to discuss research directions as well as educational issues. This book presents a fascinating collection of contributions on topics ranging from computational algebra, and parallel computing, to mathematics education. Mathematicians interested in the computational aspects of their discipline as well as computer scientists interested in mathematical applications will enjoy the integrative view provided by this book.
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Computers and Mathematics Erich Kaltofen Stephen M. Watt Editors Computers and Mathematics Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Erich Kaltofen Rensselaer Polytechnic Department of Computer Science Troy, NY 12180, U.S.A. Stephen M. Watt IBM Watson Research Center Yorktown Heights, NY 10598, U.S.A. Library of Congress Cataloging-in-Publication Data Computers and mathematics 1 Erich Kaltofen, Stephen M. Watt, editors. p. cm. To be used at conference on computers & mathematics at Massachusetts Institute of Technology, June 12, 1989. I. Mathematics-Data processing-Congresses. I. Kaltofen, Erich. I!. Watt, Stephen M. III. Massachusetts Institute of Technology. QA76.95.C64 1989 51O'.28'5-dc20 89-6259 Printed on acid-free paper. © 1989 by Springer-Verlag New York Inc. Softcover reprint of the hardcover 1st edition 1989 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag, 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc. in this pUblication, even if the fonner are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Camera-ready text provided by authors 9 8 765 4 3 2 I ISBN-13: 978-0-387-97019-6 DOl: 10.1007/978-1-4613-9647-5 e-ISBN-13: 978-1-4613-9647-5 About the Cover Page from Ramanujan's Lost Notebook. Ramanujan's Lost Notebook is a collection of pages of formulas and calculations done by Ramanujan during the last year of his life. It was apparently in the possession of G. H. Hardy and G. N. Watson between 1920 and 1965; however neither one ever mentioned it in print. R. Rankin and J. M. Whittaker assisted Watson's widow in placing the Lost Notebook in the Wren Library in Cambridge. It was examined by G. E. Andrews in 1976, and he published the first discussion of its contents in the American Mathematical Monthly in 1979. This is one of the most amazing pages in the Lost Notebook. The last four formulas are examples of the Mock Theta Conjectures (settled in 1988 by D. R. Hickerson). The formulas for F(ql/5) and f(ql/5) are, in fact, crucial to the explanation of certain partition congruences found by Dyson, Atkin, Swinnerton-Dyer and Garvan. (This page was reproduced by courtesy of Narosa Publishing House, New DeIhL) Trefoil Tube. Building a tube around a space curve provides a powerful technique for analyzing local properties like curvature and torsion as well as global properties such as knottedness. The tube around a trefoil knot, produced by Thomas Banchoff and associates at Brown Univers