E-Book Overview
This is a small book on algebra with a focus on the structure of fields. The author discusses polynomial and differential equations and the algebraic structure of their solutions. This text explores many unique and unusual subjects, including constructions with a ruler and compass, the transcendence of pi, and the impossibility of angle trisection.
This book is based on notes used by the author over the past two years for a course he taught at the Ecole Polytechnique. There are exercises at the end of each chapter, ranging in difficulty from easy to challenging. To make this book more lively, the author has included pictures of mathematical stamps and mathematicians.
E-Book Content
Undergraduate Texts in Mathematics Editors S. Axler F.W. Gehring K.A. Ribet Antoine Chambert-Loir A Field Guide to Algebra With 12 Illustrations Antoine Chambert-Loir Universite´ de Rennes 1 IRMAR, Campus de Beaulieu 35042 Rennes Cedex France Editorial Board S. Axler Mathematics Department San Francisco State University San Francisco, CA 94132 USA F.W. Gehring Mathematics Department East Hall University of Michigan Ann Arbor, MI 48109 USA K.A. Ribet Department of Mathematics University of California at Berkeley Berkeley, CA 94720-3840 USA Pictured on the cover: Constructing the square root of a real number (Pythagoras’s theorem). See page 2 for discussion. Mathematics Subject Classification (2000): 12-01, 12Fxx, 11Rxx, 13Bxx Library of Congress Cataloging-in-Publication Data Chambert-Loir, Antoine. A field guide to algebra / Antoine Chambert-Loir. p. cm. — (Undergraduate texts in mathematics, ISSN 0172-6056) Includes bibliographical references and index. ISBN 0-387-21428-3 (hardback : alk. paper) 1. Algebraic fields. I. Title. II. Series. QA247.C48 2004 512′.3—dc22 2004048103 ISBN 0-387-21428-3