Finite Sets
The concept set has a somewhat different sense in mathematics than in ordinary speech. The word set usually implies the presence of a relatively large number of objects (“a set or multitude of friends”).1 A mathematician understands a set as an absolutely
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Springer-Verlag Berlin Heidelberg GmbH
Igor R. Shafarevich
Discourses
on Algebra Translated from the Russian by William B. Everett
,
Springer
Igor R. Shajarevich
Mathematical Institute of the Russian Academy of Sciences Ul. Gubkina 8 117 966 Moscow, Russia e-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Shafarevic,lgor 1.: Discourses on aItlebra Iigor R. Shafarevich. Trans!. from the Russian by William B. Everett. - Berlin ; Heidelberg ; New York; Barcelona; Hong Kong; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Universitext) ISBN 978-3-540-42253-2 ISBN 978-3-642-56325-6 (eBook) DOI 10.1007/978-3-642-56325-6
Originally published as Izbrannye glavy algebry Matematicheskoe obrazovanie (zhurnal), Moscow 2000
ISBN 978-3-540-42253-2
Mathematics Subject Classification (2000): ll-xx,12-xx,13-xx,lS-XX
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Abstract In this book by a leading Russian mathematician and full member of the Russian Academy of Sciences, Igor Rostislavovich Shafarevich, the elements of algebra as a field of contemporary mathematics are laid out based on material bordering the school program as closely as possible. The book can be used as enrichment materials for students in grades 9-12 in both ordinary schools and schools with a deeper study of mathematics and the sciences and also as a book for mathematics teachers.
Preface I wish that algebra would be the Cinderella of our story. In the mathematics program in schools, geometry has often been the favorite daughter. The amount of geometric knowledge studied in schools is approximately equal to the level achieved in ancient Greece and summarized by Euclid in his Elements (third century B.C.). For a long time, geometry was taught according to Euclid; simplified variants have recently appeared. In spite of all the changes introduced in geometry courses, geometry retains the influence of Eu
