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A History of Abstract Algebra / edited by Israel Kleiner

データ種別 電子ブック
出版者 Boston, MA : Birkhäuser Boston
出版年 2007
本文言語 英語
大きさ XVI, 168 p. 24 illus : online resource

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EB0118226

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内容注記 History of Classical Algebra
History of Group Theory
History of Ring Theory
History of Field Theory
History of Linear Algebra
Emmy Noether and the Advent of Abstract Algebra
A Course in Abstract Algebra Inspired by History
Biographies of Selected Mathematicians
一般注記 Prior to the nineteenth century, algebra meant the study of the solution of polynomial equations. By the twentieth century algebra came to encompass the study of abstract, axiomatic systems such as groups, rings, and fields. This presentation provides an account of the intellectual lineage behind many of the basic concepts, results, and theories of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared unsolvable by classical means. A major theme of the approach in this book is to show how abstract algebra has arisen in attempts to solve some of these classical problems, providing context from which the reader may gain a deeper appreciation of the mathematics involved. Key features: * Begins with an overview of classical algebra * Contains separate chapters on aspects of the development of groups, rings, and fields * Examines the evolution of linear algebra as it relates to other elements of abstract algebra * Highlights the lives and works of six notables: Cayley, Dedekind, Galois, Gauss, Hamilton, and especially the pioneering work of Emmy Noether * Offers suggestions to instructors on ways of integrating the history of abstract algebra into their teaching * Each chapter concludes with extensive references to the relevant literature Mathematics instructors, algebraists, and historians of science will find the work a valuable reference. The book may also serve as a supplemental text for courses in abstract algebra or the history of mathematics
著者標目 Kleiner, Israel editor
SpringerLink (Online service)
件 名 LCSH:Mathematics
LCSH:Algebra
LCSH:Commutative algebra
LCSH:Commutative rings
LCSH:Field theory (Physics)
LCSH:Group theory
LCSH:Matrix theory
LCSH:History
FREE:Mathematics
FREE:Algebra
FREE:History of Mathematical Sciences
FREE:Group Theory and Generalizations
FREE:Commutative Rings and Algebras
FREE:Field Theory and Polynomials
FREE:Linear and Multilinear Algebras, Matrix Theory
分 類 DC23:512
巻冊次 ISBN:9780817646851 REFWLINK
ISBN 9780817646851
URL http://dx.doi.org/10.1007/978-0-8176-4685-1
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