A History of Abstract AlgebraPrior 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 history 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. |
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... , and Avanti Paranjpye of Birkhäuser for their outstanding cooperation in seeing this book to completion. Israel Kleiner Toronto, Ontario May 2007 Permissions Grateful acknowledgment is hereby given for permission to reprint Preface xiii.
Israel Kleiner. Permissions Grateful acknowledgment is hereby given for permission to reprint in full or in part , with minor changes , the following : I. Kleiner , “ Algebra . ” History of Modern Science and Mathematics , Scrib- ner's ...
... given in the form of “ word problems . ” Here is a typical example and its solution : I have added the area and two - thirds of the side of my square and it is 0 ; 35 [ 35/60 in sexagesimal notation ] . What is the side of my square ...
... given as a solution of a quadratic equation. Zero, negative numbers, and irrational numbers were not, as far as we know, part of the Babylonian number system. (e) The problems were often phrased in geometric language, but they were not ...
Israel Kleiner. Proposition II.11 states : “ To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment . ” It asks , in algebraic language , to solve ...
Contents
History of Field Theory | 63 |
References | 77 |
Emmy Noether and the Advent of Abstract Algebra | 90 |
A Course in Abstract Algebra Inspired by History | 103 |
Biographies of Selected Mathematicians | 113 |
Index 165 | 164 |