A History of Abstract Algebra

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Springer Science & Business Media, Sep 20, 2007 - Mathematics - 168 pages

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 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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||||||||||||||||||||| Such an excellent text. What better way to teach any subject than by its history. Perhaps an extended version of this book will serve as a proper introduction to non-elementary Abstract Algebra. Many of the reflections on historical connections of a topic help give meaning to it. Definition of Topological Spaces is universally offered with no motivating context. Definition of Continuity inspite of its deep connections to denumerability is offered using the Epsilon method; thus, leaving out meaning and purpose. THIS BOOK is well worth reading and teaching. Recall that in Mathematics, whatever you read complements whatever you further read, so that, each book or contribution to that knowledge is part of a connected whole. A network of topics in Modern Math. is a network of topics, however it is constructed. Here the author re-presents an earlier text which was enormously successful in class-room settings. 

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Contents

History of Ring Theory 41
40
History of Field Theory
63
History of Linear Algebra
79
Emmy Noether and the Advent of Abstract Algebra 91
90
A Course in Abstract Algebra Inspired by History
103
Biographies of Selected Mathematicians
113
Index 165
164
18
166
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