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. |
From inside the book
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... Course in Abstract Algebra Inspired by History 103. 6.3 Noncommutative algebra and representation theory 6.4 Applications of noncommutative to commutative algebra 6.5 Noether's legacy References 97 98 99 101 Although Lagrange did not ...
... course References ... Biographies of Selected Mathematicians 8.1 Arthur Cayley ( 1821-1895 ) .. 8.1.1 Invariants .. 8.1.2 Groups . 8.1.3 Matrices . 109 110 113 113 115 116 117 8.1.4 Geometry . 118 8.1.5 Conclusion References . 8.2 ...
... courses , for their students , and for the broader mathematical public . The core of a first course in abstract algebra deals with groups , rings , and fields . These are the contents of Chapters 2 , 3 , and 4 , respectively . But ...
... course in abstract algebra inspired by history. I have taught it in an in-service Master's Program for high school teachers of mathematics, but it can be adapted to other types of algebra courses. In each of the above chapters I mention ...
Israel Kleiner. in courses on the history of mathematics. And it may appeal to algebraists who want to familiarize themselves with the history of their subject, as well as to the broader mathematical community. Finally, I want to thank ...
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 |