| Galois' Theory of Algebraic Equations (2001) |
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| From Book News, Inc. As an example of general methodology, the evolution of the theory of equations from the Babylonian solution of a quadratic equation to its completion by Galois in 1830 is the focus of these lectures given to undergraduate math majors by Tignol (U. Catholique de Louvain, Belgium) from 1978-89. Includes technical appendices, exercises with selected solutions, and multilingual references from the 16th to 20th centuries. Earlier editions were published in 1988 by Longman and in 1980 in French.Book News, Inc.®, Portland, OR Choice 2002 "Tignol lets both the triumphs and limitations of the past illuminate our modern understanding." Mathematical Abstracts 2002 "...a methodological masterpiece and a welcome addition to the vast and ample literature on classical Galois theory." Mathematical Reviews 2002 "Anyone who wants to learn about the centuries-long effort to solve algebaic equations should study it carefully." Book Description Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the nineteenth century. The appropriate parts of works by Cardano, Lagrange, Vandermonde, Gauss, Abel and Galois are reviewed and placed in their historical perspective, with the aim of conveying to the reader a sense of the way in which the theory of algebraic equations has evolved and has led to such basic mathematical notions as "group" and "field". A brief discussion on the fundamental theorems of modern Galois theory is included. Complete proofs of the quoted results are provided, but the material has been organized in such a way that the most technical details can be skipped by readers who are interested primarily in a broad survey of the theory. This book will appeal to both undergraduate and graduate students in mathematics and the history of science, and also to teachers and mathematicians who wish to obtain a historical perspective of the field. The text has been designed to be self-contained, but some familiarity with basic mathematical structures and with some elementary notions of linear algebra is desirable for a good understanding of the technical discussions in the later chapters. Book Info Text concentrating primarily on the makings and methodology of mathematics, using the collective experience of historical mathematicians to teach it. The theme used in this text is the theory of equations, presented to illustrate the evolution of a mathematical theory in its entirety, since this particular theory has already reached its maturity. For undergraduates. Softcover. |
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| Original Publication Year | 2001 |
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| Presente de Aniversario do Josue (2003) |