Lectures on Galois Theory of Algebraic Equations - Hardcover

Tignol, J.P.

Hardcover

ISBN 10: 0582002907 ISBN 13: 9780582002906

Publisher: Longman Higher Education, 1988

Synopsis

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.

About this title

Review

Using modern notation to explain original ideas of Cardano, Viete, Descartes, etc., makes it accessible to undergraduates and mathematicians. -- European Mathematical Society

Synopsis

This book is an account of the development of the theory of algebraic equations from its origins in ancient times to its completion by Galois in the 19th century. The main emphasis is placed on developments arising between the 16th and the 19th centuries. 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 a sense of the evolution of the theory of algebraic equations, and its giving rise to such basic mathematical notions as "group" and "field". A brief discussion of 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 more technical details can be omitted by readers interested primarily in a broad survey of the theory. The book is intended for postgraduate and undergraduate students in mathematics and the history of science, and also for teachers and mathematicians seeking an historical perspective on this field.

The text is designed to be self-contained, but some familiarity with basic mathematical structures and elementary notions is needed for the technical aspects of the later chapters.

Edition details

• Publisher: Longman Higher Education
• Publication date: 1988
• Language: English
• ISBN 10: 0582002907
• ISBN 13: 9780582002906
• Binding: Hardcover
• Number of pages: 450