Galois theory for beginners : a historical perspective
著者
書誌事項
Galois theory for beginners : a historical perspective
（Student mathematical library, v. 35）
American Mathematical Society, c2006
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Algebra für Einsteiger
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注記
"This book is a translation of the second edition of my German book ..."--Pref. to the English ed
Includes bibliographical references and index
内容説明・目次
内容説明
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed.Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting an angle, and the construction of regular $n$-gons are also presented. This book is suitable for undergraduates and beginning graduate students.
目次
Cubic equations Casus irreducibilis: The birth of the complex numbers Biquadratic equations Equations of degree $n$ and their properties The search for additional solution formulas Equations that can be reduced in degree The construction of regular polygons The solution of equations of the fifth degree The Galois group of an equation Algebraic structures and Galois theory Epilogue Index.
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