CiNii Books - Galois theory for beginners : a historical perspective

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 the angle, and the construction of regular $n$-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.

Table of Contents

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 Equation 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 Galois theory according to Artin Epilogue Index Copyright page part 2

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Galois theory for beginners : a historical perspective

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