Galois Theory for Beginners A Historical Perspective
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Description: 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 regularn$-gons are also presented. This book is suitable for undergraduates and beginning graduate students.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $38.00
Copyright year: 2006
Publisher: American Mathematical Society
Publication date: 9/5/2006
Size: 5.75" wide x 8.50" long x 0.25" tall
|Casus irreducibilis: The birth of the complex numbers|
|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|