Galois theory for beginners : a historical perspective
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Bibliographic Information
Galois theory for beginners : a historical perspective
（Student mathematical library, v. 95）
American Mathematical Society, [2021], c2019
2nd ed
- : pbk
- Other Title
-
Algebra für Einsteiger : von der Gleichungsauflösung zur Galois-Theorie
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Note
First published in German: Springer Fachmedien Wiesbaden, c2019
Includes index
Description and Table of Contents
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 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
by "Nielsen BookData"