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Galois theory for beginners : a historical perspective
Autor: Bewersdorff, Jörg
Rok: c2006
ISBN: 9780821838174
OKCZID: 110233726
Citace (dle ČSN ISO 690):
BEWERSDORFF, Jörg. Galois theory for beginners: a historical perspective. Překlad David KRAMER. Providence, RI: American Mathematical Society, c2006. xx, 180 s. Student mathematical library, 35.
Hodnocení:
4.0 / 5
(6 hlasů)
Anotace
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.