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Beschreibung
Galois theory is a showpiece of mathematical unification, bringing together several different branches of the subject and creating a power ful machine for the study of problems of considerable historical and mathematical importance. This book is an attempt to present the theory in such a light, and in a manner suitable for second- and third-year undergraduates. The central theme is the application… of the Galois group to the quintic equation. As well as the traditional approach by way of the 'general' polynomial equation I have included a direct approach which demon strates the insolubility by radicals of a specific quintic polynomial with integer coefficients, which I feel is a more convincing result. The abstract Galois theory is set in the context of arbitrary field extensions, rather than just subfields of the complex numbers; the resulting gain in generality more than compensates for the extra work required. Other topics covered are the problems of duplicating the cube, trisecting the angle, and squaring the circle; the construction of regular polygons; the solution of cubic and quartic equations; the structure of finite fields; and the 'fundamental theorem of algbra'. The last is proved by almost purely algebraic methods, and provides an interesting application of Sylow theory. In order to make the treatment as self-contained as possible, and to bring together all the relevant material in a single volume, I have included several digressions. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Bis zu 50 % günstiger als neu
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Technische Daten
Erscheinungsdatum
03.10.2011
Sprache
Englisch
EAN
9789401068642
Herausgeber
Springer Netherland
Sonderedition
Nein
Autor
Ian Stewart
Einbandart
Broschiert
Höhe
235 mm
Breite
15.5 cm
-.-
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