This text offers a clear, efficient exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas, Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem (solvability by radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois groups of cubics and quartics. There are appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. This book provides a concise introduction to Galois Theory suitable for first-year graduate students, either as a text for a course or for study outside the classroom. This new edition has been completely rewritten. Proofs are now clearer because more details are given and because the exposition has been reorganized (for example, the discussion of solvability by radicals now appears later in the book). The book now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between symmetry groups of polygons and Galois groups of polynomials. This analogy can serve as a guide to help readers organize the theoretic definitions and constructions. Several new theorems have also been included; for example, the Casus Irreducibilis.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
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Paperback. Etat : new. Paperback. The first edition aimed to give a geodesic path to the Fundamental Theorem of Galois Theory, and I still think its brevity is valuable. Alas, the book is now a bit longer, but I feel that the changes are worthwhile. I began by rewriting almost all the text, trying to make proofs clearer, and often giving more details than before. Since many students find the road to the Fundamental Theorem an intricate one, the book now begins with a short section on symmetry groups of polygons in the plane; an analogy of polygons and their symmetry groups with polynomials and their Galois groups can serve as a guide by helping readers organize the various definitions and constructions. The exposition has been reorganized so that the discussion of solvability by radicals now appears later; this makes the proof of the Abel-Ruffini theo rem easier to digest. I have also included several theorems not in the first edition. For example, the Casus Irreducibilis is now proved, in keeping with a historical interest lurking in these pages. This text offers an exposition of Galois Theory with complete proofs and exercises. Topics include: cubic and quartic formulas; Fundamental Theory of Galois Theory; insolvability of the quintic; Galois's Great Theorem; and computation of Galois groups of cubics and quartics. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9780387985411
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