This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. This is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Includes supplementary material: sn.pub/extrasSolutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid. N° de réf. du vendeur 5912615
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Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Solutions of equations in integers is the central problem of number theory and is the focus of this book. The amount of material is suitable for a one-semester course. The author has tried to avoid the ad hoc proofs in favor of unifying ideas that work in many situations. There are exercises at the end of almost every section, so that each new idea or proof receives immediate reinforcement. 272 pp. Englisch. N° de réf. du vendeur 9780387955872
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Buch. Etat : Neu. Neuware -This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factorization in the arithmetic of certain generalized 'inte gers' , Kummer created in the 1840s a new kind of number to overcome the difficulty. He called them 'ideal numbers' because he did not know exactly what they were, though he knew how they behaved.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 272 pp. Englisch. N° de réf. du vendeur 9780387955872
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factorization in the arithmetic of certain generalized 'inte gers' , Kummer created in the 1840s a new kind of number to overcome the difficulty. He called them 'ideal numbers' because he did not know exactly what they were, though he knew how they behaved. N° de réf. du vendeur 9780387955872
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Etat : New. pp. 272. N° de réf. du vendeur 26290433
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Vendeur : Revaluation Books, Exeter, Royaume-Uni
Hardcover. Etat : Brand New. 1st edition. 254 pages. 9.50x6.25x0.75 inches. In Stock. N° de réf. du vendeur zk0387955879
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