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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Elements of Number Theory
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Elements of Number Theory
John Stillwell (Taschenbuch, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
03.12.2010
Sprache
Englisch
EAN
9781441930668
Herausgeber
Springer US
Serien- oder Bandtitel
Undergraduate Texts in Mathematics
Sonderedition
Nein
Autor
John Stillwell
Seitenanzahl
256
Einbandart
Taschenbuch
Schlagwörter
Euclidean algorithm, number theory, prime number
Thema-Inhalt
PBH - Zahlentheorie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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