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Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included.
The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse-Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.
The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. Part B contains, for example, complete proofs of the Hasse-Minkowski theorem and the prime number theorem, as well as self-contained accounts of the character theory of finite groups and the theory of elliptic functions. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.
Aus den Rezensionen: "... Die Grundidee besteht darin, ein Gefühl der Einheit und der Vielfalt der Mathematik beizubringen. Dazu eignet sich Zahlentheorie besonders gut ... In diesem Sinne ist das Buch eine Einführung in die Mathematik durch die Zahlentheorie ... Zunächst wird die Theorie pädagogisch entwickelt, mit Beispielen oder einfachen Ergebnissen beginnend. In einem weiteren Abschnitt werden Verallgemeinerungen, Anwendungen, Verfeinerungen ohne Beweis erwähnt, historische und fachliche Anmerkungen hinzugefügt, und eine ausführliche Literaturliste angegeben. ... ein schöner Text über klassische Zahlentheorie." (G. Barat, in: Internationale Mathematische Nachrichten, December/2009, Issue 12, S. 48 f.)