Number Theory

1. Front Matter

   Pages i-ix

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2. The arithmetic of quadratic forms

   Pages 341-383

3. The geometry of numbers

   Pages 385-426

4. The number of prime numbers

   Pages 427-464

5. A character study

   Pages 465-518

6. Uniform distribution and ergodic theory

   Pages 519-568

7. Elliptic functions

   Pages 569-619

8. Connections with number theory

   Pages 621-672

9. Back Matter

   Pages 1-28

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Undergraduate courses in mathematics are commonly of two types. On the one hand are courses in subjects - such as linear algebra or real analysis - with which it is considered that every student of mathematics should be acquainted. On the other hand are courses given by lecturers in their own areas of specialization, which are intended to serve as a preparation for research. But after taking courses of only these two types, students might not perceive the sometimes surprising interrelationships and analogies between different branches of mathematics, and students who do not go on to become professional mathematicians might never gain a clear understanding of the nature and extent of mathematics. The two-volume Number Theory: An Introduction to Mathematics attempts to provide such an understanding of the nature and extent of mathematics. It is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A, which should be accessible to a first-year undergraduate, deals with elementary number theory. Part B is more advanced than the first and should give the reader some idea of the scope of mathematics today. The connecting theme is the theory of numbers, at first sight one of the most abstruse and irrelevant branches of mathematics. Yet by exploring its many connections with other branches, we may obtain a broad picture.

• Character
• Ergodic
• Lattice
• Local–Global
• Prime
• Prime number
• number theory
• matrix theory

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.)

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