Number Theory An Introduction to Mathematics Part B [Hardcover]

This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.

This book is a modern introduction to the theory of numbers emphasizing its connections with other branches of mathematics. It provides an understanding of the nature and extent of mathematics, and covers standard topics in number theory.

The arithmetic of quadratic forms.- The geometry of numbers.- The number of prime numbers.- A character study.- Uniform distribution and ergodic theory.- Elliptic functions.- Connections with number theory.Aus den Rezensionen:... Die Grundidee besteht darin, ein Gef?hl der Einheit und der Vielfalt der Mathematik beizubringen. Dazu eignet sich Zahlentheorie besonders gut ... In diesem Sinne ist das Buch eine Einf?hrung in die Mathematik durch die Zahlentheorie ... Zun?chst wird die Theorie p?dagogisch entwickelt, mit Beispielen oder einfachen Ergebnissen beginnend. In einem weiteren Abschnitt werden Verallgemeinerungen, Anwendungen, Verfeinerungen ohne Beweis erw?hnt, historische und fachliche Anmerkungen hinzugef?gt, und eine ausf?hrliche Literaturliste angegeben. ... ein sch?ner Text ?ber klassische Zahlentheorie. (G. Barat, in: Internationale Mathematische Nachrichten, December/2009, Issue 12, S. 48 f.)

Undergraduate courses in mathematics are commonly of two types. On the one hand are courses in subjectssuch as linear algebra or real analysiswith which it is considered that every student of mathematics should be acquainted. On the other hand arl��