Number Theory: An Introduction to Mathematics: Part B

ISBN-13: 9780387298535 / Angielski / Twarda / 2006 / 360 str.

W.A. Coppel

Opis

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.

Recenzje

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.)

Spis treści

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.

Blurb

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. By exploring its many connections with other branches, we may obtain a broad picture.

 

Audience

This book is intended for undergraduate students in mathematics and engineering.