数論入門（第２版･テキスト） Number Theory : An Introduction to Mathematics (Universitext) （2ND）

数論入門（第２版･テキスト）<br>Number Theory : An Introduction to Mathematics (Universitext) （2ND）

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数論入門（第２版･テキスト）
Number Theory : An Introduction to Mathematics (Universitext) （2ND）

Coppel, William A.

ウェブストア価格 ¥22,919（本体¥20,836）
Springer（2009/09発売）
外貨定価 US$ 109.99
ポイント 208pt

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製本 Paperback:紙装版/ペーパーバック版／ページ数 610 p.／サイズ 17 illus.
商品コード 9780387894850

基本説明

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.

Full Description

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 Expanding Universe of Numbers.- Divisibility.- More on Divisibility.- Continued Fractions and Their Uses.- Hadamard#x2019;s Determinant Problem.- Hensel#x2019;s -adic Numbers.- 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.