图书信息
图书目录
无理数（Irrational Numbers）（影印版）
暂无简介
作者：
Ivan Niven
定价：
99.00 元
出版时间：
2026-03-27
ISBN：
978-7-04-065930-6
物料号：
65930-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
数论
重点项目：
暂无
版面字数：
177千字
开本：
16开
装帧形式：
精装
页数：
暂无
最新印次时间：
2026年01月
- 目录
- 前辅文
- I. RATIONALS AND IRRATIONALS
- 1. The preponderance of irrationals
- 2. Countability
- 3. Dense sets
- 4. Decimal expansions
- 1. The preponderance of irrationals
- II. SIMPLE IRATIONALITIES
- 1. Introduction
- 2. The trigonometric functions and π
- 3. The hyperbolic, exponential, and logarithmic functions
- 1. Introduction
- III. CERTAIN ALGEBRAIC NUMBERS
- 1. Introduction
- 2. Further background material
- 3. The factorization of xn-1
- 4. Certain trigonometric values
- 5. Extension to the tangent
- 1. Introduction
- IV.THE APPROXIMATION or IRRATIONALS BY RATIONALS
- 1. The problem
- 2. A generalization
- 3. Linearly dependent sets
- 1. The problem
- v. CONTINTED FEACTIONS
- 1. The Euclidean algorithm
- 2. Uniqueness
- 3. Infinite continued fractions
- 4. Infinite continued fraction expansions
- 5. The convergents as approximations
- 6. Periodic continued fractions
- 1. The Euclidean algorithm
- VI. FURTHER DIOPHANTINE APPROXIMATIONS
- 1. A basic result
- 2. Best possible approximations
- 3. Uniform distributions
- 4. A proof by Fourier analysis
- 1. A basic result
- VII. ALGEBRAIC AND TRANSCENDENTAL NUMBERS
- 1. Closure properties of algebraic numbers
- 2. A property of algebraic integers
- 3. Transcendental numbers
- 4. The order of approximation
- 1. Closure properties of algebraic numbers
- VIII. NORMAL NUMBERS
- 1. Definition of a normal number
- 2. The measure of the set of normal numbers
- 3. Equivalent definitions
- 4. A normal number exhibited
- 1. Definition of a normal number
- IX. THE GENERALIZED LINDEMANN THEOREM
- 1. Statement of the theorem
- 2. Preliminaries
- 3. Proof of the theorem
- 4. Applications of the theorem
- 5. Squaring the circle
- 1. Statement of the theorem
- X. THE GELFOND-SCHNEIDER THEOREM
- 1. Hilbert's seventh problem
- 2. Background material
- 3. Two lemmas
- 4. Proof of the Gelfond-Schneider theorem
- 1. Hilbert's seventh problem
- LIST OF NOTATION
- GLOSSARY
- REFERENCE Books
- INDEX or TOPICS
- INDEX or NAMES
- 前辅文
