无理数（Irrational Numbers）（影印版）

样章

作者：

Ivan Niven

定价：

99.00元

版面字数：

177.00千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2026-01-05

ISBN：

978-7-04-065930-6

物料号：

65930-00

出版时间：

2026-03-27

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

暂无

前辅文
I. RATIONALS AND IRRATIONALS
- 1. The preponderance of irrationals
- 2. Countability
- 3. Dense sets
- 4. Decimal expansions
II. SIMPLE IRATIONALITIES
- 1. Introduction
- 2. The trigonometric functions and π
- 3. The hyperbolic, exponential, and logarithmic functions
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
IV.THE APPROXIMATION or IRRATIONALS BY RATIONALS
- 1. The problem
- 2. A generalization
- 3. Linearly dependent sets
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
VI. FURTHER DIOPHANTINE APPROXIMATIONS
- 1. A basic result
- 2. Best possible approximations
- 3. Uniform distributions
- 4. A proof by Fourier analysis
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
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
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
X. THE GELFOND-SCHNEIDER THEOREM
- 1. Hilbert's seventh problem
- 2. Background material
- 3. Two lemmas
- 4. Proof of the Gelfond-Schneider theorem
LIST OF NOTATION
GLOSSARY
REFERENCE Books
INDEX or TOPICS
INDEX or NAMES