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  3. Irrational Numbers
  • This book is no longer available to purchase from Cambridge Core
  • Cited by 201
Publisher:
Mathematical Association of America
Online publication date:
June 2014
Print publication year:
1956
Online ISBN:
9781614440116
DOI:
https://doi.org/10.5948/9781614440116
Subjects:
Mathematics, Numerical Analysis and Computational Science
Series:
Carus Mathematical Monographs
Information

Book description

In this monograph, Ivan Niven, provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary techniques. The last third of the monograph treats normal and transcendental numbers, including the transcendence of p and its generalization in the Lindermann theorem, and the Gelfond-Schneider theorem. Most of the material in the first two-thirds of the book presupposes only calculus and beginning number theory. The book is almost wholly self-contained. The results needed from analysis and algebra are central, and well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There is a set of notes at the end of each chapter citing the main sources used by the author, and suggesting further readings.

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