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 technique. The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. The book is wholly self-contained. The results needed from analysis and algebra are central. Well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There are notes at the end of each chapter citing the main sources used by the author and suggesting further reading.
Product details
- Paperback | 174 pages
- 127 x 188 x 17mm | 170g
- 18 Aug 2005
- Mathematical Association of America
- Washington, United States
- English
- Reprint
- 0883850389
- 9780883850381
- 2,468,041
Download Carus Mathematical Monographs: Irrational Numbers Series Number 11 (9780883850381).pdf, available at greenaroundtheedges.net for free.
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