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Irrational numbers / by Ivan Niven.
- Format:
- Book
- Author/Creator:
- Niven, Ivan, 1915-1999, author.
- Series:
- Carus mathematical monographs ; no. 11.
- Carus mathematical monographs ; 11
- Language:
- English
- Subjects (All):
- Irrational numbers.
- Physical Description:
- 1 online resource (164 pages) : digital, PDF file(s).
- Edition:
- 1st ed.
- Place of Publication:
- Washington : Mathematical Association of America, 1956.
- Language Note:
- English
- Summary:
- 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.
- Contents:
- Rationals and irrationals
- Simple irrationalities
- Certain algebraic numbers
- The approximation of irrationals by rational
- Continued fractions
- Further Diophantine approximations
- Algebraic and transcendental numbers
- Normal numbers
- The generalized Lindemann theorem
- The Gelfond-Schneider theorem.
- Notes:
- Title from publisher's bibliographic system (viewed on 02 Oct 2015).
- Includes bibliographical references and indexes.
- Description based on print version record.
- ISBN:
- 0-88385-011-7
- 1-61444-011-5
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