Irrational Numbers

Ivan Niven - Collection The Carus Mathematical Monographs

170 pages, parution le 29/03/2005

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Résumé

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 π 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.

Sommaire

Rational and Irrationals
Simple Irrationlities
Certain Algebraic Numbers
The Approximation of Irrationals by Rationals
Continued Fractions
Further Diophantine Approximations
Algebraic and Transcendental Numbers
Normal Numbers
The Generalized Lindemann Theorem
The Gelfond-Schneider Theorem

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Caractéristiques techniques

	PAPIER
Éditeur(s)	The Mathematical Association of America (MAA)
Auteur(s)	Ivan Niven
Collection	The Carus Mathematical Monographs
Parution	29/03/2005
Nb. de pages	170
Format	13 x 19
Couverture	Broché
Poids	170g
Intérieur	Noir et Blanc
EAN13	9780883850381
ISBN13	978-0-88385-038-1