Irrational Numbers

Released on by Ivan Niven
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  • Irrational Numbers Book Detail

  • Author : Ivan Niven
  • Release Date : 1985-12-31
  • Publisher : American Mathematical Soc.
  • Genre : Irrational numbers
  • Pages : 164
  • ISBN 13 : 1614440115
  • File Size : 47,47 MB
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Irrational Numbers by Ivan Niven PDF Summary

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 reading.

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Irrational Numbers

Irrational Numbers

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In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete tre

Diophantine Approximations

Diophantine Approximations

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This self-contained treatment covers approximation of irrationals by rationals, product of linear forms, multiples of an irrational number, approximation of com