Irrational Numbers
Series: Carus Mathematical Monographs; 11;
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Product details:
- Publisher The Mathematical Association of America
- Date of Publication 18 August 2005
- ISBN 9780883850381
- Binding Paperback
- No. of pages174 pages
- Size 188x127x17 mm
- Weight 170 g
- Language English 0
Categories
Short description:
Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers.
MoreLong 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 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.
MoreTable of Contents:
1. Rationals and irrationals; 2. Simple irrationalities; 3. Certain algebraic numbers; 4. The approximation of irrationals by rationals; 5. Continued fractions; 6. Further diophantine approximations; 7. Algebraic and transcendental numbers; 8. Normal numbers; 9. The generalized Lindemann theorem; 10. The Gelfond-Schneider theorem; List of notation; Glossary; Reference books; Index of topics; Index of names.
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