Irrational Numbers
Irrational Numbers
£30.99
GBPIn 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.
- A complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments
- much of the material has not yet appeared in completed expository form
- The book is self-contained and complete references to standard works are provided
Product details
August 2005Paperback
9780883850381
174 pages
188 × 127 × 17 mm
0.17kg
This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
Table 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.
