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 transcendence of and its generalization in the Lindemann 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 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 if bites at the end of each chapter citing
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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.About the Author:
Ivan Niven earned his Bachelor's and Master's degrees (1934 and 1936) at the University of British Columbia, and he was awarded his Ph.D. in 1938 at the University of Chicago. He worked with the famous algebraist and number theorist Leonard Eugene Dickson. Ivan Niven published over sixty papers, some with well-known co-authors such as Samuel Eilenberg, Paul Erdos (6 times), Nathan J. Fine, R. D. James, and H. S. Zuckerman (7 times). His areas of expertise were number theory, especially the areas of diophantine approximation and questions of irrationality and transcendance of numbers, and combinatorics. He wrote seven books, for the MAA including the Carus Monograph "Irrational Numbers." In 1989 he was presented the MAA's highest award for achievement, the Award for Distinguished Service to Mathematics (now called the Yueh-Gin Gung and Charles Y. Hu Award for Distinguished Service to Mathematics). Ivan Niven died in May 1999 in Eugene, Oregon
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Descrizione libro The Mathematical Association o, 2005. Paperback. Condizione libro: New. Never used!. Codice libro della libreria P110883850389
Descrizione libro The Mathematical Association of America, 2005. Paperback. Condizione libro: New. book. Codice libro della libreria M0883850389