Neverending Fractions
An Introduction to Continued Fractions
(Sprache: Englisch)
Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results...
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Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts. Neverending Fractions brings these results together, offering fresh perspectives on a mature subject. Beginning with a standard introduction to continued fractions, the book covers a diverse range of topics, from elementary and metric properties, to quadratic irrationals, to more exotic topics such as folded continued fractions and Somos sequences. Along the way, the authors reveal some amazing applications of the theory to seemingly unrelated problems in number theory. Previously scattered throughout the literature, these applications are brought together in this volume for the first time. A wide variety of exercises guide readers through the material, which will be especially helpful to readers using the book for self-study, and the authors also provide many pointers to the literature.
Inhaltsverzeichnis zu „Neverending Fractions “
Preface; 1. Some preliminaries from number theory; 2. Continued fractions, as they are; 3. Metric theory of continued fractions; 4. Quadratic irrationals through a magnifier; 5. Hyperelliptic curves and Somos sequences; 6. From folding to Fibonacci; 7. The integer part of qa + ß; 8. The Erdos-Moser equation; 9. Irregular continued fractions; Appendix. Selected continued fractions; Bibliography; Index.
Autoren-Porträt von Jonathan Borwein, Alf van der Poorten, Wadim Zudilin
Jonathan Borwein, FRSC, FAAAS, FAA is Laureate Professor in the School of Mathematical and Physical Sciences and Director of the Priority Research Centre in Computer Assisted Research Mathematics and its Applications at the University of Newcastle, New South Wales. He is also Distinguished Professor at King Abdulaziz University in Jeddah. An ISI highly cited scientist and former Chauvenet prize winner, he has published widely in various fields of mathematics.
Bibliographische Angaben
- Autoren: Jonathan Borwein , Alf van der Poorten , Wadim Zudilin
- 224 Seiten, Maße: 15,2 x 22,9 cm, Taschenbuch, Englisch
- Verlag: Cambridge University Press
- ISBN-10: 0521186498
- ISBN-13: 9780521186490
- Erscheinungsdatum: 31.05.2014
Sprache:
Englisch
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