Jonathan Borwein: Neverending Fractions

Cover: 9780521186490 | Neverending Fractions | An Introduction to Continued Fractions | Buch

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

This contemporary introduction to the fascinating theory of continued fractions covers a variety of applications that will interest graduates, postgraduates and researchers, as well as teachers and even amateur enthusiasts.

Inhaltsverzeichnis

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 q¿ + ß; 8. The Erd¿s-Moser equation; 9. Irregular continued fractions; Appendix. Selected continued fractions; Bibliography; Index.

Erscheinungsjahr:	2014
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
ISBN-13:	9780521186490
ISBN-10:	0521186498
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Borwein, Jonathan Poorten, Alf van der Zudilin, Wadim
Hersteller:	Cambridge University Press
Maße:	229 x 152 x 13 mm
Von/Mit:	Jonathan Borwein (u. a.)
Erscheinungsdatum:	31.05.2014
Gewicht:	0,371 kg

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