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OverviewDespite 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. Full Product DetailsAuthor: Jonathan Borwein (Professor, University of Newcastle, New South Wales) , Alf van der Poorten (Macquarie University, Sydney) , Jeffrey Shallit (University of Waterloo, Ontario) , Wadim Zudilin (University of Newcastle, New South Wales)Publisher: Cambridge University Press Imprint: Cambridge University Press Volume: 23 Dimensions: Width: 15.40cm , Height: 1.40cm , Length: 23.00cm Weight: 0.350kg ISBN: 9780521186490ISBN 10: 0521186498 Pages: 224 Publication Date: 03 July 2014 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPreface; 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 qα + β; 8. The Erdős-Moser equation; 9. Irregular continued fractions; Appendix. Selected continued fractions; Bibliography; Index.ReviewsAuthor InformationJonathan 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. Alf van der Poorten was Emeritus Professor of Mathematics at Macquarie University, Sydney, until his death in 2010. Jeffrey Shallit is Professor of Computer Science at the University of Waterloo, Ontario. Wadim Zudilin is a Professor in the School of Mathematical and Physical Sciences at the University of Newcastle, New South Wales. Tab Content 6Author Website:Countries AvailableAll regions |
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