Neverending Fractions

An Introduction to Continued Fractions

AvJonathan Borwein,Alf van der Poorten

Häftad, Engelska, 2014

Del 23 i serien Australian Mathematical Society Lecture Series

485 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2014-07-03
Mått:154 x 230 x 14 mm
Vikt:350 g
Format:Häftad
Språk:Engelska
Serie:Australian Mathematical Society Lecture Series
Antal sidor:224
Förlag:Cambridge University Press
ISBN:9780521186490

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Mer om författaren

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. 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.

Innehållsförteckning

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 qα + β; 8. The Erdős-Moser equation; 9. Irregular continued fractions; Appendix. Selected continued fractions; Bibliography; Index.