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Look Inside Neverending Fractions

Neverending Fractions
An Introduction to Continued Fractions

Part of Australian Mathematical Society Lecture Series

Authors:
Jonathan Borwein, University of Newcastle, New South Wales
Alf van der Poorten, Macquarie University, Sydney
Jeffrey Shallit, University of Waterloo, Ontario
Wadim Zudilin, Radboud Universiteit Nijmegen

Date Published: July 2014
availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
format: Adobe eBook Reader
isbn: 9781139989060

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About the Authors

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.
- Offers fresh perspectives on a classical subject
- Derived from the authors' many years of experience teaching the subject at different levels
- Includes unpublished work of the late Alf van der Poorten
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Product details
- Date Published: July 2014
- format: Adobe eBook Reader
- isbn: 9781139989060
- contains: 11 b/w illus. 75 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
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.
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Authors
Jonathan Borwein, University of Newcastle, New South Wales
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, Macquarie University, Sydney
Alf van der Poorten was Emeritus Professor of Mathematics at Macquarie University, Sydney, until his death in 2010.
Jeffrey Shallit, University of Waterloo, Ontario
Jeffrey Shallit is Professor of Computer Science at the University of Waterloo, Ontario.
Wadim Zudilin, Radboud Universiteit Nijmegen
Wadim Zudilin is a Professor in the School of Mathematical and Physical Sciences at the University of Newcastle, New South Wales.