Solving the Pell equation Jacobson, Michael J.

By:

Jacobson, Michael J

Contributor(s):

Williams, Hugh C

Material type: Text

TextSeries: CMS Books in MathematicsPublication details: New York Springer 2010Description: xx, 495 pISBN:

9781441927477

Subject(s):

DDC classification:

513.72 J2S6

Summary: Describes modern (and surprising) applications to cryptography Includes the most recent advances, with a deeper approach than any other book Hugh Williams is Canada’s most famous computational number theorist who has published close to 200 articles in top journals Michael Jacobson is the known expert on subexponential methods, and a former student of Hugh Williams Both authors are recognized as outstanding expositors Pell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks and recreational books concerning elementary number theory, but usually not in much depth. This book provides a modern and deeper approach to the problem of solving the Pell equation. The main component of this will be computational techniques, but in the process of deriving these it will be necessary to develop the corresponding theory. One objective of this book is to provide a less intimidating introduction for senior undergraduates and others with the same level of preparedness to the delights of algebraic number theory through the medium of a mathematical object that has fascinated people since the time of Archimedes. To achieve this, this work is made accessible to anyone with some knowledge of elementary number theory and abstract algebra. Many references and notes are provided for those who wish to follow up on various topics, and the authors also describe some rather surprising applications to cryptography. The intended audience is number theorists, both professional and amateur, and students, but we wish to emphasize that this is not intended to be a textbook; its focus is much too narrow for that. It could, however be used as supplementary reading for students enrolled in a second course in number theory.

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Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Book	Ahmedabad	Non-fiction	513.72 J2S6 (Browse shelf(Opens below))	Available		180933

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Previous	513.26 B6N3 Neverending fractions: an introduction to continued fractions	513.5 A2F4 Finding zero: a mathematician's odyssey to uncover the origins of numbers	513.6 S2E5 Eliptic curves: a computational approach	513.72 J2S6 Solving the Pell equation	513.83 B6I6 Introduction to topology	513.83 S4I6 Introduction to topology and modern analysis	513.92 K3S4 Short-cut math	Next

Describes modern (and surprising) applications to cryptography
Includes the most recent advances, with a deeper approach than any other book
Hugh Williams is Canada’s most famous computational number theorist who has published close to 200 articles in top journals
Michael Jacobson is the known expert on subexponential methods, and a former student of Hugh Williams
Both authors are recognized as outstanding expositors

Pell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks and recreational books concerning elementary number theory, but usually not in much depth. This book provides a modern and deeper approach to the problem of solving the Pell equation. The main component of this will be computational techniques, but in the process of deriving these it will be necessary to develop the corresponding theory.

One objective of this book is to provide a less intimidating introduction for senior undergraduates and others with the same level of preparedness to the delights of algebraic number theory through the medium of a mathematical object that has fascinated people since the time of Archimedes. To achieve this, this work is made accessible to anyone with some knowledge of elementary number theory and abstract algebra. Many references and notes are provided for those who wish to follow up on various topics, and the authors also describe some rather surprising applications to cryptography.

The intended audience is number theorists, both professional and amateur, and students, but we wish to emphasize that this is not intended to be a textbook; its focus is much too narrow for that. It could, however be used as supplementary reading for students enrolled in a second course in number theory.

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