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Synopsis
Algorithmic Number Theory provides a thorough introduction to the design and analysis of algorithms for problems from the theory of numbers. Although not an elementary textbook, it includes over 300 exercises with suggested solutions. Every theorem not proved in the text or left as an exercise has a reference in the notes section that appears at the end of each chapter. The bibliography contains over 1,750 citations to the literature. Finally, it successfully blends computational theory with practice by covering some of the practical aspects of algorithm implementations.The subject of algorithmic number theory represents the marriage of number theory with the theory of computational complexity. It may be briefly defined as finding integer solutions to equations, or proving their non-existence, making efficient use of resources such as time and space. Implicit in this definition is the question of how to efficiently represent the objects in question on a computer. The problems of algorithmic number theory are important both for their intrinsic mathematical interest and their application to random number generation, codes for reliable and secure information transmission, computer algebra, and other areas.Publisher's Note: Volume 2 was not written. Volume 1 is, therefore, a stand-alone publication.
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About the Author
Eric Bach is Professor, Computer Sciences Department, University of Wisconsin. Jeffrey Shallit is Associate Professor, Department of Computer Science, University of Waterloo.
Review
"[Algorithmic Number Theory] is an enormous achievement andan extremely valuable reference." Donald E. Knuth, Emeritus, Stanford University
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- PublisherMit Pr
- Publication date1996
- ISBN 10 0262024055
- ISBN 13 9780262024051
- BindingHardcover
- LanguageEnglish
- Number of pages496
- Rating
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Algorithmic Number Theory, Vol. 1: Efficient Algorithms
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ISBN 10: 0262024055
ISBN 13: 9780262024051
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