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Synopsis
Algorithmic Number Theory provides a thorough introduction to the design and analysisof algorithms for problems from the theory of numbers. Although not an elementary textbook, itincludes over 300 exercises with suggested solutions. Every theorem not proved in the text or leftas an exercise has a reference in the notes section that appears at the end of each chapter. Thebibliography contains over 1,750 citations to the literature. Finally, it successfully blendscomputational theory with practice by covering some of the practical aspects of algorithmimplementations.The subject of algorithmic number theory represents the marriage of number theorywith the theory of computational complexity. It may be briefly defined as finding integer solutionsto equations, or proving their non-existence, making efficient use of resources such as time andspace. Implicit in this definition is the question of how to efficiently represent the objects inquestion on a computer. The problems of algorithmic number theory are important both for theirintrinsic mathematical interest and their application to random number generation, codes forreliable 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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Review
"[Algorithmic Number Theory] is an enormous achievement andan extremely valuable reference." Donald E. Knuth, Emeritus, Stanford University
From the Author
web page for _Algorithmic Number Theory_ by Bach and Shallit
Readers of _Algorithmic Number Theory_ may want to visit the web page for the book, http://math.uwaterloo.ca/~shallit/ant.html which gives the user access to (a) an errata page and (b) electronic copies of the bibliography files used to generate the book.
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Algorithmic Number Theory, Vol. 1: Efficient Algorithms
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The MIT Press, Cambridge, 1996
ISBN 10: 0262024055
ISBN 13: 9780262024051
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Algorithmic Number Theory, Vol. 1: Efficient Algorithms (Foundations of Computing)
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