Modular Forms: A Computational Approach
by William A. Stein
Publisher: American Mathematical Society 2007
Number of pages: 282
This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout.
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by Andrew Granville - Universite de Montreal
The analysis of many number theoretic algorithms turns on the role played by integers which have only small prime factors -- 'smooth numbers'. It is important to have accurate estimates for the number of smooth numbers in various sequences.
by J.P. Buhler, P. Stevenhagen - Cambridge University Press
This text provides a comprehensive introduction to algorithmic number theory for beginning graduate students. It covers the fundamental algorithms of elementary number theory, lattice basis reduction, elliptic curves, algebraic number fields, etc.
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The author uses computers to explore the solutions to some problems in number theory. The emphasis is on the statement of a problem and the examination of the solutions for numbers in a selected range. Many of the problems are very hard.
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This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes. It is accessible to a broad audience. Prerequisites are a typical undergraduate course in calculus and some experience in doing proofs.