Surfing on the ocean of numbers
by Henry Ibstedt
Publisher: Erhus University Press 1997
Number of pages: 76
In this book, Henry Ibstedt takes us on a journey where computers are used to explore the solutions to some simple problems in number theory. Very little is proven in the book, 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 in the very hard to impossible category, although you never really know about problems in number theory.
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by Victor Shoup - Cambridge University Press
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.
by William A. Stein - American Mathematical Society
This 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.
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.