Computational Number Theory

e-books in Computational Number Theory category

Smooth Numbers: Computational Number Theory and BeyondSmooth Numbers: Computational Number Theory and Beyond
by Andrew Granville - Universite de Montreal , 2008
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.
Modular Forms: A Computational ApproachModular Forms: A Computational Approach
by William A. Stein - American Mathematical Society , 2007
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.
Algorithmic Number TheoryAlgorithmic Number Theory
by J.P. Buhler, P. Stevenhagen - Cambridge University Press , 2008
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.

A Computational Introduction to Number Theory and AlgebraA Computational Introduction to Number Theory and Algebra
by Victor Shoup - Cambridge University Press , 2005
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.
Computer analysis of number sequencesComputer analysis of number sequences
by Henry Ibstedt - American Research Press , 1998
This is a book on empirical number theory concentrating on the analysis of number sequences. Its focus is on a small part of integer sequences defined by Florentin Smarandache. The author has also included some other results of his research.
Surfing on the ocean of numbersSurfing on the ocean of numbers
by Henry Ibstedt - Erhus University Press , 1997
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.