Synopses & Reviews
This text will be a modern introduction to number theory, a course taught at most colleges and universities, primarily to math and c.s. majors, and will place heavy and continuing emphasis on algorithmic aspects of the subject. The language of the algorithms used will be the popular Mathematica, and a comprehensive set of notebooks will be included on a book web site. While the emphasis will be on modern topics like factorization and primality testing techniques, there will be extensive coverage of traditional number theory. Among its features willbe lots of displayed computations, and the inclusion of many computer exercises for students.
Synopsis
A Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the book also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Includes CD-ROM with Mathematica files.