Product Details

• Amazon Sales Rank: #1572694 in Books
• Published on: 2000-05-01
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 367 pages

Review
"The book presents the standard curriculum of a first course in number theory: the fundamental theorem of arithmetic, congruences, Fermat's theorem and Euler's generalization, primitive roots, facts about the distribution of primes, quadratic residues, Pell's equation and sums of squares. The proofs are constructive and the emphasis is on computing. Algorithms are given for GCD, solving linear congruences, factoring, primality testing, finding large primes, evaluating Jacobi symbols, computing square roots modulo a prime, finding continued fractions of quadratic irrationals, solving Pell's equation and expressing an integer as the sum of two squares. The diverse applications include repeating decimals, the RSA cipher, digital signatures, the Yao millionaire problem, check digits, the cattle problem of Archimedes and the crystal structure of salt. There is an excellent survey of many (probable) prime tests with Lucas sequences. The computer algebra system Mathematica is used throughout the book and summarized in an appendix. On nearly every page, Mathematica instructions illustrate algorithms and provide examples. An accompanying CD-ROM holds a rich assortment of Mathematica programs from the text. Three color plates display the power residues modulo small primes and the Gaussian primes reachable from $1+i$ in steps of bounded length."--MATHEMATICAL REVIEWS

Synopsis
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.

Customer Reviews

A new kind of Number Theory Textbook
By switching between careful and precise exposition and hands-on experiments, the two authors succeed in covering the fundamentals of number theory in more depth than most textbooks in a pleasant but efficient manner.
This is a constant invitation to really grasp (and possibily uncover new) aspects of prime number distribution, divisability properties, analytical approaches.
While many proposed activities can be used with other Symbolic Computation Systems, using Mathematica is clearly an advantage for using the book and tailoring it to one's need. One truly enjoys it with one's computer turned on.
One may hope it will help train the future generation of number theorists.