by Richard Crandall
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by Gareth A. Jones
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by Jorg Bewersdorff
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by Joseph Gallian
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by John H. Conway
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Product Description
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.
"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
Product Description
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.
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Inside This Book
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Fermat's Little Theorem, Chinese Remainder Theorem, Prime Number Theorem, Bertrand's Postulate, Prove Proposition, Remainders Quotients, Riemann Hypothesis, Twin Prime Conjecture, Fermat's Last Theorem, Kevin Ford, Maurice Kraitchik, Partial Quotients Convergents, United States of America Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Fermat's Little Theorem, Chinese Remainder Theorem, Prime Number Theorem, Bertrand's Postulate, Prove Proposition, Remainders Quotients, Riemann Hypothesis, Twin Prime Conjecture, Fermat's Last Theorem, Kevin Ford, Maurice Kraitchik, Partial Quotients Convergents, United States of America Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 19
books:
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1
book
cites this book:
- Prime Numbers: A Computational Perspective by Richard Crandall on 4 pages
- Problems in Algebraic Number Theory (Graduate Texts in Mathematics) by M. Ram Murty in Back Matter
- A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics) by Henri Cohen in Back Matter
- Prime Numbers and Computer Methods for Factorization (Progress in Mathematics) by Hans Riesel in Back Matter
- The New Book of Prime Number Records by Paulo Ribenboim in Back Matter
See all 19 books this book cites
- Smarandache Notions, Vol. 14 by W.B. Vasantha Kandasamy on page 362
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