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E-raamat: Introduction to Number Theory with Cryptography

3.14/5 (14 hinnangut Goodreads-ist)
(University of Maryland, College Park, USA), (Gilman School, Baltimore, Maryland, USA)
  • Formaat: 572 pages
  • Ilmumisaeg: 19-Apr-2016
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781482214420
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Introduction to Number Theory with CryptographySuurem pilt
  • Formaat: 572 pages
  • Ilmumisaeg: 19-Apr-2016
  • Kirjastus: Chapman & Hall/CRC
  • Keel: eng
  • ISBN-13: 9781482214420
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Kraft (Gilman School, Baltimore) and Washington (U. of Maryland-College Park) introduce a field that used to be pure mathematics and was studied just for fun, but is now being called into service by cryptography and other disciplines. They cover both the wild and the domesticated elements. The book can be used in a number theory course at the undergraduate or even advanced high school level, and should work for self-study as well. Their topics include divisibility, polynomial congruences, quadratic reciprocity, the geometry of numbers, and algebraic integers. An epilogue (of course) considers Fermat's last theorem. Answers and hints are appended for odd-numbered exercises. Annotation ©2014 Book News, Inc., Portland, OR (booknews.com)

Number theory has a rich history. For many years it was one of the purest areas of pure mathematics, studied because of the intellectual fascination with properties of integers. More recently, it has been an area that also has important applications to subjects such as cryptography. An Introduction to Number Theory with Cryptography presents number theory along with many interesting applications. Designed for an undergraduate-level course, it covers standard number theory topics and gives instructors the option of integrating several other topics into their coverage. The "Check Your Understanding" problems aid in learning the basics, and there are numerous exercises, projects, and computer explorations of varying levels of difficulty.

Arvustused

" provides a fine history of number theory and surveys its applications. College-level undergrads will appreciate the number theory topics, arranged in a format suitable for any standard course in the topic, and will also appreciate the inclusion of many exercises and projects to support all the theory provided. In providing a foundation text with step-by-step analysis, examples, and exercises, this is a top teaching tool recommended for any cryptography student or instructor." California Bookwatch, January 2014

Introduction. Divisibility. Unique Factorization. Applications of Unique Factorization. Congruences. Cryptographic Applications. Polynomial Congruences. Order and Primitive Roots. More Cryptographic Applications. Quadratic Reciprocity. Primality and Factorization. Geometry of Numbers. Arithmetic Functions. Continued Fractions. Gaussian Integers. Algebraic Integers. Analytic Methods. Epilogue: Fermat's Last Theorem. A Supplementary Topics.

James S. Kraft, Lawrence C. Washington
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