Fundamental Number Theory with Applications

Fundamental Number Theory with Applications

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An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition * Removal of all advanced material to be even more accessible in scope * New fundamental material, including partition theory, generating functions, and combinatorial number theory * Expanded coverage of random number generation, Diophantine analysis, and additive number theory * More applications to cryptography, primality testing, and factoring * An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with more

Product details

  • Hardback | 384 pages
  • 152.4 x 236.22 x 25.4mm | 635.03g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 2nd Revised edition
  • 3 black & white illustrations, 16 black & white tables
  • 1420066595
  • 9781420066593
  • 1,851,136

Review quote

This is an introductory text in number theory from a well-known name ... it covers most of the material traditionally expected in such a course. ... One of the most interesting features of this book is the extensive (and crunchy) biographical sketches of relevant mathematicians (both living and dead). ... I heartily recommend this book to undergraduates and the passing layman, as it is the work of a master and is lucidly explained. ... -IACR book reviews, March 2010 The second edition of this very interesting book includes a revision of its contents and a pledge for the publication of a second volume with advanced material for a second course in number theory. -Panayiotis Vlamos, Zentrablatt Math, 1175 Praise for the First Edition ...a very useful addition to the many books on number theory with applications, and it is meant to be accessible to anyone from the novice to the research scientist ... [it] provides an excellent supplementary source of information for the reader, not least in the many biographical footnotes on the mathematicians involved in the subject matter, and there are also more than a thousand exercises and examples in the text. ... -P. Shiu, Zentralblatt MATH, Vol. 943show more

Table of contents

Preface Arithmetic of the Integers Induction Division Primes The Chinese Remainder Theorem Thue's Theorem Combinatorial Number Theory Partitions and Generating Functions True Primality Tests Distribution of Primes Modular Arithmetic Basic Properties Modular Perspective Arithmetic Functions: Euler, Carmichael, and Mobius Number and Sums of Divisors The Floor and the Ceiling Polynomial Congruences Primality Testing Cryptology Primitive Roots Order Existence Indices Random Number Generation Public-Key Cryptography Quadratic Residues The Legendre Symbol The Quadratic Reciprocity Law Factoring Simple Continued Fractions and Diophantine Approximation Infinite Simple Continued Fractions Periodic Simple Continued Fractions Pell's Equation and Surds Continued Fractions and Factoring Additivity-Sums of Powers Sums of Two Squares Sums of Three Squares Sums of Four Squares Sums of Cubes Diophantine Equations Norm-Form Equations The Equation ax2 + by2 + cz2 = 0 Bachet's Equation Fermat's Last Theorem Appendix A: Fundamental Facts Appendix B: Complexity Appendix C: Primesshow more

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