Elementary Number Theory

James S. Kraft, Lawrence C. Washington

November 24, 2014 by Chapman and Hall/CRC
Textbook - 411 Pages - 9 B/W Illustrations
ISBN 9781498702683 - CAT# K24624

USD$88.00

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Features

  • Offers a flexible presentation that allows instructors to match the text to their syllabus
  • Describes exciting applications of number theory to various problems in cryptography
  • Discusses recent developments
  • Includes "check your understanding" problems that test students on fundamental ideas, with solutions at the end of each chapter
  • Provides numerous examples as well as standard and computational exercises, with selected answers or hints in an appendix
  • Reviews the prerequisites in an appendix

Solutions manual available upon qualifying course adoption

Summary

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas.

The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat’s, Euler’s, and Wilson’s theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous cryptographic topics, such as RSA and discrete logarithms, along with recent developments.

The book offers many pedagogical features. The "check your understanding" problems scattered throughout the chapters assess whether students have learned essential information. At the end of every chapter, exercises reinforce an understanding of the material. Other exercises introduce new and interesting ideas while computer exercises reflect the kinds of explorations that number theorists often carry out in their research.

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