Introduction to Number Theory

Anthony Vazzana, Martin Erickson, Anthony Vazzana, David Garth

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October 30, 2007 by Chapman and Hall/CRC
Textbook - 536 Pages - 26 B/W Illustrations
ISBN 9781584889373 - CAT# C9373
Series: Textbooks in Mathematics

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Features

  • Presents a modern treatment of the fundamentals of number theory, including primes, congruences, and Diophantine equations
  • Contains an entire chapter on cryptography
  • Covers special topics in number theory, including elliptic curves and Hilbert’s tenth problem
  • Uses Mathematica and Maple calculations to elucidate and expand on the theory covered
  • Applies number theory to real-world problems, such as the ISBN system, RSA codes, and the construction of tournaments
  • Provides a supplemental web page with Mathematica notebooks, Maple worksheets, and links to Internet resources
  • Includes over 100 worked examples and over 500 exercises, along with a solutions manual for qualifying instructors
  • Summary

    One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.

    This classroom-tested, student-friendly text covers a wide range of subjects, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments that include cryptography, the theory of elliptic curves, and the negative solution of Hilbert’s tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Euler’s theorem in RSA encryption, and quadratic residues in the construction of tournaments. The book interweaves the theoretical development of the material with Mathematica® and Maple™ calculations while giving brief tutorials on the software in the appendices.

    Highlighting both fundamental and advanced topics, this introduction provides all of the tools to achieve a solid foundation in number theory.