Introduction to Number Theory, 2nd Edition

Anthony Vazzana, David Garth

December 1, 2015 by Chapman and Hall/CRC
Textbook - 414 Pages - 23 B/W Illustrations
ISBN 9781498717496 - CAT# K25444
Series: Textbooks in Mathematics

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Features

  • Presents a contemporary approach to the fundamentals of number theory, including primes, congruences, and Diophantine equations
  • Applies number theory to real-world problems, such as the ISBN system, RSA codes, and the construction of tournaments
  • Uses worked examples, numerous exercises, and popular software packages to ensure a practical understanding
  • Covers special topics in number theory, including cryptography, elliptic curves, and Hilbert’s tenth problem
  • Provides calculations, tutorials, and code online via a robust, author-maintained website

Solutions manual available with qualifying course adoption

Summary

Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments such as 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.

Ideal for a one- or two-semester undergraduate-level course, this Second Edition:

  • Features a more flexible structure that offers a greater range of options for course design
  • Adds new sections on the representations of integers and the Chinese remainder theorem
  • Expands exercise sets to encompass a wider variety of problems, many of which relate number theory to fields outside of mathematics (e.g., music)
  • Provides calculations for computational experimentation using SageMath, a free open-source mathematics software system, as well as Mathematica® and Maple™, online via a robust, author-maintained website
  • Includes a solutions manual with qualifying course adoption

By tackling both fundamental and advanced subjects—and using worked examples, numerous exercises, and popular software packages to ensure a practical understanding—Introduction to Number Theory, Second Edition instills a solid foundation of number theory knowledge.

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