Introduction to number theory
Author(s)
Bibliographic Information
Introduction to number theory
（Textbooks in mathematics）
CRC Press, Taylor & Francis Group : Chapman & Hall, c2016
2nd ed
- : hardback
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Note
Includes bibliographical references (p. 405-407) and index
Description and Table of Contents
Description
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 (R) and Maple (TM), 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.
Table of Contents
Introduction. Divisibility. Greatest Common Divisor. Primes. Congruences. Special Congruences. Primitive Roots. Cryptography. Quadratic Residues. Applications of Quadratic Residues. Sums of Squares. Further Topics in Diophantine Equations. Continued Fractions. Continued Fraction Expansions of Quadratic Irrationals. Arithmetic Functions. Large Primes. Analytic Number Theory. Elliptic Curves.
by "Nielsen BookData"