Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and Mathematica 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 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. Mathematica 6 compatible notebooks, containing all Mathematica calculations in the text, can be downloaded from a supplemental web page. Contents
Introduction | Divisibility and Primes | Congruences | Cryptography | Quadratic Residues
Arithmetic Functions | Large Primes | Continued Fractions | Diophantine Equations
Analytic Number Theory | Elliptic Curves | Logic and Number Theory | Mathematica Basics | Web Resources | Notation Additional Resources
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