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Introduction to Number Theory

Martin Erickson
Anthony Vazzana
Book information

Publisher: Chapman & Hall/CRC (Boca Raton, FL)
Copyright year: 2007
ISBN: 1584889373
Medium: Hardcover
Pages: 521
Out of print?: N
Additional cataloguing information: From the series Discrete Mathematics and Its Implications, ed. Kenneth H. Rosen
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Introduction | Divisibility and Primes | Congruences | Cryptography | Quadratic Residues
Further Topics
Arithmetic Functions | Large Primes | Continued Fractions | Diophantine Equations
Advanced Topics
Analytic Number Theory | Elliptic Curves | Logic and Number Theory | Mathematica Basics | Web Resources | Notation

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.

*Mathematics > Algebra
*Mathematics > Calculus and Analysis
*Mathematics > Discrete Mathematics > Combinatorics
*Mathematics > Number Theory

Mathematica 5.2, Mathematica 6, Catalan, Cauchy, Chebyshev, continued fraction, Diophantine representation, Diophantine equation, Dirichlet, elliptic curve, Euclid, Euler, facotrization methods, Fermat, Fundamental Theorem, Gauss, Hadamard, Lagrange, Massey-Omura, Mersenne, prime number, Pythagorean, quadratic, Riemann, Robinson, Wiles