








Introduction to Number Theory












Publisher:  Chapman & Hall/CRC (Boca Raton, FL) 
Additional cataloguing information:  From the series Discrete Mathematics and Its Implications, ed. Kenneth H. Rosen 
  






CoreTopics 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 twosemester course, Introduction to Number Theory uses worked examples, numerous exercises, and Mathematica to describe a diverse array of number theory topics. This classroomtested, studentfriendly 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 realworld 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.












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, MasseyOmura, Mersenne, prime number, Pythagorean, quadratic, Riemann, Robinson, Wiles






http://www2.truman.edu/~erickson/introduction_to_number_theory







   
 
