Enhanced descriptions from Syndetics:

This text presents a logical development of number theory, focusing on the axiomatic development of number theory, showing how to prove theorems and understand the nature of number theory. Drawing applications from physics, statistics, computer science, mathematics, astronomy, cryptography and mechanics, this book features extensive worked examples which illustrate many number theory patterns. It treats applications in depth with substantive discussion of the context of each application.

Table of contents provided by Syndetics

• 0 SETS
• 1 Sets and Relations
• 2 Functions
• 3 Generalized Set Operations
• 1 Elementary Properties of Integers
• 1 Introduction
• 2 Axioms for the Integers
• 3 Principle of Induction
• 4 Division
• 5 Representation
• 6 Congruence
• 7 Application: Random Keys
• 8 Application: Random Number Generation I
• 9 Application: Two's Complement
• 2 Primes
• 1 Introduction
• 2 Prime Factorization
• 3 Distribution of the Primes
• 4 Elementary Algebraic Structures in Number Theory
• 5 Application: Pattern Matching
• 6 Application: Factoring by Pollard's r
• 3 Congruences And The Function
• 1 Introduction
• 2 Chinese Remainder Theorem
• 3 Matrices and Simultaneous Equations
• 4 Polynomials and Solutions of Polynomial Congruences
• 5 Properties of the Function f
• 6 The Order of an Integer
• 7 Primitive Roots
• 8 Indices
• 9 Quadratic Residues and the Law of Reciprocity
• 10 Jacobi Symbol
• 11 Application: Unit Orthogonal Matrices
• 12 Application: Random Number Generation II
• 13 Application: Hashing Functions
• 14 Application: Indices
• 15 Application: Cryptography
• 16 Application: Primality Testing
• 4 Arithmetic Functions
• 1 Introduction
• 2 Multiplicative Functions
• 3 The M"bius Function
• 4 Generalized M"bius Function
• 5 Application: Inversions in Physics
• 5 Continued Fractions
• 1 Introduction
• 2 Convergents
• 3 Simple Continued Fractions
• 4 Infinite Simple Continued Fractions
• 5 Pell's Equation
• 6 Application: Relative Rates
• 7 Application: Factoring
• 6 Bertrand's Postulate
• 1 Introduction
• 2 Preliminaries
• 3 Bertrand's Postulate
• 7 Diophantine Equations
• 1 Linear Diophantine Equations
• 2 Pythagorean triples
• 3 Integers as Sums of Two Squares
• 4 Quadratic Forms
• 5 Integers as Sums of Three Squares
• 6 Integers as Sums of Four Squares
• 7 The Equation ax2 + by2 + cz = 0
• 8 The Equation x4 + y4 = z
• 2 Logic And Proofs
• 1 Axiomatic Systems
• 2 Propositional Calculus
• 3 Arguments
• 4 Predicate Calculus
• 5 Mathematical Proofs
• Appendix B Peano's Postulates And Construction Of The Integers
• Appendix C

Reviews provided by Syndetics

CHOICE Review

This is not a traditional number theory text (such as those by Niven and Zuckermann or Rosen). Anderson and Bell suggest that it contains material appropriate for science majors, education majors, and mathematics majors. This is true, but instructors need to plan their courses carefully. There is a core of material presented and then several chapters on different topics that require only that core material. Besides the many applications, there are also exercises following each section, few in number but well chosen to illustrate the topics in the sections. The text itself is well written with many historical notes. As in most books designed for a diverse audience, there is always the question of how the book will compare with the specialized works designed for a more narrow audience (e.g., a number theory text aimed specifically at mathematics majors). A worthy book. Undergraduates. J. R. Burke; Gonzaga University