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Elementary Number Theory and Its Applications

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Number theory, one of the last bastions of pure mathematics, has now succumbed to the vice of having applications. And one of those applications provides the security that maintains the integrity of most major financial transactions. Therefore, it is time for the textbooks on beginning number theory to reflect the changing environment.
The material in this work is standard fare, so the emphasis here will be on the applications, as that is what makes the book stand out. The chapter devoted to applications of congruences explains divisibility tests, perpetual calendars, scheduling round-robin tournaments, computer file storage, and error checking. A chapter on cryptology takes one from the simple substitution cipher on to public key ciphers. Another hot topic introduced is the idea of the zero-knowledge proof, where a person can prove that they have a proof, without revealing significant details. Like the "pure" material, this is presented in a clean, easy-to-follow framework. Each section ends with two sets of exercises, one to do by hand and the other a set of programming projects. The exercises are generally routine, but some of the programming problems will be beyond the capability of most. The answers to the odd non-programming exercises are given at the end of the book.
With approximately one-eighth devoted to applications, this book is on the crest of the wave of changes taking place in number theory. It is the best text for this material that I have ever seen.

Published in Journal of Recreational Mathematics, reprinted with permission.