The Theory of Remainders

An imaginative introduction to number theory, this unique approach employs a pair of fictional characters, Ant and Gnam. Ant leads Gnam through a variety of theories, and together, they put the theories into action?applying linear diophantine equations to football scoring, using a black-magic device to simplify problems in modular structures, and developing intriguing modifications to the rules of chess.Appropriate for anyone familiar with algebra at the high-school level, The Theory of Remainders offers a captivating introduction to both number theory and abstract algebra. Both elementary and challenging, it provides a view of mathematics as a conceptual net and illustrates the differences between conceptual and paraconceptual claims?an excellent start to expanding students' perspectives on mathematics.Exercises throughout the book form an integral part of the text, extending students' experience with the concepts under discussion and presenting opportunities to observe patterns. In addition to the exercises, a series of optional problems allows more advanced readers to further develop the concepts.

Preface1. The Black Magic Device2. The Modular Systems 3. Basic Concepts of Factorization and Divisibility 4. The Algebraic Structure of the Modular Systems5. Remainder Tests6. The Football Problem: Linear Diophantine Equations 7. Forward-Looking and Right-Thinking Male Chauvinist Chess 8. Miscellaneous Problems 9. Solutions to Problems CommentaryIndex