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Full Description
This innovative textbook leads students on a carefully guided discovery of introductory number theory. The book has two equally significant goals. The first is to help students develop mathematical thinking skills, particularly theorem-proving skills. The other goal is to help students understand some of the wonderfully rich ideas in the mathematical study of numbers. This book is appropriate for a proof transitions course, for independent study, or for a course designed as an introduction to abstract mathematics. It is designed to be used with an instructional technique variously called guided discovery or Modified Moore Method or Inquiry Based Learning (IBL). Instructors' materials explain the instructional method, which gives students a totally different experience compared to a standard lecture course. Students develop an attitude of personal reliance and a sense that they can think effectively about difficult problems; goals that are fundamental to the educational enterprise within and beyond mathematics.
Contents
0. Introduction; 1. Divide and conquer; 2. Prime time; 3. A modular world; 4. Fermat's Little theorem and Euler's theorem; 5. Public key cryptography; 6. Polynomial congruences and primitive roots; 7. The golden rule: quadratic reciprocity; 8. Pythagorean triples, sums of squares, and Fermat's Last Theorem; 9. Rationals close to irrationals and the Pell equation; 10. The search for primes; Appendix A. Mathematical induction: the domino effect; Index.
