This book is an outgrowth of the authors' work in conducting problem solving seminars for undergraduates and high school teachers, in directing mathematics contests for undergraduates and high school students, and in the supervision of an undergraduate research participation program. Their experience has shown that interest in and knowledge of mathematics can be greatly strengthened by an opportunity to acquire some basic problem solving techniques and to apply these techniques to challenging problems for which the prerequisite knowledge is available.
Many students who have not had this opportunity lose confidence in themselves when they try unsuccessfully to solve non-routine problems such as those in the Mathematics Magazine or in the Putnam Intercollegiate Mathematics Competitions, conducted by the Mathematical Association of America. Those who gain self-confidence by work on challenging material at the proper level also generally have increased motivation for mastering significant mathematical concepts and for making original contributions to mathematical knowledge.
The topics chosen for this book are particularly appropriate since they are at a fairly elementary level and exhibit the interdependence of mathematical concepts. Many generalizations are suggested in the problems; the perceptive reader will be able to discover more.
The authors express their debt to all who have influenced this effort. We are especially grateful to Leonard Klosinski, Roseanna Torretto, and Josephine Hillman for their invaluable assistance.
Albuquerque, New Mexico - Abraham P. Hillman
Santa Clara, California - Gerald L. Alexanderson
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