Mathematics as Problem Solving

This book joins several other books available for the preparation of young scholars for a future that involves solving mathematical pr- lems. The introductory explanations and worked problems help guide the reader without turning the additional problems into rote repe- tions of the solved ones. Retelling the best solutions and sharing the secrets of discovery are part of the process of teaching problem solving. Ideally, this process is characterized by mathematical skill, good taste, and wit. It is a characteristically personal process and the best such teachers have surely left their personal marks on students and readers. Alexander Soifer is a teacher of problem solving and his book, Mathematics as Problem Solving, is designed to introduce problem solving to the next generation. --Cecil Rousseau The American Mathematical Monthly The problems faithfully reflect the world famous Russian school of mathematics, whose folklore is carefully interwoven with more traditional topics. Many of the problems are drawn from the author's rich repertoire of personal experiences, dating back to his younger days as an outstanding competitor in his native Russia, and spanning decades and continents as an organizer of competitions at the highest level. --George Bersenyi The book contains a very nice collection of problems of various difficulty. I particularly liked the problems on combinatorics and geometry. --Paul Erdos Professor Soifer has put together a splendid collection of elementary problems designed to lead students into significant mathematical concepts and techniques. Highly recommended. --Martin Gardner To assemble so much material of the type used in Mathematical Olympiads, which has been tried and tested there, is unusual. To then present it in a form which develops themes, supported by relevant examples and problems for the reader, does the author great credit. --R. W. Whitworth The Mathematical Gazette Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this new second edition, "Mathematics as Problem Solving". Each new chapter builds off the previous one, enhancing the reader to reach new levels of using logic to solve problems. Every topic is presented in self-contained chapters, offering classical solutions as well as Soifer's own discoveries that he found through his problem-solving experiences. With roughly 200 different problems and multiple proofs for each, the reader is challenged to approach problems from different angles, and in this way can experience the beauty of mathematics. Review from the first edition: "Retelling the best solutions and sharing the secrets of discovery are part of the process of teaching problem solving. Ideally, this process is characterized by mathematical skill, good taste, and wit. It is a characteristically personal process and the best such teachers have surely left their personal marks on students and readers. Alexander Soifer is a teacher of problem solving and his book, "Mathematics as Problem Solving", is designed to introduce problem solving to the next generation".The American Mathematical Monthly Originally self-published by Alexander Soifer, 1987 at the Center for Excellence in Mathematical Education, Colorado Springs, CO.