Mathematics as Problem Solving

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.§Topics are presented in self-contained chapters, with 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.