Mathematics as Problem Solving - 2nd Edition by Alexander Soifer (Paperback)

About the Book

Various elementary techniques for solving problems in algebra, geometry, and combinatorics are explored in this second edition of Mathematics as Problem Solving. Topics are presented in self-contained chapters, with classical solutions as well as Soifer's own discoveries that he found in 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 by these means, experience the beauty of mathematics.

Book Synopsis

This book joins several other books available for the preparation of young scholars for a future that involves solving mathematical pr- lems. This training not only increases their ?tness in competitions, but may also help them in other endeavors they may engage in the future. The book is a diversi?ed collection of problems from all areas of high school mathematics, and is written in a lively and engaging way. The introductory explanations and worked problems help guide the reader without turning the additional problems into rote repe- tions of the solved ones. The book should become an essential tool in the armamentarium of faculty involved with training future competitors. Branko Grunbaum ] Professor of Mathematics University of Washington June 2008, Seattle, Washington Foreword This was the ?rst of Alexander Soifer's books, I think, preceding How Does One Cut a Triangle? by a few years. It is short on anecdote and reminiscence, but there is charm in its youthful brusqueness and let- get-right-to-business muscularity. And, mainly, there is a huge lode of problems, very good ones worked out and very good ones left to the reader to work out.

From the Back Cover

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

Review Quotes

From the reviews:

"How does one describe a mathematician? I know no better way than to read this delightful book. For Alexander Soifer has not just written another book about mathematics. He has opened up his heart---and in the process his great love for mathematics, his creative ability, his respect for and skill in teaching, his joy in living all shine through. I invite you to come meet a dear friend and share his exhilaration and insight." --- PHILIP L. ENGEL

From the reviews of the second edition:

"...this book can be the portal that leads the reader into the world of mathematics."
--- Cristinel Mortici (Targoviste)ür Mathematik, Zentralblatt f

"This is a very readable collection of interesting problems of varying levels of difficulty. ... It is so delightfully written that anyone who simply likes working on challenging problems could read it independently. ... More than 150 problems are included in this collection. ... helpful for an instructor who is looking for ways of integrating problem solving into a particular course, and might be useful for coaching a mathematics competition team. This ... book would be a good resource for an instructor or coach." ---Sr. Barbara E. Reynolds, The Mathematical Association of America

"The author grew up in the problem solving atmosphere in Moscow and collected about 200 problems from his experience in mathematical clubs, schools, and Olympiads. ... Many problems ... are discussed in detail and in a way that can be followed easily. So the book can also be recommended to young students." (H. Humenberger, Monatshefte für Mathematik, Vol. 159 (1-2), January, 2010)

"Clearly attractiveness of problems and beauty of solution have been major criteria in the selection for this book. The author devised many of the problems, and his enthusiasm is evident. ... I am confident that readers will find this bookto be a valuable showcase for 'what (pure) mathematics is really like'." (John Baylis, The Mathematical Gazette, Vol. 95 (532), March, 2011)