Mathematics as Problem Solving

1. Front Matter

   Pages 1-16

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2. Language and Some Celebrated Ideas

   • Alexander Soifer

   Pages 1-18

3. Numbers

   • Alexander Soifer

   Pages 19-25

4. Algebra

   • Alexander Soifer

   Pages 27-43

5. Geometry

   • Alexander Soifer

   Pages 45-75

6. Combinatorial Problems

   • Alexander Soifer

   Pages 77-92

7. Chess 7 × 7

   • Alexander Soifer

   Pages 93-102

8. Farewell to the Reader

   • Alexander Soifer

   Pages 103-104

9. Back Matter

   Pages 1-2

   PDF

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.

• Algebra
• Problem-solving
• combinatorial problems
• geometry
• induction
• mathematics
• pigeonhole principle
• proof
• proof writing
• combinatorics

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 book to be a valuable showcase for ‘what (pure) mathematics is really like’.” (John Baylis, The Mathematical Gazette, Vol. 95 (532), March, 2011)

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