Exploring, Investigating and Discovering in Mathematics

We present here the English version of the Romanian first edition (V. Berinde: Ex­ plorare, investigare si descoperire in matematica, Editura Efemeride, Baia Mare, 2001). There are no major changes. Only a few printing errors were corrected. When transcribing Romanian names or denominations we did not use the diacrit­ ical marks. Our purpose is to provide an introduction to creative problem solving tech­ niques with particular emphasis on how to develop inventive skills in students. We present an array of 24 carefully selected themes that range over all the main chapters in elementary mathematics: arithmetic, algebra, geometry, analysis as well as applied mathematics. Main goal is to offer a systematic illustration of how to organize the natural transition from problem solving activity toward exploring, investigating and discovering new facts and results. The book is addressed mainly to students, young mathematicians, and teach­ ers, involved or/and actively working in mathematics competitions and training gifted people. It collects many valuable techniques for solving various classes of difficult problems and, simultaneously, offers a comprehensive introduction to cre­ ating new problems. The book should also be of interest to anybody who is in any way connected to mathematics or interested in the creative process and in mathematics as an art.

"In the spirit of George Polya's classic treatise How to Solve It: A New Aspect of Mathematical Method, this book is Vasile Berinde's attempt to "algorithmetize" the creative process involved in problem-solving.... The author's stated goals are twofold. The most obvious aim is to provide methods for solving some difficult problems. But on a deeper level, he is trying to grow new research mathematicians by planting the seeds that will develop into the skills they will need to do original research.... Each of the 24 chapters begins with a source or starting problem and its solution. Then the fun begins! Remarks about the "essence" of the problem and its solution suggest new directions to explore, and these investigations lead to generalizations and the formulation of related problems, sometimes building a "factory" of new problems.

From the first page I eagerly grabbed my pencil and a stack of scratch paper, and set to work as I happily read along.... I recommend the book for all lovers of mathematics, but especially students and teachers who participate in mathematics contests and practice problem solving."

―MAA Online