Di Pasquale A., Do N., Mathews D. Problem Solving Tactics

Canberra: AMT Publishing, 2014. — 316 p. — ISBN: 9781876420758.What is this book about ?Each year the Australian Mathematical Olympiad Committee (AMOC) runs two training schools. These are designed to extend and challenge the mathematical skills of the 25 secondary school students who are invited to attend. Particular emphasis is given to honing the skill of problem solving. This book is based on past and present lectures given at the two annual AMOC training schools. As such it is suitable for:Anyone who wishes to qualify for an Olympiad training school in mathematics, either in Australia or overseas.
Anyone who has attended an Olympiad training school in mathematics and who would like to be better prepared should they qualify again for an invitation.
Interested students, teachers and parents, as it will give an idea of the sorts of mathematics considered there. Any mathematically able students, hobbyists or problem solvers, whether local or abroad, who would find this publication enriching.What is in this book ?The authors have gone to considerable care to showcase many of the tricks and problem-solving tactics they consider to be important for Olympiad mathematics and problem solving in general. Apart from the first chapter the topics are grouped into the four broad traditional Olympiad divisions of number theory, geometry, algebra and combinatorics. Most of the sections within each main chapter highlight a particular idea important for problem solving, thus providing over 150 such ideas in total. Each idea is illustrated with one or two problems along with solutions. For extra practice, most chapters begin with a list of problems. Although they are not necessarily in order of difficulty, we have tried to arrange them so that the first few problems tend to be easier than the later ones. Mathematics can be quite hard to read and digest and so the style has purposely been kept rather informal and conversational. The book often gives the impression that it is conversing with the reader.How do you use this book ?Most chapters do not depend much on other chapters. Therefore, apart from the first chapter, most can be studied almost independently of each other. However, where dependencies arise there are cross references. It is the opinion of the authors and many others involved in AMOC training schools that the chief way to improve one’s problem-solving ability is to go through the struggle of trying to solve problems oneself. So we recommend that:The focus of the user of this book should not be on reading solutions but on trying to solve problems.That is why solutions are not provided to the problems at the beginning of each chapter. It is also why we recommend that a problem be tried thoroughly with the showcased idea of the section in mind, before the solution is studied. We recognise that some problems are relatively easy exercises while others are of the difficulty of the International Mathematical Olympiad (IMO)—the pinnacle of problem-solving mathematics for high school students the world over. So the reader definitely should not expect to be able to solve all of the problems straight away.A4 format