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Lecture notes on mathematical Olympiad courses. For senior section. Vol. 1 and 2. (English)
Mathematical Olympiad Series 8. Hackensack, NJ: World Scientific (ISBN 978-981-4368-94-0/set; 978-981-4368-95-7/v.1; 978-981-4368-96-4/v.2). xiv, 246~p./v.1; xiv, 282~p./v.2. (2012).
This nice two-volume collection of mathematical Olympiad problems is based on the editor’s lecture notes used for Olympiad training courses offered at different schools in Singapore during the last fifteen years. The materials are designed to help students to improve mathematical skills and logical thinking required for analyzing and solving nonstandard tasks. All problems in two volumes are organized into thirty sections; there are also nine appendices with additional information. Each section starts with a very concise explanation of methods used for solving different classes of problems. Whenever necessary, definitions and theoretical material are introduced. The ideas and techniques are illustrated on a sufficient number of examples, including Olympiad problems. At the end of each section, the reader finds two groups of questions. Those in Part A are easier and can be used for routine practice, whereas much more challenging problems from real competitions are collected in Part B. Coming from mathematical Olympiads in Australia, China, Columbia, Russia, Singapore, USA, other Asian and European countries, these problems can be used to test student’s problem-solving skills. Solutions to test problems are provided in the final part of each volume, followed by a useful index. It goes without saying that, in addition to harder problems based on traditional teaching subjects, readers are also introduced to a variety of notions, ideas and advanced techniques from modern mathematics that are not included into standard school curricula. The book is warmly recommended to school teachers searching for original ideas and challenging problems, as well as to students interested in improving their problem solving skills.
Reviewer: Svitlana P. Rogovchenko (Kristiansand)
Classification: U40
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