Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well. In each lecture, the concepts, theories and methods are taken as the core. The examples serve to explain and enrich their intentions and to indicate their applications. Besides, appropriate number of test questions is available for the readers’ practice and testing purpose. Their detailed solutions are also conveniently provided. The examples are not very complicated so readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions originate from many countries all over the world. This book will serve as a useful textbook of mathematical Olympiad courses, a self-study lecture notes for students, or as a reference book for related teachers and researchers. Key Features: • For the past ten years, the level of the mathematical Oylmpiad competitions has been further raised, with the competition questions increased in depth, and the same can be said for the requirement on the ability of using knowledge synthetically. To adopt to this development, the examples and competition questions in this book are chosen for their recency • The book is self-contained, enclosing several Appendixes to equip readers with the necessary knowledge that cannot be learned from the present syllabus in schools • The detailed solutions are provide for most readers, so that it is possible for them to learn by themselves. Considering that the readers are students but not specialists, the explanations of the examples and solutions are detailed

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