TAILIEUCHUNG - Math Problem Book I

A first major defect lies in its insistence that (real world) problem solv- ing must be the focus of school mathematics ([N1], ) and the particular way this decision is implemented. A second major defect is that the floor of mathematics education has been set far too low (cf. [N1], ). The ceiling, which is described as “the NCTM Standards for College-Intending Students”, is consequently also dragged down. A third major defect is [N1]’s failure to confront the pressing issue of how one single mandated curriculum can be used for all students, no matter their mathematical capabilities. All these defects are inter-related | Math Problem Book I compiled by Kin Y. Li Department of Mathematics Hong Kong University of Science and Technology Copyright 2001 Hong Kong Mathematical Society IMO HK Committee. Printed in Hong Kong Preface There are over fifty countries in the world nowadays that hold mathematical olympiads at the secondary school level annually. In Hungary Russia and Romania mathematical competitions have a long history dating back to the late 1800 s in Hungary s case. Many professional or amateur mathematicians developed their interest in math by working on these olympiad problems in their youths and some in their adulthoods as well. The problems in this book came from many sources. For those involved in international math competitions they no doubt will recognize many of these problems. We tried to identify the sources whenever possible but there are still some that escape US at the moment. Hopefully in future editions of the book we can fill in these missing sources with the help of the knowledgeable readers. This book is for students who have creative minds and are interested in mathematics. Through problem solving they will learn a great deal more than school curricula can offer and will sharpen their analytical skills. We hope the problems collected in this book will stimulate them and seduce them to deeper understanding of what mathematics is all about. We hope the international math communities support our efforts for using these brilliant problems and solutions to attract our young students to mathematics. Most of the problems have been used in practice sessions for students participated in the Hong Kong IMO training program. We are especially pleased with the efforts of these students. In fact the original motivation for writing the book was to reward them in some ways especially those who worked so hard to become reserve or team members. It is only fitting to list their names along with their solutions. Again there are unsung heros iii who contributed solutions but .

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