Cecil Rousseau – författare

Problem-solving competitions for mathematically talented sec­ ondary school students have burgeoned in recent years. The number of countries taking part in the International Mathematical Olympiad (IMO) has increased dramatically. In the United States, potential IMO team members are identified through the USA Mathematical Olympiad (USAMO), and most other participating countries use a similar selection procedure. Thus the number of such competitions has grown, and this growth has been accompanied by increased public interest in the accomplishments of mathematically talented young people. There is a significant gap between what most high school math­ ematics programs teach and what is expected of an IMO participant. This book is part of an effort to bridge that gap. It is written for students who have shown talent in mathematics but lack the back­ ground and experience necessary to solve olympiad-level problems. We try to provide some of that background and experience by point­ out useful theorems and techniques and by providing a suitable ing collection of examples and exercises. This book covers only a fraction of the topics normally rep­ resented in competitions such as the USAMO and IMO. Another volume would be necessary to cover geometry, and there are other v VI Preface special topics that need to be studied as part of preparation for olympiad-level competitions. At the end of the book we provide a list of resources for further study.

The Mathematical Olypiad books, covering the USA Mathematical Olypiad (USAMO) and the International Mathematical Olypiad (IMO), have been published annually by the MAA American Mathematics Competitions since 1976. This is the sixth volume in that series published by the MAA in its Problem Book series. The IMO is the work mathematics championship for high school students. It takes place annually in a different country each year. The aims of the IMO are (1) to discover, encourage and challenge mathematically gifted young people in all countries; (2) to foster friendships between mathematicians around the world; (3) to create an opportunity for the exchange of information on school syllabi and practice throughout the world. The USAMO and the Team Selection Test (TST) are the last two stages of the selection process for the United states of America IMO team. The preceding examinations are the AMC 10 or AMC12 and the American Invitational Mathematics Examination (AIME). Participation in the AIME, USAMO, and the TST is by invitation only, based on performance in the preceding exams of the sequence. Through the AMC contests and the IMO, young gifted mathematicians are identified and recognized while they are still in secondary school. Participation in the competitions provides them with the chance to measure themselves against other exceptional students from all over the world. This work was prepared by Zuming Feng, Melanie Matchett Wood, the Leader and Deputy Leader of the 2004 USA IMO team, and by Cecil Rousseau, the chair of the USAMO Committee. In addition to presenting their own carefully written solutions to the problems, Zuming and Melanie provide remarkable solutions developed by the examination committees, contestants, and experts, during or after the contests. They also provide a detailed report of the 2000 2004 USAMO/IMO results and a comprehensive guide to other material that emphasize advances problem-solving.This collection of excellent problems and beautiful solutions is a valuable companion for students who wish to develop their interest in mathematics outside the school curriculum and to deepen their knowledge of mathematics.