Enhanced descriptions from Syndetics:

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.

Reviews provided by Syndetics

CHOICE Review

"Long overdue" is the best way to describe this book. Anyone who has tried to prepare high school students to take on an olympiad-level problem in mathematics knows the frustration of trying to build competence in concepts and techniques not found in the standard math curriculum. Lozansky and Rousseau's text is a great step in the direction of filling gaps. At the difficulty level of an olympiad exam, the key areas explored include number theory (e.g., congruences, Diophantine equations, quadratic reciprocity), algebra (e.g., polynomial equations, symmetric functions, classical inequalities), and combinatorics (e.g., counting theorems, recurrence, generating functions, pigeonhole principle, external problems). The best feature is the exploration of these areas within the context of solving problems from exams in previous American Invitational Mathematics Examinations and US Mathematical Olympiads. A reference list and a hints/answers section complement the text. Though designed for coaches of olympiad-level students, high school teachers also can use this text as an enrichment resource to both instruct and challenge accelerated students. General readers; lower-division undergraduates. J. Johnson Western Washington University