Mathematical Gems II

Ross Honsberger

PREFACE

This book contains fourteen short, expository essays on elementary topics from number theory, combinatorics, and geometry. Mathematics is full of amazing things and these essays are presented in the hope that you will come to know the excitement of some of its most accessible treasures.

No matter what the level, the reader must possess an appropriate background in order to proceed comfortably. To say that a topic is elementary is not necessarily to imply that it is easy or simple. For much of this book, the reader need have little technical knowledge beyond high school mathematics. It is assumed that he is familiar also with the binomial theorem, mathematical induction, and arithmetic congruences. However, it is not expected that the book will be easy reading for many graduates straight out of high school. Some degree of mathematical maturity is presumed, and upon occasion one is required to do some rather careful thinking. It is hoped that the book will be of special interest to high school mathematics teachers and to prospective teachers.

The essays are independent and they may be read in any order. Exercises and references conclude each topic. The reader is encouraged to consider the exercises carefully, for among them are to be found some splendid problems. Complete solutions to the exercises are included.

Ross HONSBERGER

University of Waterloo

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