ROSS HONSBERGER was born in Toronto, Canada, in 1929 and attended the University of Toronto. After more than a decade of teaching mathematics, mainly in metropolitan Toronto, he took advantage of a sabbatical leave to continue his studies at the University of Waterloo, Canada. He joined its faculty in 1964 (Department of Combinatorics and Optimization) and has been there ever since.

Combining his love of mathematics with his interest in secondary education, Professor Honsberger designed courses (e.g. one on problem solving in the spirit of G. Polya, one in combinatorial geometry, and others) especially for prospective teachers; some of these have been audiotaped. He frequently addresses high school students and teachers in Southern Ontario and is managing editor of the Ontario Secondary School Mathematics Bulletin.

Professor Honsberger has a strong interest in classical music. He asserts his acceptance of Christianity.

The nineteen essays contained in this volume are independent of one another; they represent many different aspects of mathematical thinking. Standard high school courses in algebra and geometry furnish a sufficient basis for understanding each essay.

The author was motivated by a deep desire to share his appreciation of the elegant and ingenious approaches used in thinking even about elementary mathematical topics. He was inspired by Rademacher's and Toeplitz's The Enjoyment of Mathematics, which he admires as one of the best mathematical expositions in this spirit.

The topics treated in the present volume include number theory, geometry, combinatorics, logic, probability; and the methods used often involve an interaction of these various disciplines. Some essays are easy to read, others are more challenging; some exercises are routine, others lead the reader deeper into the subject.

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