Fibonacci and Catalan Numbers: An Introduction

Preface

In January of 1992, I presented a minicourse at the joint national mathematics meetings held that year in Baltimore, Maryland. The minicourse had been approved by a committee of the Mathematical Association of America—the mission of that committee being the evaluation of proposed minicourses. In this case, the minicourse was especially promoted by Professor Fred Hoffman of Florida Atlantic University. Presented in two two-hour sessions, the first session of the minicourse touched upon examples, properties, and applications of the sequence of Fibonacci numbers. The second part investigated comparable ideas for the sequence of Catalan numbers. The audience was comprised primarily of college and university mathematics professors, along with a substantial number of graduate students and undergraduate students, as well as some mathematics teachers from high schools in the Baltimore and Washington, D.C. areas.

Since its first presentation, the coverage in this minicourse has expanded over the past 19 years, as I delivered the material nine additional times at later joint national mathematics meetings—the latest being the meetings held in January of 2010 in San Francisco. In addition, the topics have also been presented completely, or in part, at more than a dozen state sectional meetings of the Mathematical Association of America and at several workshops, where, on occasion, some high school students were in attendance. Evaluations provided by those who attended the lectures ...