This book is the second collection of essays that originated as talks in the Bay Area Mathematical Adventures (BAMA) lecture series. The first collection, Mathematical Adventures for Students and Amateurs, was published in 2004. In the preface to Expeditions in Mathematics, the editors note that these talks were originally intended for middle school and high school students and teachers but they now attract a broader audience, including students at other levels, parents, and the general public. The list of speakers and authors is impressive, and the topics range from general interest, number theory, geometry, topology, combinatorics, graph theory, and applied mathematics.
There are many books which provide a collection of topics. By way of comparison, I also like Five-Minute Mathematics (Ehrhard Behrends), which provides a wider range of topics presented in less detail. An interested reader of Five-Minute Mathematics will probably want to look for more material to supplement their reading. Expeditions in Mathematics gives a thorough presentation for each topic. As might be expected, some of the papers collected here are more technical than others, but a dedicated reader could spend an hour or an afternoon on one of these papers. Many of these papers are best read with pencil and paper nearby. After the reading is finished, most of the essays include a brief answers to some of the problems posed, additional problems, references, and items for further reading.
These essays could be used as an initial reading assignment for an independent study or guided research project. In a course for mathematics majors, an instructor could use one of these essays to introduce a topic or to give a summary. Some of the essays in Expeditions in Mathematics are accessible to bright younger students, the original audience of the BAMA talks, but that would require more time and guidance. Certainly these essays would make for interesting reading if you wanted to see what is going on in an area of mathematics that is beyond your own field of expertise.
As I browsed through this book, I wished that I had access to this series of talks, and imagined myself and my students in the audience. Expeditions in Mathematics is a testimony to what certainly must be an engaging lecture series.
Mike Daven is a professor of mathematics at Mount Saint Mary College in Newburgh, New York. His background is in graph theory and combinatorics, and he has recently become interested in math trails on campus and nearby.