Every generation requires persuasion (or at least reminding) of the coolness of mathematics. Many books, and even most pages of certain journals, dedicate themselves to this goal. Now certain topics seem immortally cool, e.g., transfinite cardinals, the Fibonacci sequence, knots, non-Euclidean geometry, soap bubbles, zero-knowledge proofs (revisited here by B. Poonen, J.H. Conway, and T. Hsu, J. Haas and A. Thompson, F. Farris, F. Morgan, and S. Krantz, respectively). There is special interest when breaking research developments and open problems make contact with the world of stuff everyone can understand--as here in articles about twin primes, the Riemann hypothesis, and celestial mechanics (by D. Goldston, J. Conrey, and D. Saari, respectively). Coolness can also have a grounding in grim practicality, as in H. Moore's article about mathematical attacks on HIV and leukemia. but the gem of this collection? Perhaps T. Davis's article, ""The Mathematics of Sudoku,"" which reveals the unexpected depth underlying a mathematician's viewpoint concerning a widely popular pastime that one might otherwise dismiss as a trivial distraction; Davis will get many a student hooked on the joy of critically rethinking the otherwise familiar. Highly recommended."" - D.V. Feldman, CHOICE""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 paper and pencil nearby. After the reading is finished, most of the essays include a brief answer 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 experience. 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, MAA Reviews""Expeditions in Mathematics is a collection of articles that stem from talks given at the Bay Area Mathematical Adventures (BAMA) program (events are held at San Jose State University and Santa Clara University). BAMA invites mathematicians to speak on a wide range of topics to middle and high school students, parents, teachers, college students, and the public. The topics range from number theory to geometry to combinatorics to applied mathematics. This variety of topics could interest a wide variety of mathematics enthusiasts. However, if a reader is not familiar with college-level mathematics, only parts of this book will be accessible. The collection is divided into five parts. The articles in part 1, categorized as general topics, would work with younger ages or a general audience. One example is ""The Mathematics of Sudoku,"" by Tom Davis (chapter4), which deals with strategies for solving the popular puzzle. ""Maximum Volume Space Quadrilaterals,"" by Thomas Banchoff with Nicholas Haber and Aaron Mazel-Gee (chapter 13 in part 3), is difficult to follow, partly because of the lack of text references to the numbered figures. Expeditions in Mathematics would be a valuable resource for high school teachers who are working with very bright students looking for a challenge and wanting to delve deeper into an area or an application of mathematics."" - Mathematics Teacher
