Expeditions in Mathematics

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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

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