Preface; 1. The problems; 2. The solutions; Appendix 1. Prerequisites by problem number; Appendix 2. Problem numbers by subject; Index.
An entertaining collection of 208 accessible yet challenging mathematical puzzles, designed to appeal to problem solvers at many different levels.
Mark I. Krusemeyer is a Professor of Mathematics at Carleton College, Minnesota. George T. Gilbert is an Associate Professor of Mathematics at Texas Christian University. Loren C. Larson is an Emeritus Professor of Mathematics at St Olaf College, Minnesota.
A Mathematical Orchard by Krusemeyer (Carleton College), Gilbert
(Texas Christian Univ.), and Larson (emer., St. Olaf College) is a
book of 208 problems and solutions. It is a reworking and expansion
of The Wohascum County Problem Book (CH, Dec 93', 31-2163) by the
same authors. As is typical of problem books, the problems occupy a
small percentage of the text; in this case, just the first 43
pages. The meat of this book comes in its solutions. Each problem
is restated (some abridged) in the solutions section along with its
answer followed by one or two well-written solutions. Typical
undergraduates would find these problems quite challenging and
would need guidance from a coach to make sense of this text, but
this is where it would be most useful: as a resource for student
teams preparing for mathematics competitions. The book includes two
appendixes: one listing the problems with their prerequisites, and
a second which groups problems by subject matter. These make the
book useful for teachers looking for extra challenges for their
students."" - J.T. Noonan, CHOICE
""The book is very thoughtfully organized. Each problem is followed
by a solution page number; there are also three indices (a thorough
term indes, prerequisites by problem number, and problem numbers by
subject); that and the fact that about 25% of the problems come
with more than one solution attest to the effort made by the
authors and the sincerity of their desire to accomodate diverse
skills and interests. On the whole, the book is very easy to work
with. The metaphorical title A Mathematical Orchard is supposed to
""evoke images of such good things as vigorous growth, thoughtful
care, and delectable fruit..."" The problems are loosely ordered by
difficulty. Earlier problems are generally more difficult than the
later ones, but this is not necessarily true for nearly adjacent
problems. The solutions are lovely, very detailed and structured:
some even contain lemmas. Several are preceded with an Ideas
paragraph or two, others are followed by Comments for broader
perspective. As the authors write, ""In an ideal world, may be no
one would look at a solution before trying seriously to solve the
problems, but if you're feeling curious and are pressed for time,
you can still appreciate the problem by reading the solution and
the underlying ideas behind it."" The solutions in the book are
truly designed to be read not just to navigate the reader to an
answer. The problems in the book are all but routine; all are
original with the authors....The problems have been tried on
undergraduates at Carleton and St. Olaf Colleges and participants
at Canada/USA Mathcamp. If you are not as lucky as those kids, you
may still enjoy solving the book problems or benefit from reading
the solutions. The book does not require knowledge beyond beginning
calculus and linear algebra."" - MAA Reviews
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