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.

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.