A MATHEMATICAL ORCHARD

A Mathematical Orchard by Mark I. Krusemeyer, George T. Gilbert, & Loren C. Larson

Here is a collection of 208 challenging, original problems, with carefully worked, detailed solutions. In addition to problems from The Wohascum County Problem Book, there are about 80 new problems, many of which involve experimentation and pattern finding.

The problems are intended for undergraduates; although some knowledge of linear or abstract algebra is needed for a few of the problems, most require nothing beyond calculus. In fact, many of the problems should be accessible to high school students. On the other hand, some of the problems require considerable mathematical maturity, and most students will find few of the problems routine.

Over four-fifths of the book is devoted to presenting instructive, clear, and often elegant solutions. For many problems, multiple solutions are given. Appendices list the prerequisites for individual problems and arrange them by topic. This should be helpful to classes on problem solving and to individuals or teams preparing for contests such as the Putnam. The index can help, as well, in finding problems with a specific theme, or in recovering a half-remembered problem.