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CHOICE Review

Much can be expected of this book, considering the stature of its author. What more could one ask than to have Halmos offer a collection of his favorite mathematical problems complete with a commentary? Fortunately, the book delivers, in that the problems and commentary are fascinating. Also, they are presented in a format that allows each reader to browse and extend at will. The 165 problem situations are diverse, ranging across all of the common subject areas in mathematics (e.g., geometry and calculus). Directed at an audience ranging from high school students to professional mathematicians, both the difficulty and prerequisite levels vary for the problem sets. Given the problem statements, hints, and possible solution approaches, readers are encouraged to select those problems that are appropriate to their level of interest and ability. This delightful work can challenge the independent reader or serve as the basis of a college-level seminar on problem solving. It could have been improved with a reference list of "favorite" resources. J. Johnson; Western Washington University