Unlike its rigorous and detailed predecessor William Lowell Putnam Mathematical Competition Problems and Solutions: 1938–1964, this book is quite concise: it covers a roughly similar time span in one-fifth the space. The competition problems are presented chronologically in the first section. The second section contains the solutions, roughly three to five per page, taking up the last four-fifths of the book.
Students participating in competition mathematics will benefit from these actual species of problem, seen “in the field.” However, anyone interested in problem solving at the advanced collegiate level will find the quality and diversity of the problems presented here both challenging and fun. Having the official solution safely several pages away allows one to solve first and compare later.
Winning teams and students from 1965 through 1984 are listed in an appendix. An index of problems by type, ranging from abstract algebra to Wallis product, allows the work to serve as a reference for challenging student questions on many topics. This compendium is a problem solver’s delight and the unadorned presentation (as compared to the previous volume) in no way distracts from the historical interest and value of this potpourri of mathematics.
Tom Schulte is a Senior Software Engineer at Plex Systems in Auburn Hills, Michigan.