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The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions and Commentary

Kiran S. Kedlaya, Bjorn Poonen and Ravi Vakil
Mathematical Association of America
Publication Date: 
Number of Pages: 
Problem Books
Problem Book
[Reviewed by
Leo Livshits
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The William Lowell Putnam Mathematical Competition, 1995-2000 follows the now familiar structure of its two predecessors, with a few notable exceptions. The most important of these are the inclusion of a significant bibliography and of a section of hints, both of which make the book a better teaching resource for problem-solving seminars. Students will also benefit from a nicely brief and focused section "Advice to the student reader" in the introduction. The well-balanced and structured introduction, written in a friendly style, also includes a section on "The Putnam Competition over the years." It goes on to discuss scoring and basic notation. All of this should be helpful and anxiety-reducing for students picking up the book.

The solutions are well presented and many include helpful diagrams, very informative remarks and references, as well as cross-references to other Putnam problems. One gets a feeling that the authors took care to present the Putnam Competition as a mathematical endeavor firmly connected to the mainstream of mathematics, rather than an esoteric event for the lovers of mathematical puzzles.

The book concludes with a chapter presenting the winners (both individual and team) of the 1985-2000 competitions, as well as one on Putnam trivia, followed by a lively article by Bruce Reznick entitled "Some Thoughts on Writing for the Putnam," which gives readers a glimpse into the process of generating problems for the competition.

I cannot end before mentioning the typography. I appreciate the choice of the font, spacing and paper, all of which make the book more pleasant to behold than its predecessors. The use of bold font in the index to indicate references with the detailed explanation of the entry is a characteristic example of the smart choices made by the creators of the book. All in all, I consider this tome to be a must have resource for college libraries as well as for individual readers interested in ingenuity and problem solving in mathematics.

Leo Livshits ( is associate professor of mathematics at Colby College, and has directed many problem seminars and problem competitions.

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