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Journals ACM SIGACT News Volume 31 Issue 4

less information t h a n the characteristic polynomial from Chapter 8. Polynomials can also be used to describe knots, including the Jones and Kauffman polynomials which were discovered in the 1980's. Using these polynomials, which are closely related to Tutte's polynomial, one can prove such things as the inequivalence of two knots. This chapter is very introductory, and only begins to scratch the surface, as Bollob~s notes. Opinion As an introduction to the mathematical study of graph theory, I enjoyed the book. T h e pacing early in each chapter was slow for me, but it sped up before the pacing got tedious, and the book made pleasant evening reading, as well as good discussion fodder. The problems were enjoyable and challenging, and m a n y of the proofs were interesting, including some t h a t were positively lyrical. A grounding in the different fields of mathematics t h a t Bollob~s discusses is not absolutely necessary, since he takes care to provide the relevant definitions, although comfort with these other fields makes for easier reading. The mathematical grounding is useful for students of m a t h e m a t i c s

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Review of A=B 5 by Marko Petkovsek, Herbert S. Wilf, and Doron Zeilberger

Kreinovich, Vladik
ACM SIGACT News , Volume 31 (4)
Association for Computing Machinery – Dec 1, 2000

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