Barbara Hall Partee, Fundamentals of mathematics for linguistics . Dordrecht and London: D. Reidel, and Stamford, Conn.: Greylock, 1978. Pp. xiii + 242.

Why should a linguist study mathematics? Certainly, there are several branches of applied mathematics of more than purely intellectual interest to linguists: a psycholinguist or sociolinguist, or indeed anyone who proposes to interpret numerical data or relative rankings, must not be ignorant of STATISTICS; INFORMATION THEORY has on occasion been appealed to in discussions of linguistic theory; CYBERNETICS (one area of the mathematical theory of optimization) holds some interest for linguists, languages and language users being complex systems, such systems being in turn the subject matter of cybernetics; AUTOMATA THEORY, which developed from an analogy between abstract automata and the nervous systems of living things, similarly shows promise; and even MATHEMATICAL PHYSICS is not without relevance, since the human articulatory mechanism is, among other things, a physical system involving both organs with important limiting mechanical properties and also the flow of a fluid. What of pure mathematics? The giant area of ANALYSIS, which deals with continuity and infinity, and for which the concept of derivative is central, encompasses several fields of importance to at least some linguists, in particular Fourier analysis as it applies to acoustics, probability theory in statistics, and even differential equations (the predictions of glottochronology being based on the solution of a particular differential equation). Recent attempts by the French mathematician Rene Thorn to apply his catastrophe theory to linguistic analysis invoke the concepts and methods of TOPOLOGY. The areas of GEOMETRY and NUMBER THEORY I believe to be essentially without professional appeal to linguistics, but the basic apparatus of the two remaining areas of pure mathematics, SET THEORY and (abstract) ALGEBRA, can be argued to be virtual prerequisites for theoretical linguistics. It is to these last two areas to the fundamentals of mathematical logic (closely related to both set theory and algebra) and to automata theory (as a theory of the characterization of certain infinite sets) that Partee's book is devoted; it does not, fortunately, cover the ' fundamentals of mathematics for linguistics', but rather something more along the lines of'fundamentals of discrete mathematics for theoretical linguistics', quite a large and challenging field as it is.