but not KI and NaCl. In Table 2
a vision," which is apparently not infew carbonates and about 35 silicates tended to be humorous. are included among the oxides. SeveralWhat is more serious is that there formulas and names are listed without are a good many mathematical statedata. No explanation is offered for ments which will confuse or be meanthis seemingly capricious coverage.ingless to the average reader. One ex-This compilation may prove useful ample is on page 93: "Interestingly to those who work within the undeenough, one may write, 1 = 0.99999 fined limits of its particular range and . . . and 23 -22.99999. .. " There is do not require such comprehensive and no explanation. In the discussion of the authoritative treatment as that given postulates for a complete ordered field by the new edition of Crystal Data, re-(pp. 96-102), it is not pointed out that cently reviewed in Science [140, 1230 the subset P is the set of positive real (1963)].numbers. Finally, some of the proofs A. PABST are probably too difficult for the read-Department of Geology and ers for whom the book was intended. Geophysics, University of California, Topics in Modern Mathematics con-Berkeley tains ten independent chapters with the following titles: "Groups and fields," "Set theory," "Boolean algebra," "Logic and computing," "Vector spaces and Mathematics matrices," "Numerical analysis," "Functions of a single variable," "Funda-Mathematical Discourses. The heart of mental concepts of calculus," "Probamathematical science. Carroll V. bility theory and statistics," and "Some Newsom. Prentice-Hall, Englewood types of geometry." There is an epi-Cliffs, N.J., 1964. x + 125 pp. Illus. logue, in which the editors express $5. their misgivings about many aspects of Topics in Modern Mathematics. Ralph the current curriculum reform in G. Stanton and Kenneth D. Fryer, American high schools. Eds. Prentice-Hall, Englewood Cliffs, Most high school teachers could N.J., 1964. xii + 187 pp. Illus. profit from reading this book. Many $5.95.topics are discussed which they will soon be teaching, if they are not al-Although a few of the same topics ready doing so. However, there is, unare discussed in both of these books, fortunately, not a single chapter about the books were written with very difwhich I do not have serious reservaferent purposes in mind. Carroll New-tions. The treatment simply does not som's Mathematical Discourses is an have the accuracy and clarity required attempt to explain to the layman what in a book of this sort. It is impossible, a deductive, or axiomatic, system is. in a brief review, to argue the point in (Why the author prefers the name detail, but perhaps the following exam-"mathematical discourse" is not clear.)ples will show what I mean.
Topics in Modern Mathematics, editedThe discussion of the null set (p. 20) by Ralph Stanton and Kenneth D.does not make it clear that what is in-Fryer, is intended chiefly for high volved is merely a convention. The school teachers.proof that 3 has no rational square In the first three chapte...