Modern Mathematics for the Elementary Teacher. By Leslie A. Dwight. Pp. viii, 598. 1966. (Holt, Rinehart and Winston.)

Abstract

THE MATHEMATICAL GAZETTE in sequence spaces is explored much more deeply, using the methods of functional analysis. I t is implicit in the results here that many matrix transformations are automatically bounded. I t would have been in the spirit of functional analysis to make these conclusions explicit. Also, this would have simplified and illuminated the proof that the class (c, c) of matrices which transform c into itself is a Banach algebra. By observing that (c, c) is precisely the class of bounded linear transformations of c into itself, it is immediate from the general results in Chapter 4 that it is a Banach space. A disadvantage of this book for private reading is the vast number of definitions which occur. For instance, the student who needs a really elementary text might find semi-norm, paranorm, p-norm and norm too much to swallow. As a course book, however, where guidance on the relative importance of these concepts can be given, it should prove very useful for those classes for whom the standard texts are too sophisticated.