Introduction to Algebra, for the Use of Secondary Schools and Technical Colleges

Abstract

THE appearance of this book marks another stage in the improvement which is at last being effected in English treatises on elementary algebra. How different it is from the old-fashioned text-book will be partly realised by observing that the first sixty-two pages are assigned to the discussion of the fundamental laws of algebra; that upwards of fifty pages are devoted to elementary curve-tracing; and that the elementary theory of rational functions is presented in a correct and fairly methodical shape. The notions of degree, homogeneity, and symmetry are introduced, as they ought to be, at an early opportunity, and their importance duly emphasised, and illustrated; in this and other ways the student's attention is directed to the all-important subject of algebraic form. The chapter on the resolution of integral functions into factors is both clear and scientific; this fact alone distinguishes Prof. Chrystal's work from the great majority of its predecessors. The binomial theorem, for a positive integral exponent, instead of having a special chapter devoted to it, and being treated as a sort of mathematical Rubicon, is deduced, in passing, as a particular case of distributing a product. Finally we may remark (à Propos of a recent correspondence in this journal) that the solution of a quadratic equation is made to depend on the factorising of its characteristic, and the ordinary method by “completing the square” is ignored, except, oddly enough, in one example, where it is quite unnecessary, and the factorisation is otherwise obvious.

Introduction to Algebra, for the Use of Secondary Schools and Technical Colleges.

By G. Chrystal Pp. xviii + 412 + xxvi. (London: Adam and Charles Black, 1898.)