REVIEWS 



MATHEMATICS 



The Teaching of Algebra (including Trigonometry). By T. Percy Nunn 

 M.A., D.Sc. [Pp. xiv + 616.] (London: Longmans, Green & Co. 

 Price js. 6d.) 



Exercises in Algebra (including Trigonometry). By T. Percy Nunn, M.A., 

 D.Sc. Parti. [Pp.x + 421.] (London: Longmans, Green & Co. With- 

 out answers, price 3^. 6d. With answers, price 4s.) 



Exercises in Algebra (including Trigonometry). By T. Percy Nunn, M.A., 

 D.Sc. Part II. [Pp. xi+551.] (London: Longmans, Green & Co. 

 Without answers, price 6s. With answers, price 6s. 6d.) 



"There are situations," Dr. Middleton remarks, "too delicate to be clothed in 

 positive definitions." Perhaps algebra is one of them ; at any rate Prof. Nunn 

 confesses in his opening paragraph that "the proper definition of algebra may 

 easily be carried to a point where its interest becomes academic rather than 

 practical." But though an author may, with propriety, evade the issue at the 

 opening of his book, he cannot do so for long. His book is the answer to the 

 question proposed in the title. Certainly the answer given in this threefold 

 volume is one of striking originality. 



Writers on algebra work in two fields — the well known and frequently ploughed 

 tracts which extend " up to and including quadratic equations," and then the 

 unenclosed pastures of higher algebra. Tradition seems alone to mark out the 

 bounds of the latter course : its items are unrelated, their discussion is partial and 

 generally unscientific. A mathematician who has not been acquainted in his 

 training with our higher algebras would wonder at the arrangement and selection 

 of the topics discussed in such a study. He would wonder why theory of numbers 

 was included and might also be surprised at a chapter, or chapters, devoted to the 

 reduction of quadratic surds ; and he would certainly condemn the divorce of two 

 such closely related subjects. Now Prof. Nunn has once and for all cut himself 

 adrift from tradition and made every reader think for himself what should, and 

 should not, be included in a course of algebra. For this every teacher owes 

 him gratitude, and it is not only for originality that we should be grateful : there 

 is throughout these books such an unusual refreshment and novelty of treatment 

 that even when we are not convinced we are stimulated and helped. 



The first volume is described by the title of the Teaching of Algebra : it is 

 perhaps, judging from a hint in the preface, based upon lectures to teachers, and 

 here and there, but fortunately not too often, it shows signs of its origin. It is 

 really an illuminating and instructive talk about algebra and other mathematical 

 topics. Philosophy and history pleasantly season the discourse. A general 

 introduction, in which the nature of algebra is the theme, is followed by Part I., 

 which is divided into three sections dealing with non-directed nupbers, directed 

 numbers, and logarithms, and Part II., which contains trigonometry of the sphere, 

 complex numbers, periodic functions, limits, and statistics. Many of the sections 



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