76 



SCIENCE 



[N. S. Vol. XXVIII. No. 707 



is interested or is likely to have experience 

 with in the future. 



As has been pointed out, a change in the 

 character of the problems is gradually 

 taking place in our mathematical texts. 

 Perhaps a word of caution should be given 

 lest we go too far in the opposite direc- 

 tion, by introducing problems which re- 

 quire a technical knowledge and experience 

 beyond the comprehension of our students. 

 Perry's calculus is a conspicuous illustra- 

 tion of this danger. The subjects discussed 

 in that book would form a good sequel to a 

 certain work in engineering, but the book 

 seems to be hardly suited to meet the needs 

 of American schools as a preparation for 

 engineering study. We should aim to 

 make the mathematical work practical and 

 in harmony with engineering practise, but 

 without making it at the same time tech- 

 nical in its applications, or without going 

 too far afield by teaching mathematical 

 physics. 



Another improvement which has recently 

 become noticeable in the teaching of mathe- 

 matics in this country is the breaking down 

 of the traditional barriers between the dif- 

 ferent branches and a corresponding closer 

 correlation of the different subjects in the 

 mathematical curriculum. In several of 

 our institutions the sharp division of 

 freshman work into algebra, trigonometry, 

 and analytic geometry is being more or 

 less disregarded and these subjects taught 

 as a single unit. It is thought that the 

 student is thus enabled to grasp more read- 

 ily these subjects as a whole, and that the 

 instructor can introduce much earlier the 

 principles of analytic geometry and of cal- 

 culus and postpone to the later part of the 

 course those topics which are relatively 

 difficult and not so essential to the elemen- 

 tary work of the course. 



This plan is now being followed some- 

 what closely at the University of Wiscon- 

 sin. In the first semester fifteen or twenty 



recitations are devoted to the elementary 

 portions of trigonometry. This is followed 

 by work in algebra, including the theory 

 of complex numbers, using trigonometry 

 and a large amount of graphic work, and 

 the elementary principles of analytic geom- 

 etry. In this work trigonometric compu- 

 tation and the use of the slide rule form 

 an important part. In the second semester 

 the algebra and trigonometry are continued 

 and combined with the essentials of an- 

 alytic geometry. 



This correlation of the work of the fresh- 

 man year seems to have been most thor- 

 oughly worked out at the Massachusetts 

 Institute of Technology, where Professors 

 Woods and Bailey have recently prepared 

 a text covering the work given there in the 

 freshman year, excluding, however, trig- 

 onometry. The indications are that other 

 institutions are also contemplating a revi- 

 sion and better correlation of the work of 

 the first year. 



In some of the recent books, the sharp 

 division of the calculus into differential 

 and integral calculus is done away with, 

 thus making it possible to introduce the 

 student to a wide range of easy applica- 

 tions at an early point in the course and 

 to relegate to its proper place some of the 

 more difficult parts of the differential cal- 

 culus. There is a tendency also to intro- 

 duce the methods of the calculus earlier and 

 make them the basis of portions of the an- 

 alytic geometry. For example. Rose Poly- 

 technic Institute gives a short course of 

 thirty-six recitations in the subject before 

 analytic geometry is taken, and what is 

 accomplished there in this formal way is 

 undertaken at other institutions by intro- 

 ducing into the analytics the elementary 

 notion of derivatives or by teaching the 

 two subjects simultaneously. 



While all are agreed that for engineers 

 mechanics should stand in a close and vital 

 relation to the calculus, that in fact it is 



