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SCIENCE 



[N. S. Vol. XXVIII. No. 710 



present mathematical program of the engi- 

 neering schools on the ground that it is 

 unnecessarily extensive. From personal 

 observation, I can say that the program 

 there covers a considerably wider range 

 than in the average American college. In 

 the first place, a student entering an engi- 

 neering college on the European continent 

 must already know the analytical geom- 

 etry, the descriptive geometry, the rudi- 

 ments of differential and integral cal- 

 culus, none of which are taught here until 

 the student enters college. The average 

 length of a college engineering course 

 abroad is four years, one of the exceptions 

 being the Ecole Centrale, of Paris, France, 

 where the course is only three years, but 

 where the entering examinations are of a 

 comparatively high standard and the stu- 

 dents must be above the average in ability 

 and application in order to hold their own 

 during the college course. It is obvious, 

 therefore, that in American colleges, time 

 is spent on pure mathematics which could 

 be devoted to practical study. I believe 

 the time will come when only applied 

 mathematics wiU be taught in colleges, and 

 all necessary abstract mathematics will 

 form a part of the conditions for enter- 

 ing. 



As time goes on, every profession tends 

 more and more towards specialization. 

 This tendency is quite marked in the engi- 

 neering profession. It would take too 

 long to enumerate all of these special 

 branches of engineering, but nearly every 

 branch demands a somewhat different 

 mathematical training. The time may 

 come when this specialization will extend 

 over the study of abstract mathematics, 

 differing with each student. according to 

 the branch of engineering he intends to 

 follow. For instance, a railway engineer 

 who may aspire to become a railroad 

 official requires less knowledge of calculus 

 than an electrical or a bridge engineer ; on 



the other hand, he requires a greater 

 knowledge of geology than the electrical 

 engineer, and a greater knowledge of com- 

 mon law than the bridge engineer. As 

 my remarks are merely intended to fur- 

 nish topics for discussion, I will put the 

 following question: In view of the fact 

 of the steadily growing scope of special 

 education will it be desirable and possible 

 to specialize mathematical courses in col- 

 leges and adapt them to each branch of 

 engineering? This, as I understand, is 

 done at present only to a small extent in 

 applied mathematics. 



Bridge engineering, of which I have 

 made a specialty, requires probably as high 

 a mathematical training as any other 

 branch of the profession, and yet, I find 

 that part of the higher mathematics which 

 I have studied in college, apart from the 

 drilling features of such studies, has been 

 entirely useless ; for instance, the theory of 

 differential equations. The time I spent 

 on it, though considerable, was not suffi- 

 cient to make me understand it thoroughly, 

 and would have been better employed in 

 the study of the methods of least work, for 

 instance, which no bridge engineer should 

 neglect to study. 



On perusing the elementary books used 

 in high schools, I have been often struck 

 with the dry, uninteresting manner in which 

 the various subjects are being treated. The 

 examples are mostly abstract, very few 

 practical problems to work out. Unless 

 the student is very intelligent, his mind re- 

 tains nothing beyond a chaos of formulae 

 hard to remember and a few mechanical 

 means of solving abstract problems. He is 

 incapable of applying an equation to a 

 practical problem. The methods of pre- 

 sentation should, therefore, be such that the 

 student knows the why and wherefore of 

 each operation — in other words, that he 

 learns to think mathematically. This 

 training in mathematical thinking should 



