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SCIENCE 



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



essential for the sound training of the spe- 

 cial student of mathematics with his limited 

 opportunity for the application of his sub- 

 ject to physical phenomena than it is for 

 the engineering student who in the future 

 is to have opened up to him that wide 

 range of applications which his technical 

 studies provide. In other words, what is 

 essential in the way of applications for the 

 engineering student in the first two years 

 of his mathematical work gives the very 

 best training for the student who is taking 

 mathematics as an element in a liberal edu- 

 cation. The proper place for diiiPerentia- 

 tion, so far as the content of the course is 

 concerned, would seem to be after the com- 

 pletion of the course in calculus rather 

 than before. I present this as a plea for 

 the general student, that he should have 

 more of the applications of his mathematics 

 rather than that the engineering student 

 should have less. Both should have thor- 

 ough drill in the fundamental principles 

 of the subject and in addition all of the 

 applications of those principles which their 

 limited experience and knowledge of phys- 

 ical phenomena will permit. No student, 

 enginering or otherwise, should be led to 

 regard his mathematical work in the same 

 light in which a carpenter may properly 

 regard his jack-plane, a mere tool with 

 which to accomplish certain results ; neither 

 should the instructor teach mathematics in 

 the spirit in which a skilled operator might 

 regard a finely-equipped machine shop 

 whose sole purpose is to make more ma- 

 chines. Both extremes are to be avoided 

 in the early courses in mathematics. The 

 opportunity for specialization and differ- 

 entiation should come later; and any stu- 

 dent who is not capable of grasping the 

 fundamental principles of the mathematics 

 usually required in an engineering course 

 should not aspire to a bachelor's degree 

 from a large university or technical school. 

 "What training is essential or desirable. 



then, on the part of the mathematical in- 

 structor of engineering students to best 

 accomplish the general results here set 

 forth? There is no doubt that the ideal 

 thing would be to take men who have 

 completed an engineering course and later 

 supplemented it by special work in mathe- 

 matics. This, however, does not seem feas- 

 ible because of the few who could be in- 

 duced to take such a course of training. 

 It would be quite impossible to induce a 

 sufficient number of engineers to take up 

 the teaching of mathematics to meet the 

 demand, even if that seemed desirable. In 

 most cases the boy enters the engineering 

 course with the view of practising his pro- 

 fession when he has completed the course. 

 As a rule he has little taste or inclination 

 for teaching, and those few who can be in- 

 duced to enter the less remunerative pro- 

 fession of teaching are absorbed, as indeed 

 they should be, by the engineering depart- 

 ments of our technical schools. To put an 

 engineering graduate at teaching mathe- 

 matics without first having had special 

 training in mathematics would be wholly 

 undesirable. Such an instructor knows 

 but little about pure mathematics beyond 

 the elementary courses which he is present- 

 ing, and, what is even worse, often has but . 

 little interest. If he can be induced to 

 take up in a serious way the study of 

 mathematics, he is in a fair way of becom- 

 ing a good teacher of the subject. I am 

 thoroughly convinced that mathematics 

 should be taught by mathematicians just 

 as engineering should be taught by trained 

 engineers; but the mathematical instructor 

 who wishes to teach engineers should be 

 familiar with the general field of applied 

 mathematics— mechanics, strength of ma- 

 terials, thermodynamics, and in addition 

 so much of the broader field of mathe- 

 matical physics as possible. 



While the mathematical instructor should 

 have some knowledge of its applications, it 



