132 



SCIENCE 



[N. S. Vol. XXVIII. No. 709 



The practical questions which the dis- 

 cussion of this subject presents are these : 



What mathematical subject-matter should 

 be covered? And, 



How should it be taught? 



The first difficulty is that there is not, 

 and can not be, a differentiation in tech- 

 nical education which is at all comparable 

 with the wide range of occupations into 

 which graduates will enter. We may as- 

 sume, therefore, that we are considering the 

 case of the average engineering student, 

 taking for granted that options may be 

 used by the best students for enabling 

 them to take up the more advanced and 

 difficult mathematics. Obviously the stu- 

 dent should have enough mathematics to 

 enable him to demonstrate the important 

 engineering laws and formulas and to read 

 intelligently mathematically written engi- 

 neering literature. While only the rela- 

 tively simple mathematics is commonly 

 used by engineers, yet the ability to handle 

 new problems with confidence requires a 

 thorough understanding and appreciation 

 of the significance of the mathematical and 

 physical basis of the laws and phenomena 

 he is to use. A man who is a thorough 

 mathematician and knows how to apply 

 his knowledge has a great advantage over 

 the pure mathematician or the man with- 

 out mathematical equipment. The better 

 knowledge one has of the complex, the 

 more certainty he has in applying the 

 simple. A student should understand 

 something of the power of the advanced 

 mathematics and the field of its effi- 

 cient application. Although he may 

 not be expert in using it himself, he 

 will know when to call for a mathematical 

 expert. 



An engineer of fairly wide experience 

 remarked a short time ago : ' ' The ordinary 

 engineer does not use higher mathematics 

 because he doesn't know how. He does 

 not have the proper conception of the 



fundamental principles of the calculus be- 

 cause the subject has been taught by men 

 whose ideals are those of pure mathe- 

 matics. ' ' 



If mathematics is something for engi- 

 neers to use, let its use be taught to engi- 

 neering students. After the fundamentals 

 ape learned, the students should attack the 

 engineering problem at once and bring in 

 mathematics as a means of solving it. 

 Mathematics is often advocated for de- 

 veloping the reasoning powers and the 

 ability to reason from cause to effect. 

 There is danger, however, that mathe- 

 matical machinery may make the mere 

 process obscure the cause and the effect. 

 Let them be foremost, with the process 

 secondary or auxiliary to them. 



The way mathematics is brought to bear 

 on some engineering problems reminds one 

 of the story of the old lady who greatly 

 admired her preacher because he could 

 take a simple text and make it so very 

 complicated. 



Old traditions have not wholly disap- 

 peared, the fear of degrading the pure 

 science of mathematics by applying it to 

 useful things still lingers— in influence, if 

 not in precept. We must go further and 

 adapt mathematics to engineering, not only 

 in subject matter, but in method. A 

 mathematical teacher with no patience for 

 anything except mathematics will probably 

 teach a kind of mathematics which has no 

 connection with anything except mathe- 

 matics. Engineering mathematics may be 

 better taught as a part of engineering by 

 an engineer, than as a part of mathe- 

 matics by a pure mathematician. Tke 

 maker of levels and transits who is expert 

 in the construction of the instruments and 

 an enthusiast over the accuracy of the sur- 

 faces, the excellence of the bearings, the 

 near approach to perfection in the gradua- 

 tion and the general refinement and beauty 

 of workmanship, may make a good in- 



