UNIVERSITY TEACHING 103 



is to be a tool really useful to the engineer. There 

 is a real danger that such students may learn to re- 

 gard Mathematics as consisting merely of formulae 

 and rules which provide the means of performing 

 the numerical computations necessary for solving 

 certain kinds of problems which occur in the 

 practical sciences. Apart from the deplorable 

 effect, on the educational side, of degrading Mathe- 

 matics to this level, the practical effect of reducing 

 it to a number of rule-of-thumb processes can only 

 be to make those who learn it in so unintelligent 

 a manner incapable of applying mathematical 

 methods to any practical problem in which the 

 data differ even slightly from those in the model 

 problems which they have studied. Mathematics 

 cannot be effectively studied in a frame of mind 

 in which impatience is excited whenever the 

 application to practical problems of what is learned 

 is not immediately obvious. The mathematical 

 instruction of students of Engineering is likely to 

 be more efficient when it is imparted by a mathe- 

 matician who has acquired a sympathetic com- 

 prehension of the points of view and of the needs 

 of such students than if it is in the hands of an 

 engineer who regards Mathematics merely as a 

 subsidiary subject. 



Many important questions connected with the 

 teaching of the more advanced parts of mathematics 

 in our Universities must here be left aside. In 

 the older Universities at least, fewer students than 



