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SCIENCE 



[N. S. Vol. XXVIII. No. 714 



ment the application of two of these 

 principles. 



First, it is necessary for the engineering 

 student to have an ample undergraduate 

 course in mathematics, and such an ex- 

 tended drill in and habitual acquaintance 

 with its processes that when he has for- 

 gotten nine tenths of it, just as he will of 

 this and all other subjects which he studies 

 in college, what remains with him will be 

 a sufficient equipment in this line for his 

 professional career. In other subjects his 

 residuum of knowledge is easily refreshed 

 and increased. Not so in mathematics. 

 The stock of mathematical knowledge of 

 which he is easily master on entering his 

 profession will practically be the end of 

 his attainments in \hat direction. Re- 

 stricting the course in mathematics to bare 

 essentials is suicidal, for of it a small frac- 

 tion only will remain as a permanent pos- 

 session, and that fraction is likely to be 

 smaller, the smaller the amount originally 

 attempted. 



Second, the teacher of mathematics is 

 prone to think that a clear presentation of 

 mathematical truth on his part, and a 

 logical demonstration by the student, are 

 all that is required in this subject. But 

 important as these things assuredly are, 

 they are insufficient to produce successful 

 results. The question is one in which 

 human interest is really of more im- 

 portance than logic, for mathematical 

 knowledge can not be successfully im- 

 parted unless genuine interest on the part 

 of the student can be in some way aroused. 

 It goes without saying, that the teacher 

 must first of all have that interest himself 

 or he ceases to be a fit teacher. How he 

 will awaken interest in his pupil depends 

 upon his own personality. Many do this 

 by help of problems which elucidate and 

 apply the principles. Just here lies the 

 reason for the usual inability of pro- 

 fessional engineers to teach mathematics. 



They have no interest in mathematics 

 itself. It is the engineering problem alone 

 that interests them. To this matter of 

 interest, or the lack of it, may be traced 

 the failure which is apt to attend the sepa- 

 ration of classes into divisions according 

 to scholarship, for in that case the divisions 

 made up of poor students lose the impetus 

 to be derived from the interest which the 

 good students exhibit in their work in 

 which all participate to some degree. 



By S. M. Barton, Professor of Mathe- 

 matics, University of the South. 

 While standing here in the heart of the 

 modern, bustling city of Chicago, and 

 listening to this discussion, my mind goes 

 back to the ancient city of Tarentum and 

 her distinguished governor, Archytas. 

 Archytas, while an able mathematician, 

 was too practical, as we learn, to suit the 

 ideas of the Platonic School, who objected 

 to his mechanical solutions of certain 

 mathematical problems as interfering with 

 pure reasoning. Now, while I take an im- 

 mense interest in applied mathematics 

 (what mathematician at this day would 

 not!) yet I confess to a feeling of sym- 

 pathy with Plato in his condemnation of 

 Archytas. At any rate I wish to enter 

 my protest against a possible tendency to 

 degrade mathematical teaching to the 

 memorizing of thumb-rules, and to urge the 

 advantage of a strong backbone of pure 

 mathematics in our engineering courses. 



I read with interest a paper presented 

 at the Ithaca meeting of the Society for 

 the Promotion of Engineering Education, 

 by Professor Arthur E. Haynes of the 

 University of Minnesota, in justification of 

 the use of the expression "engineering- 

 mathematics." I must say I was at first 

 somewhat shocked by the expression, for 

 I had always believed that mathematics is 

 mathematics take it when and where you 

 will. While I would agree heartily with 



