Septembeb 4, 1908] 



SCIENCE 



293 



algebra is more difficult than trigonometry 

 and this determines their order in our 

 program. 



Placing trigonometry first and giving it 

 so much time has developed with us several 

 interesting facts. 



1. Being easy to understand and having 

 interesting applications, it naturally fol- 

 lows secondary work. 



2. While trigonometry is easy to under- 

 stand, yet to acquire facility in its use and 

 absolute mastery over it as a fundamental 

 science requires close and long-continued 

 study, yet the student, ambitious to become 

 an engineer, quickly sees that he must have 

 facility in this subject and mastery over it. 



As a subject of study, therefore, at the 

 beginning of a young man's college career 

 it is well adapted to give power and to 

 instill habits of thoroughness, application, 

 concentration and mastery. 



3. Engineers have been recommending 

 that a generous amount of time shall be 

 given to trigonometry, at the expense of 

 the calculus if necessary. 



4. The subject is used to review and 

 emphasize much of the preparatory mathe- 

 matics, while it is also used to clear the 

 way for that which is to come. 



Another peculiarity in which Purdue 

 stands almost alone we are quite prepared 

 to defend. We do not crowd the pure 

 mathematical work into the first two years, 

 much less into the first year, but give it 

 an hour less in the second year, than the 

 first, yet at the outset of the third year, 

 with his first course of calculus fairly 

 mastered, we have the student well pre- 

 pared to begin attack upon theoretical me- 

 chanics and kindred subjects. However, 

 with two hours a week during junior year 

 devoted to the further exploration of the 

 calculus carried on side by side with its ap- 

 plication to studies of a nature more or 

 less professional, like thermodynamics, the 

 student is likely to come finally into living 



contact with calculus ideas. Through 

 three years, then, mathematical ideas are 

 held persistently and prominently before 

 the mind of the student, so that at the end 

 of that time the mental change which I 

 call the mathematical transformation is 

 quite complete. If you are intent upon 

 making a physical transformation by 

 which a weak man becomes robust and 

 powerful, you give one, two or three years 

 for the muscles to grow and the chest to 

 expand through long-continued and sys- 

 tematic exercise. Similarly the average 

 student does not become habitually mathe- 

 matical and exact in his thinking unless 

 you give him careful direction and devote 

 plenty of time to his development. The 

 man who uses his memory and copies 

 slavishly must disappear. In his place 

 must stand the man of trained intellect, 

 thoughtful, persistent, rich in expedients, 

 powerful in attack. To produce him there 

 are on the mathematical side two in- 

 dispensable requisites, thoroughness in the 

 fundamentals, and a sufficient time to 

 make the mathematical attack of a prob- 

 lem habitual and natural, and to give such 

 a control of and power in the use of the 

 tools of mathematics that the solution of a 

 problem of average difficulty shall be easy 

 and pleasurable. 



In the required mathematical part of the 

 engineering courses at Purdue these are the 

 considerations that determine the distribu- 

 tion of the work in the four-year program, 

 and all of the time we are teaching not 

 alone the particular subject that happens 

 to be named in the curriculum— but mathe- 

 matics. 



Some years ago it was my fortune to 

 study descriptive geometry under Marx 

 and Von Berlin in Munich. They taught 

 their subject from the standpoint of the 

 mathematician rather than that of the 

 draftsman. They made their students 

 visualize geometric form in space and by 



