72 



SCIENCE 



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



tificate to the freshman class, and when a 

 pupil is once graduated from an accredited 

 school, he has earned the right to com- 

 mence upon his technical course. At the 

 University of Illinois, the problem has 

 been solved by saying to the freshmen in 

 mathematics that while there is no disposi- 

 tion to deprive them of their entrance 

 credit, the department of mathematics may 

 nevertheless determine the conditions 

 under which credit in college algebra can 

 be secured. Accordingly, those students 

 who fail to pass the review quiz are re- 

 quired to take two additional hours per 

 week in the subject for the remainder 

 of the semester in order to earn the same 

 credit that is given to others at the close 

 of the course. This has the advantage of 

 placing aU of the students practically upon 

 the same basis, so far as attainments in 

 algebra are concerned, when they enter 

 upon the second semester's work. 



A somewhat similar plan as that out- 

 lined here is followed also at the Univer- 

 sity of Wisconsin, and perhaps at other 

 institutions. It will be seen from Table 

 I. that a large number of technical schools 

 are now requiring work in logarithms for 

 entrance. This might very well be intro- 

 duced in connection with theory of ex- 

 ponents and used with advantage in high- 

 school physics. It is also gratifying to 

 observe that the more recent texts on 

 algebra provide work in the use of the 

 graph and in the plotting of curves. It is 

 very desirable that the work in elementary 

 algebra, including the work of curve-plot- 

 ting, should also include applications to 

 some of the simpler phenomena studied in 

 the high-school course in physics, and this 

 again is made a feature in some of the 

 more recent texts. Such an arrangement 

 affords an additional reason for putting 

 some of the work in algebra late in the 

 high-school course in order that it may 

 follow rather than precede the work in 



physics, thus making it possible to intro- 

 duce a wider range of physical applica- 

 tions than could otherwise be done. 



In Table II. is shown the number of 

 restrictions given in each of the various 

 mathematical subjects required of engi- 

 neering 'students. The average number 

 given to each subject for the seventeen 

 institutions is approximately as follows: 

 college algebra 50, plane trigonometry 46, 

 analytic geometry 80, and calculus 130. 

 In a number of the institutions named, 

 spherical trigonometry is taught by one of 

 the engineering departments, usually the 

 civil-engineering department, in connec- 

 tion with its applications to geodesy. The 

 number of recitations assigned to cal- 

 culus usually includes also a short course 

 in differential equations. In two cases 

 where a course of more than usual length 

 in the subject is given for the students of 

 a particular engineering department, the 

 subject has been listed separately.^ One 

 institution, Rose Polytechnic Institute, is 

 unique among strictly engineering schools 

 in offering throughout the four years of 

 undergraduate work a rather large amount 

 of elective mathematics, including short 

 courses in advanced calculus, least squares, 

 projective geometry and quaternions. In 

 all of the universities listed, and at the 

 Massachusetts Institute of Technology the 

 mathematical department offers a rather 

 wide range of advanced subjects, all of 

 which are open to engineering students so 

 far as the demands of their technical 

 course wiU permit. 



By a study of Table II., it will be seen 

 that a considerable difference exists in the 

 amount of attention given to the various 

 subjects. In making comparisons in 

 algebra and trigonometry, however, the 

 difference in entrance conditions must be 



'Table III. shows the number of recitations 

 given to diflFerential equations in each case when 

 that subject was reported separately. 



