858 



SCIENCE 



[N. S. Vol. XXXIV. No. S 



IV. To awaken the love of knowledge 

 and to impart scholarly ideals. 



The first of these aims, without attention 

 to which the other three can not be ob- 

 tained, has led to the great development of 

 the lecture system which we find in all 

 graduate schools, and to the use of the text- 

 book and treatise either in connection with 

 these lecture courses or independently of 

 them, and of the original memoir, the read- 

 ing of which constitutes an art by no means 

 easy to acquire, and which deserves special 

 cultivation at the hands of the members of 

 the teaching staff. 



As means used under II. may be men- 

 tioned: First, the solution of problems by 

 students either in connection with the lec- 

 ture courses or in special seminars or pro- 

 seminars, and secondly, the writing of 

 theses which may or may not be connected 

 with the doctor's degree. This last is also 

 the chief means employed under III., al- 

 though the quiz (cf. subcommittee 3, sec- 

 tion IV.) is sometimes employed effectively 

 for this purpose, and even the brief written 

 problem is not without some value here. 



Both II. and III, above should receive 

 more attention than is now commonly 

 given to them, while I. is at present ade- 

 quately treated, except, perhaps in the 

 relative weakness of applied as distin- 

 guished from pure mathematics. 



The aim indicated under IV. depends 

 for its attainment less on special methods 

 of instruction and more on the personality 

 of the instructor and his attitude towards 

 science than do I., II. or III. To secure 

 adequately the end in view, an instructor 

 is needed who combines high scientific 

 ideals with a commanding or sympathetic 

 personality. Such men could do much to 

 counteract the tendency noted in the 

 closing lines of section II., but, on the 

 other hand, it is precisely this tendency 



which makes them difficult to secure. 

 Their influence on undergraduate instruc- 

 tion should be no less valuable than in the 

 graduate school. 



We must come back once more to the lec- 

 ture courses which everywhere form the 

 backbone of graduate mathematical instruc- 

 tion. Such a course usually extends either 

 through the whole academic year, that is, 

 from the end of September till early in 

 June, or through the first or second half of 

 this year.® The lectures, of somewhat less 

 than an hour each, come usually three times 

 (less frequently twice) a week. While 

 much depends on the local traditions and 

 the personality of the instructor, it may in 

 a general way be said that these lectures 

 have a far less formal character than is the 

 case in European universities. Students 

 will frequently interrupt the lecturer Vi^ith 

 a question, and short discussions between 

 the instructor and one or more students will 

 not infrequently take place, and at times 

 the more formal quiz (cf. subcommittee 1, 

 section VI., and subcommittee 3, section 

 IV.) finds its place here. Some tact and 

 firmness are occasionally necessary to pre- 

 vent the loquacious or thick-headed student 

 from monopolizing the time of the class, 

 but on the whole this frequent contact dur- 

 ing the lecture between teacher and stu- 

 dent is an admirable feature of American 

 higher education, and counteracts, to a 

 certain extent, some evils which usually 

 accompany the lecture system. It is made 

 possible by the smallness of the classes, an 

 audience of twenty-five in a graduate 

 course in mathematics being distinctly un- 

 usual. 



The range of subjects covered by the 

 courses offered in each graduate school is 



' Attention must also be called to work in the 

 summer schools and summer quarters. Cf. subcom- 

 mittee 1, section IV. 



