sciences. That is, the idea of rendering direct and
efficient services to other departments should animate the
mathematical department more deeply than any other department of the
university. The tendency toward disintegration to which we referred
above has forcefully directed attention to the great need of
emphasizing this aspect of our subject, since such disintegration is
naturally accompanied by a weakening of mathematical vigor. It may be
noted that such a disintegration would mean a reverting to primitive
conditions, since some of the older works treated mathematics merely
as a chapter of astronomy. This was done, for instance, in some of the
ancient treatises of the Hindus.

=Mathematics and technical education=

The great increase in college students during recent years and the
growing emphasis on college activities outside of the work connected
with the classroom, especially on those relating to college athletics,
would doubtless have left college mathematics in a woefully neglected
state if there had not been a rapidly growing interest in technical
education, especially in engineering subjects, at the same time. Naval
engineering was one of the first scientific subjects to exert a strong
influence on popularizing mathematics. In particular, the teaching of
mathematics in the Russian schools supported by the government began
with the founding of the government school for mathematics and
navigation at Moscow in 1701. It is interesting to note that the
earlier Russian schools established by the clergy after the adoption
of Christianity in that country did not provide for the teaching of
any arithmetic whatever, notwithstanding the usefulness of arithmetic
for the computing of various dates in the church calendar, for land
surveying, and for the ordinary business transactions.[9]

The direct aims in the teaching of college mathematics have naturally
been somewhat affected by the needs of the engineering students, who
constitute in many of our leading institutions a large majority in the
mathematical classes. These students are usually expected to receive
more drill in actual numerical work than is demanded by those who seek
mainly a deeper penetration into the various mathematical theories.
The most successful methods of teaching the former students have much
in common with those usually employed in the high schools and are
known as the recitation and problem-solving methods. They involve the
correction and di