of
Collegiate Mathematics" in 1897, with the understanding that he should
devote himself to the interests of the undergraduates. In many of the
larger universities the younger members of the department usually
teach only undergraduate courses, while some of the older members
devote either all or most of their time to the advanced work; but
there is no uniformity in this direction, and the present conditions
are often unsatisfactory.

The undergraduate courses in mathematics in the American colleges and
universities differ considerably. The normal beginning courses now
presuppose a year of geometry and a year and a half of algebra in
addition to the elementary courses in arithmetic, but much higher
requirements are sometimes imposed, especially for engineering
courses. In recent years several of the largest universities have
reduced the minimum admission requirement in algebra to one year's
work, but students entering with this minimum preparation are
sometimes not allowed to proceed with the regular mathematical classes
in the university.

=Variety of college courses in mathematics=

Freshmen courses in mathematics differ widely, but the most common
subjects are advanced algebra, plane trigonometry, and solid geometry.
The most common subjects of a somewhat more advanced type are plane
analytic geometry, differential and integral calculus, and spherical
trigonometry. Beyond these courses there is much less uniformity,
especially in those institutions which aim to complete a well-rounded
undergraduate mathematical course rather than to prepare for graduate
work. Among the most common subjects beyond those already named are
differential equations, theory of equations, solid analytic geometry,
and mechanics.

A very important element affecting the mathematical courses in recent
years is the rapid improvement in the training of our teachers in the
secondary schools. This has led to the rapid introduction of courses
which aim to lead up to broad views in regard to the fundamental
subjects. In particular, courses relating to the historical
development of concepts involved therein are receiving more and more
attention. Indirect historical sources have become much more plentiful
in recent years through the publication of various translations of
ancient works and through the publication of extensive historical
notes in the _Encyclopedie des Sciences Mathematiques_ and in other
less extensive works of reference.

The prob