lem presented by those who are preparing to teach mathematics
may at first appear to differ widely from that presented by those who
expect to become engineers. The latter are mostly interested in
obtaining from their mathematical courses a powerful equipment for
doing things, while the former take more interest in those
developments which illumine and clarify the elements of their subject.
Hence the prospective teacher and the prospective engineer might
appear to have conflicting mathematical interests. As a matter of
fact, these interests are not conflicting. The prospective teacher is
greatly benefited by the emphasis on the serviceableness of
mathematics, and the prospective engineer finds that the generality
and clarity of view sought by the prospective teacher is equally
helpful to him in dealing with new applications. Hence these two
classes of students can well afford to pursue many of the early
mathematical courses together, while the finishing courses should
usually be different.

The rapidly growing interest in statistical methods and in insurance,
pensions, and investments has naturally directed special attention to
the underlying mathematical theories, especially to the theory of
probability. Some institutions have organized special mathematical
courses relating to these subjects and have thus extended still
further the range of undergraduate subjects covered by the
mathematical departments. The rapidly growing emphasis on college
education specially adapted to the needs of the prospective business
man has recently led to a greater emphasis on some of these subjects
in several institutions.

The range of mathematical subjects suited for graduate students is
unlimited, but it is commonly assumed to be desirable that the
graduate student should pursue at least one general course in each one
of broader subjects such as the theory of numbers, higher algebra,
theory of functions, and projective geometry, before he begins to
specialize along a particular line. It is usually taken for granted
that the undergraduate courses in mathematics should not presuppose a
knowledge of any language besides English, but graduate work in this
subject cannot be successfully pursued in many cases without a reading
knowledge of the three other great mathematical languages; viz.,
French, German, and Italian. Hence the study of graduate mathematics
necessarily presupposes some linguistic training in addition to an
acquaintance wit