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ADMISSION AND CLASSIFICATION. 47
of triedral angles ; and the solution of right and oblique spherical tri
angles, including the determination of the ambiguous cases.
The trigonometric functions must be defined as ratios, not as lines ;
and both the definitions and the proofs of trigonometry must be so
broad as to apply to all angles, and all triangles, whatever the size or
sign of the parts involved.
Special Directions. Of the preparatory work in Mathematics two
things are specially demanded.
That it shall have developed in the student a certain degree of
mathematical maturity, and familiarized him with the subject matter
and methods of mathematical work.
That it shall have furnished him with those specific facts, an
accurate and ready knowledge of which is indispensable in the further
prosecution of his professional study.
The first of these demands is fairly well satisfied in the case of stu
dents who have conscientiously performed the mathematical work re
quired for a Regents'
diploma or for a diploma from one of our better
high schools. A careful review of this part of the student's work,
given immediately before entering the University, would give him a
broader and more comprehensive knowledge, would make clear to
him the reasons for many things which he did not understand when he
first went over them, and would equip him with better and more rapid
methods of work. Thus informed, his work in the University would
not only be much easier for him, but it would also mean much more
to him, and such a review is therefore advisable.
On the other hand, most students who fail in their university mathe
matics fail because they are poorly equipped in the second require
ment above mentioned. For example : they cannot perform the
ordinary operations of algebra rapidly nor accurately, they do not know
the of quadratic theory equations, they are lost among trigonometric
formulae, and they blunder when use they logarithms. Instead of
spending their time and energy upon their new work, they must
spend much of it in studying up those things with which they ought
to be familiar, and, thus handicapped, they cannot keep up the pace
set by men who are properly prepared, and cannot they do the work
that must be done to fit them for the professional work that follows.
They become discouraged and disheartened, and soon they rank as
third-rate men, when a little care in their preparation might have
made them first-rate men.
It is not sufficient that the student should once have known his pre
mathematics : paratory
he must know them at the time when he begins
his work here. It seems absolutely essential, therefore, that these
subjects be very carefully reviewed just prior to entrance.