An introduction to mathematics, by A. N. Whitehead.

BIBLIOGRAPHY
NOTE ON THE STUDY OF MATHEMATICS
THE difficulty that beginners find in the study of this
science is due to the large amount of technical detail which
has been allowed to accumulate in the elementary textbooks, obscuring the important ideas.
The first subjects of study, apart from a knowledge of
arithmetic which is presupposed, must be elementary
geometry and elementary algebra. The courses in both
subjects should be short, giving only the necessary ideas;
the algebra should be studied graphically, so that in practice the ideas of elementary coordinate geometry are also
being assimilated. The next pair of subjects should be
elementary trigonometry and the coordinate geometry of
the straight line and circle. The latter subject is a short
one; for it really merges into the algebra. The student
is then prepared to enter upon conic sections, a very short
course of geometrical conic sections and a longer one of
analytical conics. But in all these courses great care
should be taken not to overload the mind with more
detail than is necessary for the exemplification of the
fundamental ideas.
The differential calculus and afterwards the integral
calculus now remain to be attacked on the same system.
A good teacher will already have illustrated them by the
consideration of special cases in the course on algebra
and coordinate geometry. Some short book on three
dimensional geometry must also be read.
This elementary course of mathematics is sufficient for
some types of professional career. It is also the necessary
preliminary for any one wishing to study the subject for its
intrinsic interest. He is now prepared to commence on a
more extended course. He must not, however, hope to be
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