Excerpt from Introduction to the Elementary Functions
This book is an attempt to solve the problem of the first-year collegiate course in mathematics. That the problem is a very real one is attested by the many discussions constantly taking place among teachers of mathematics and others interested in education. The traditional Freshman course, consisting of "college algebra," trigonometry, and solid geometry or elementary analytic geometry, is very generally regarded as unsatisfactory.
There are three main objections to this traditional course: first, it is not unified, so that it sacrifices time and fails to hold the student's interest; secondly, much of the subject matter should come after a first course in calculus, when it would gain vastly in significance; thirdly, the usual plan has deprived the large majority of college students of any introduction to the calculus, which is the heart and soul of modern mathematics and natural science. Only that small number electing to go beyond the first year of collegiate mathematics have the opportunity to become acquainted with the subject, which unquestionably represents one of the most important lines of development of human thought during the past two centuries.
Accordingly, we decided to construct a course with the fundamental idea of functionality as its unifying principle, and leading up to some elementary work in calculus as its culmination. The advantages of this arrangement are that it not only meets the objections stated in the preceding paragraph, but saves time by avoiding the repetition inevitable in the triple arrangement of subjects; and, what is more important, it leads to a deeper understanding of the significance of mathematical principles and relations than the student is likely to gain through the traditional course.
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