Unified Mathematics

An excerpt from the Preface: THIS text presents a course in elementary mathematics adapted to the needs of students in the freshman year of an ordinary college or technical school course, and, of students in the first year of a junior college. The material of the text includes the essential and vital features of the work commonly covered in the past in separate courses in college algebra, trigonometry, and analytical geometry. The fundamental idea of the...
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An excerpt from the Preface:

THIS text presents a course in elementary mathematics adapted to the needs of students in the freshman year of an ordinary college or technical school course, and, of students in the first year of a junior college. The material of the text includes the essential and vital features of the work commonly covered in the past in separate courses in college algebra, trigonometry, and analytical geometry.

The fundamental idea of the development is to emphasize the fact that mathematics cannot be artificially divided into compartments with separate labels, as we have been in the habit of doing, and to show the essential unity and harmony and interplay between the two great fields into which mathematics may properly be divided; viz., analysis and geometry.

A further fundamental feature of this work is the insistence upon illustrations drawn from fields with which the ordinary student has real experience. The authors believe that an illustration taken from life adds to the cultural value of the course in mathematics in which this illustration is discussed. Mathematics is essentially a mental discipline, but it is also a powerful tool of science, playing a wonderful part in the development of civilization. Both of these facts are continually emphasized in this text and from different points of approach.

The student who has in any sense mastered the material which is presented will at the same time, and without great effort, have acquired a real appreciation of the mathematical problems of physics, of engineering, of the science of statistics, and of science in general.

A distinctly new feature of the work is the introduction of series of "timing exercises" in types of problems in which the student may be expected to develop an almost mechanical ability. The time which is given in the problems is wholly tentative; it is hoped, in the interest of definite and scientific knowledge concerning what may be expected of a freshman, that institutions using this text will keep a somewhat detailed record of the time actually made by groups of their students. The authors invite the cooperation of teachers of elementary college mathematics in the attempt to secure this valuable information. The authors will make every effort to put information thus secured at the service of the public interested.

In general, the diagrams are carefully drawn on paper with subdivisions of twentieths of an inch. It is expected that this kind of paper will be used as far as possible in the graphical work, as students will be found to acquire rapidly the ability to use intelligently this type of coordinate paper. Considerable attention should be paid by the teacher to the intelligent reading and interpretation of the diagrams which appear in the text, as the student will in this way gain power to handle his own diagrams, and appreciation of the vital importance of the method. The photographic illustrations should also be used in a somewhat similar manner.

The material can be covered without systematic omissions in a course which devotes five hours per week for one year to the study of mathematics. In a four-hour course there are certain omissions which can be made by the teacher at his own discretion; the three chapters on solid analytical geometry are not commonly presented in the ordinary four-hour course; the chapter on "Poles and Polars" may also be omitted. The exercises are so numerous that any teacher can make a selection, which can be varied, if desired, in succeeding years.

No attempt has been made to introduce the terminology of the calculus as it is found that there is ample material in the more elementary field which should be covered before the student embarks upon what may properly be called higher mathematics. However, the fundamental idea of the derivative is presented and utilized without the new terminology.