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University Press :
This work has been prepared expressly for beginners, and in response to a call for an Algebra for the higher classes in Grammar Schools.
It is taken for granted that the pupil is familiar with the principles of ordinary Arithmetic.
Few rules and definitions are given; the use of algebraic language is illustrated by numerous exercises; and the elementary principles of Algebra are made clear by the introduction of
In order to awaken the interest of the pupil, the Equation, its reduction, and numerous problems are introduced at the very beginning of the book.
The examples given are carefully graded from the very simple to the more difficult. A considerable part of them have been tested by teachers of the grade for which they are designed. After the earlier problems, care has been taken to introduce for the most part such as require algebraic principles in their solution rather than those that can be more easily and naturally solved without the aid of Algebra. There is nothing better for training the intellectual powers than putting into algebraic language the conditions of a mathematical problem.
The subjects introduced and the method of treatment are such as to give the pupil a substantial ground-work for the more advanced work in Algebra.
It is not essential that every example and problem given in any topic should be done before the pupil passes to the succeeding subject. The teacher should use his judgment in each case, varying the number of exercises taken according to the ability of the pupil and the time allowed for the study. This is especially true in the subject of Factoring, of the Greatest Common Divisor of Polynomials, and of the Least Common Multiple of Polynomials. Further, it is not essential to follow in every respect the order of topics given in the book. If the teacher does not approve of the plan, adopted by the authors, of beginning with the Equation, he can defer the whole or any part of the first four chapters till a part or the whole of Chapters V.-XIV. is completed.
Some of the miscellaneous equations and problems at the end of the book are a little more difficult than those in the body of the work, and are to be selected for use at the discretion of the teacher.
W. F. B.
G. C. E.
CAMBRIDGE, Mass., March, 1894.