which are drawn from the fields of science and everyday life, will commend themselves to the progressive teacher. The oldtime "puzzles" are omitted, and the more difficult problems are placed in the latter part of the lists. Artificial difficulties, such as curious combinations of the symbols of aggregation, complicated fractions never met with in practice, elaborate expressions in factoring, unused combinations of indices, needlessly involved equations, etc., have been purposely omitted. By the elimination of these labor-wasting difficulties the student is given time for the important practical matter that is abundantly supplied. The treatment of factoring and its application to the solution. of equations is especially thorough. The difficulties which so frequently confuse the student as a result of following the axioms blindly are cleared away by a comprehensive treatment of Equivalent Equations. The Binomial and Remainder Theorems are presented in a simple manner at an early stage in order to give the student as quickly as possible the practical use of these important principles. Many cautions on the errors that beginners are likely to fall into are given throughout the book, especially in the illustrative solutions. These solutions are intended to be models in neatness and orderly procedure, while the frequent use of "checks" will lead to accuracy and tend to make the student independent of book and teacher. The value of early and frequent use of graphical representation to make algebraic abstractions seem real is recognized. Particular attention has therefore been given to the Graphs of Equations; and to the end that the graphical treatment may have practical value, it is presented where most needed to throw light upon the algebraic solution. In explaining the conditions which render equations simultaneous, inconsistent, or impossible, the graphic method has been effectively employed. The method of presentation is such as to lead the student into a clear understanding of the truths set forth, to think logically, to reason accurately, and to express his thoughts clearly. The authors acknowledge their special obligation to Professor F. W. Duke, of Hollins Institute, Hollins, Va., for his able assistance in revising the various chapters of the book. J. M. COLAW, MONTEREY, VA. J. K. ELLWOOD, PITTSBURG, PA. |