WILLIAM J. MILNE, PH.D., LL.D.

PRESIDENT OF NEW YORK STATE NORMAL COLLEGE
ALBANY, N. Y.

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PREFACE

Scope. - This work has been written to meet the requirements of colleges and universities for general admission and of the course outlined by the Regents of the State of New York for both elementary and intermediate algebra. Every kind of question asked in recent examinations has been covered.

Method. -The author adheres to the inductive method of presentation, but uses declarative statements and observations instead of questions. These are followed by illustrative problems and explanations which bring out the important points that should be emphasized, and the treatment is rounded out by abundant practice.

Progress is from the known to the related unknown, and in this way is combined the student's knowledge of arithmetic with the algebraic knowledge to be acquired. New ideas of number are introduced whenever the development of the science demands it.

Exercises. The number of exercises is extremely large, and the variety is great. The concrete work is well balanced with the abstract, so that both skill in algebraic processes and ability to solve problems are properly sustained.

Problems. - The problems are more distinctly related to real life and business than those found in most algebras. Some of the traditional problems have been retained because they are often given in examinations; and besides, they are useful in developing a sort of intellectual power. tains a large number of fresh and interesting problems drawn But the work confrom commercial life, from physics and geometry, and from various topics of modern interest. physics and of geometry are employed to familiarize the pupils While the formulæ of with solutions for other letters than x, y, and z, no attempt has been made to present the subject-matter of physics or geometry.

Algebraic Representation. Throughout the early part of the book there are sets of exercises designed to teach algebraic language. By them the student is required

algebraic