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BY

WILLIAM J. MILNE, Ph.D., LL.D.

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

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NEW YORK ::. CINCINNATI ::: CHICAGO
AMERICAN BOOK COMPANY

Educ T 129.01.575

HARVARD COLLEGE LIBRARY

GIFT OF
GINN & COMPANY
MARCH 17, 1927

1

COPYRIGHT, 1901, BY

WILLIAM J. MILNE.

ENTERED AT STATIONERS' HALL, LONDON.

ACADEMIC ALGEBRA.

E-PI

PURPOSE AND PLAN OF THIS BOOK

The Academic Algebra has been prepared to meet the requirements of the most exacting entrance examination of any College or University in the United States.

The book contains a thorough treatment of the science, so far as it is taught in the secondary schools. A full development of each subject, and a clear statement of its principles and laws, precedes the proofs of the principles - an arrangement that makes it possible for a teacher, without hindrance to the progress of the student, to postpone, if he sees fit, the rigorous proofs. The examples and problems are sufficiently numerous and complex to test the student's skill in applying all the principles that are developed. They are carefully graded, increasing in difficulty in each subject, so that, if desired, a brief and easier course may be conveniently provided by omitting the more difficult problems at the end of each list.

In several respects, the order of the topics deviates from that which is usually followed. These innovations, made in accordance with sound pedagogical principles, will arouse and sustain a greater interest in the science. The method of presentation also is unique. The principles are developed by appropriate questions designed to lead the student to infer and apprehend clearly the truth that is presented; these are followed, first, by a brief, yet clear and complete statement of the principles, and then by full and rigorous proofs of the principles. Thus the natural method of mathematical teaching has been followed, the student being led, first, to make proper inferences; second, to express the inferences briefly and accurately; and, third, to prove their truth by the method of deductive reasoning.

The acknowledgments of the author are due to Prof. J. H. Tanner, of the Department of Mathematics, Cornell University, for many valuable suggestions in connection with the preparation of this book.

WILLIAM J. MILNE. STATE NORMAL COLLEGE, Albany, N.Y.

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