•Theo. THE MACMILLAN COMPANY NEW YORK BOSTON • CHICAGO MACMILLAN & CO., LIMITED LONDON BOMBAY CALCUTTA THE MACMILLAN CO. OF CANADA, LTD. TORONTO BY ARTHUR SCHULTZE, PH.D. FORMERLY ASSISTANT PROFESSOR OF MATHEMATICS, NEW YORK UNIVERSITY New York THE MACMILLAN COMPANY 1918 All rights reserved Set COPYRIGHT, 1910, BY THE MACMILLAN COMPANY. up and electrotyped. Published May, 1910. Reprinted [ 9 For Gead. R.R.3 PREFACE In this book the attempt is made to shorten the usual course in algebra, while still giving to the student complete familiarity with all the essentials of the subject. While in many respects similar to the author's "Elementary Algebra," this book, owing to its peculiar aim, has certain distinctive features, chief among which are the following: 1. All unnecessary methods and "cases" are omitted. These omissions serve not only practical but distinctly pedagogic ends. Until recently the tendency was to multiply "cases" as far as possible, in order to make every example a special case of a memorized method. Such a large number of methods, however, not only taxes a student's memory unduly but invariably leads to mechanical modes of study. The entire study of algebra becomes a mechanical application of memorized rules, while the cultivation of the student's reasoning power and ingenuity is neglected. Typical in this respect is the treatment of factoring in many text-books. In this book all methods which are of real value, and which are applied in advanced work are given, but "cases" that are taught only on account of tradition, short-cuts that solve only examples specially manufactured for this purpose, etc., are omitted. All 2. All parts of the theory which are beyond the comprehension of the student or which are logically unsound are omitted. practical teachers know how few students understand and appreciate the more difficult parts of the theory, and conse |