BY ARTHUR SCHULTZE, PH.D. ASSISTANT PROFESSOR OF MATHEMATICS, NEW YORK UNIVERSITY New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., LTD. 1906 All rights reserved PREFACE Most teachers of mathematics agree that a number of topics taught in the customary courses in advanced algebra may be omitted without injuring the course. Some of these topics can be more advantageously studied after the student is familiar with calculus, as multiple roots, Sturm's theorem, etc.; while others are so seldom applied in higher mathematics that they may be entirely omitted, as recurring series, continued fractions, etc. In accordance with this view, the College Entrance Examination Board has considerably reduced the number of topics required in advanced algebra. All subjects no longer required for the examinations of this board are omitted from the regular course of this book, with the exception of inequalities, which were retained since familiarity with the symbols of inequality seemed to be necessary for future work. If, however, a subject appeared too important for entire omission, it was placed in the appendix, as was done in the case of indeterminate equations, logarithms, summation of series, etc. On the other hand, graphical methods have been more emphasized than customary. The graphical method for solving cubics given in Section 578 is not met with in other text-books, and the method for representing a cubic function by means of one standard curve (§ 583) is entirely new. The summation of series has also been treated in a novel manner (Appendix IX). While the method given is almost identical with a method used in many text-books, it has been represented in a more practical form, which made it possible to treat all cases by a single method. |