BY ARTHUR SCHULTZE, PH.D. ASSISTANT PROFESSOR OF MATHEMATICS, NEW YORK UNIVERSITY HEAD OF THE MATHEMATICAL DEPARTMENT, HIGH SCHOOL OF COMMERCE, NEW YORK CITY DEPARTMENT OF RECEIVED NOV 1 5 1909 LELAND STANFORD New York All rights reserved 629175 COPYRIGH 1905, 1906, Set up and electrotyped. Published January, 1906. PREFACE Most teachers of mathematics agree that a number of the topics ordinarily taught to classes in advanced algebra may be omitted without injury to the course. Some of these topics, such as multiple roots, Sturm's theorem, etc., can be more satisfactorily taken up after the student is familiar with calculus, while others, such as recurring series, continued fractions, etc., are so seldom applied in higher mathematics that they may be entirely omitted. 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 is retained, since familiarity with the symbols of inequality seems to be necessary for future work. If, however, a subject appears too important for entire omission, it is placed in the Appendix. This is done in the case of indeterminate equations, logarithms, summation of series, and some other subjects. On the other hand, graphical methods are emphasized more than is usual in text-books of this grade. The graphical method for solving cubics given in Section 578 is not met with in any other text-book, and the method for representing a cubic function by means of one standard curve (Section 583) is entirely new. Summation of series is also treated in a novel manner (Appendix IX). While the method given is almost identical with that used in many text-books, it is here presented in a more practical form, which makes it applicable to all cases. |