COLLEGE ALGEBRA BY JAMES HARRINGTON BOYD, PH.D. CHICAGO SCOTT, FORESMAN AND COMPANY 4-12-33 PREFACE The selection and arrangement of topics in this book and the method of treatment represent that which the author's experience has led him to believe is best adapted to the requirements of a good college course. Of the topics usually treated in college algebras, continued fractions, choice and chance, and probabilities have been omitted, since few applications of these subjects are made until the student reaches more advanced courses. Their omission also gives time for more extended study of such topics as irrational and complex numbers, series, the elementary properties of determinants, and the properties and solutions of numerical equations of higher order. Throughout the book, great care has been taken to secure that rigor and logical sequence which are being demanded by the best teachers. Special attention is called to the mode of presenting the number concepts in the earlier part of the book, to the use of geometrical illustrations, and to the extensive collection of exercises, in large part hitherto unused in American colleges. In developing the fundamental laws and theorems of the number system of Common Algebra, the notation used by H. B. Fine in the first articles of his book The Number System of Algebra has been adopted for the sake of uniformity. Since the discovery of Quaternions by Hamilton, of Linear Associative Algebra by Benjamin Peirce, and the Ausdehnungslehre by Grassman, mathematicians have generally accepted the doctrine that Algebra is completely defined formally by the laws of combination which the fundamental operations are required to obey. In the development of the principles of the number system of Common Algebra, emphasis is placed upon the principle of the |