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PREFACE MOST teachers of mathematics agree that a number of the topics ol'dinarily 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 mOl'e satisfactorily taken up after the stl!-dent 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 uumber 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 Table of Contents CONTENTS; CHAPTER I; INTRODUCTION •; Algebraic Solution of Problems; Negative Numbers; Numbers represented by Letters; Factors, Powers, and Roots; •; •; Algebraic Expressions and Numerical Substitutions; CHAPTER II; ADDITION, SUBTRACTION, AND PARENTHESES •; Addition of Monomials; Addition of Polynomials; Subtraction; Review Exercise I; Signs of Aggregation •; Exercises in Algebraic Expression; CHAPTER III; MULTIPLICATION; Multiplication of Algebraic Numbers •; Multiplication of Monomials; •; Multiplication of a Polynomial by a Monomial •; Multiplication of' Polynomials; Special Cases in Multiplication •; CHAPTER IV; DIVISION •; Divi