Elements of Algebra

ELEMENTS OF ALGEBRA by ARTHUR SCHULTZE. Originally published in 1910. 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 authors 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 social case of a memorized method. Such a large number of methods, however, not only taxes a students memory unduly but in variably leads to mechanical modes of study. The entire study of algebra becomes a mechanical application of memorized rules, while the cultivation of the students 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. 2. All parts of the theory which are beyond the comprehension of the student or which are logically unsound are omitted. All practical teachers know how few students understand and appreciate the more difficult parts of the theory, and consequently hardly ever emphasize the theoretical aspect of algebra. Moreover, a great deal of the theory offered in the aver age text-book is logically unsound e. g. all proofs for the sign of the product of two negative numbers, all elementary proofs of the binomial theorem for fractional exponents, etc. 3. The exercises are slightly simpler than in the larger look. The best way to introduce a beginner to a new topic is to offer a large number of simple exercises. For the more ambitious student, however, there has been placed at the end of the book a collection of exercises which contains an abundance of more difficult work. With very few exceptions all the exercises in this book differ from those in the Elementary Algebra hence either book may be used to supplement the other. 4. Topics of practical importance, as quadratic equations and graphs, are placed early in the course. This arrangement will enable students who can devote only a minimum of time to algebra to study those subjects which are of such importance for further work. In regard to some other features of the book, the following may be quoted from the authors Elementary Algebra Particular care has been bestowed upon those chapters which in the customary courses offer the greatest difficulties to the beginner, especially problems and factoring. The presentation of problems as given in Chapter V will be found to be quite a departure from the customary way of treating the subject, and it is hoped that this treatment will materially diminish the difficulty of this topic for young students. The book is designed to meet the requirements for admission to our best universities and colleges, in particular the requirements of the College Entrance Examination Board.