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Elements Of Algebra (Paperback)
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Elements Of Algebra (Paperback)
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ELEMENTS OF ALGEBRA BY ARTHUR SCHULTZE, PH. D. FORMERLY ASSISTANT
PROFESSOR OF MATHEMATICS, NKW YORK ITNIVEKSITT HEAD OF THK
MATHEMATICAL DKIA KTM EN T, HIH SCHOOL OF COMMERCE, NEW 1 ORK CUT
THE MACMILLAN COMPANY 1917 All rights reserved COPYRIGHT, 1910, BY
THE MACMILLAN COMPANY. Set up and electrotyped. Published May,
1910. Reprinted September, 1910 January, 1911 July, February, 1913,
January, 1915 May, September, 1916 August, 1917. . J. 8. Cushlng
Co. Berwick Smith Co. Norwood, Mass., U. S. A. 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 thesubject,
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. This made it necessary to introduce the theory
of proportions and graphical methods into the first years work, an
innovation which seems to mark a distinct gain from the pedagogical
point of view...
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