Often I have considered the fact that most of the difficulties
which block the progress of students trying to learn analysis stem
from this: that although they understand little of ordinary
algebra, still they attempt this more subtle art. From this it
follows not only that they remain on the fringes, but in addition
they entertain strange ideas about the concept of the infinite,
which they must try to use. Although analysis does not require an
exhaustive knowledge of algebra, even of all the algebraic
technique so far discovered, still there are topics whose con
sideration prepares a student for a deeper understanding. However,
in the ordinary treatise on the elements of algebra, these topics
are either completely omitted or are treated carelessly. For this
reason, I am cer tain that the material I have gathered in this
book is quite sufficient to remedy that defect. I have striven to
develop more adequately and clearly than is the usual case those
things which are absolutely required for analysis. More over, I
have also unraveled quite a few knotty problems so that the reader
gradually and almost imperceptibly becomes acquainted with the idea
of the infinite. There are also many questions which are answered
in this work by means of ordinary algebra, although they are
usually discussed with the aid of analysis. In this way the
interrelationship between the two methods becomes clear."
General
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