This fairly self-contained work embraces a broad range of topics
in analysis at the graduate level, requiring only a sound knowledge
of calculus and the functions of one variable. A key feature of
this lively yet rigorous and systematic exposition is the
historical accounts of ideas and methods pertaining to the relevant
topics. Most interesting and useful are the connections developed
between analysis and other mathematical disciplines, in this case,
numerical analysis and probability theory.
The text is divided into two parts: The first examines the
systems of real and complex numbers and deals with the notion of
sequences in this context. After the presentation of natural
numbers as a subset of the reals, elements of combinatorics and a
discussion of the mathematical notion of the infinite are
introduced. The second part is dedicated to discrete processes
starting with a study of the processes of infinite summation both
in the case of numerical series and of power series.
General
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