Mathematical analysis serves as a common foundation for many
research areas of pure and applied mathematics. It is also an
important and powerful tool used in many other fields of science,
including physics, chemistry, biology, engineering, finance, and
economics. In this book, some basic theories of analysis are
presented, including metric spaces and their properties, limit of
sequences, continuous function, differentiation, Riemann integral,
uniform convergence, and series.After going through a sequence of
courses on basic calculus and linear algebra, it is desirable for
one to spend a reasonable length of time (ideally, say, one
semester) to build an advanced base of analysis sufficient for
getting into various research fields other than analysis itself,
and/or stepping into more advanced levels of analysis courses (such
as real analysis, complex analysis, differential equations,
functional analysis, stochastic analysis, amongst others). This
book is written to meet such a demand. Readers will find the
treatment of the material is as concise as possible, but still
maintaining all the necessary details.
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