The book targets undergraduate and postgraduate mathematics students and
helps them develop a deep understanding of mathematical analysis.
Designed as a first course in real analysis, it helps students learn how
abstract mathematical analysis solves mathematical problems that relate
to the real world. As well as providing a valuable source of inspiration
for contemporary research in mathematics, the book helps students read,
understand and construct mathematical proofs, develop their
problem-solving abilities and comprehend the importance and frontiers of
computer facilities and much more.
It offers comprehensive material for both seminars and independent study
for readers with a basic knowledge of calculus and linear algebra. The
first nine chapters followed by the appendix on the Stieltjes integral
are recommended for graduate students studying probability and
statistics, while the first eight chapters followed by the appendix on
dynamical systems will be of use to students of biology and
environmental sciences. Chapter 10 and the appendixes are of interest to
those pursuing further studies at specialized advanced levels. Exercises
at the end of each section, as well as commentaries at the end of each
chapter, further aid readers' understanding. The ultimate goal of the
book is to raise awareness of the fine architecture of analysis and its
relationship with the other fields of mathematics.
