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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.
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.
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