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Starting with the Zermelo-Fraenhel axiomatic set theory, this book
gives a self-contained, step-by-step construction of real and
complex numbers. The basic properties of real and complex numbers
are developed, including a proof of the Fundamental Theorem of
Algebra. Historical notes outline the evolution of the number
systems and alert readers to the fact that polished mathematical
concepts, as presented in lectures and books, are the culmination
of the efforts of great minds over the years. The text also
includes short life sketches of some of the contributing
mathematicians. The book provides the logical foundation of
Analysis and gives a basis to Abstract Algebra. It complements
those books on real analysis which begin with axiomatic definitions
of real numbers.The book can be used in various ways: as a textbook
for a one semester course on the foundations of analysis for
post-calculus students; for a seminar course; or self-study by
school and college teachers.
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