This lively introductory text exposes the student to the rewards of a
rigorous study of functions of a real variable. In each chapter,
informal discussions of questions that give analysis its inherent
fascination are followed by precise, but not overly formal, developments
of the techniques needed to make sense of them. By focusing on the
unifying themes of approximation and the resolution of paradoxes that
arise in the transition from the finite to the infinite, the text turns
what could be a daunting cascade of definitions and theorems into a
coherent and engaging progression of ideas. Acutely aware of the need
for rigor, the student is much better prepared to understand what
constitutes a proper mathematical proof and how to write one.

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