EAN: 9781493950263

UNDERGRADUATE TEXTS IN MATHEMATICS UNDERSTAND...

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. Fifteen years of classroom experience with the first edition of Understanding
Analysis have solidified and refined the central narrative of the second edition. Roughly 150
new exercises join a selection of the best exercises fromthe first edition  and three more
project-style sections have been added. Investigations of Euler's computation of zeta(2)  the
Weierstrass Approximation Theorem  and the gamma function are now among the book's cohort of
seminal results serving as motivation and payoff for the beginning student to master the
methods of analysis.

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