This new edition of Real Analysis: A Historical Approach
continues to serve as an interesting read for students of analysis.
Combining historical coverage with a superb introductory treatment,
this book helps readers easily make the transition from concrete to
abstract ideas.
The book begins with an exciting sampling of classic and famous
problems first posed by some of the greatest mathematicians of all
time. Archimedes, Fermat, Newton, and Euler are each summoned in turn,
illuminating the utility of infinite, power, and trigonometric series
in both pure and applied mathematics. Next, Dr. Stahl develops the
basic tools of advanced calculus, which introduce the various aspects
of the completeness of the real number system as well as sequential
continuity and differentiability and lead to the Intermediate and Mean
Value Theorems. The Second Edition features:
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A chapter on the Riemann integral, including the subject of
uniform continuity
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Explicit coverage of the epsilon-delta convergence
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A discussion of the modern preference for the viewpoint of
sequences over that of series
Throughout the book, numerous applications and examples reinforce
concepts and demonstrate the validity of historical methods and
results, while appended excerpts from original historical works shed
light on the concerns of influential mathematicians in addition to the
difficulties encountered in their work. Each chapter concludes with
exercises ranging in level of complexity, and partial solutions are
provided at the end of the book.
Real Analysis: A Historical Approach, Second Edition is an
ideal book for courses on real analysis and mathematical analysis at
the undergraduate level. The book is also a valuable resource for
secondary mathematics teachers and mathematicians.
SAUL STAHL, PhD,
is Professor in the Department of Mathematics at The University of
Kansas. He has published numerous journal articles in his areas of
research interest, which include combinatorics, discrete mathematics,
and topological graph theory. Dr. Stahl is the author of Introductory
Modern Algebra: A Historical Approach and Introduction to Topology and
Geometry, both published by Wiley. He was awarded the Carl B.
Allendoerfer Award from the Mathematical Association of America for
expository articles in both 1986 and 2006.
