Preface.- 1 The Real Numbers.- 2 Sequences and Series.- 3 Basic Topology of R.- 4 Functional Limits and Continuity.- 5 The Derivative.- 6 Sequences and Series of Functions.- 7 The Riemann Integral.- 8 Additional Topics.- Bibliography.- Index.
Stephen D. Abbott is Professor of Mathematics at Middlebury College. He is a two-time winner of Middlebury’s Perkins Award for Excellence in Teaching (1998, 2010). His published work includes articles in the areas of operator theory and functional analysis, the algorithmic foundations of robotics, and the intersection of science, mathematics and the humanities.
“The choice of topics is a happy combination of the essential and
the interesting, all truly leading to an understanding of what
analysis is and what questions it addresses, aided by the author’s
extraordinarily lucid exposition. … Summing Up: Highly recommended.
Upper-division undergraduates.” (D. Robbins, Choice, Vol. 53 (2),
October, 2015)“This is the second edition of a text for an
undergraduate course in single-variable real analysis. … The topics
covered in this book are the ones that have, by now, become
standard for a one-semester undergraduate real analysis course … .
Overall, this book represents, to my mind, the gold standard among
single-variable undergraduate analysis texts.” (Mark Hunacek, MAA
Reviews, June, 2015)
“This is a dangerous book. Understanding Analysis is so
well-written and the development of the theory so well-motivated
that exposing students to it could well lead them to expect such
excellence in all their textbooks. … Understanding Analysis is
perfectly titled; if your students read it, that’s what’s going to
happen. This terrific book will become the text of choice for the
single-variable introductory analysis course; take a look at it
next time you’re preparing that class.”— Steve Kennedy, MAA
Reviews“Each chapter begins with a discussion section and ends with
an epilogue. The discussion serves to motivate the content of the
chapter while the epilogue points tantalisingly to more advanced
topics. … I wish I had written this book! The development of the
subject follows the tried-and-true path, but the presentation is
engaging and challenging. Abbott focuses attention immediately on
the topics which make analysis fascinating … and makes them
accessible to an inexperienced audience.”— Scott Sciffer, The
Australian Mathematical Society Gazette
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