Understanding Analysis

Stephen D. Abbott is a mathematics professor at Middlebury College. He has twice received Middlebury's Perkins Award for Excellence in Teaching (1998, 2010). His publications include essays on operator theory and functional analysis, robotics algorithmic underpinnings, and the interaction of science, mathematics, and the humanities.

This engaging introductory text introduces students to the benefits of rigorously studying functions of a real variable. In each chapter, informal discussions of the questions that captivate analysts are followed by explicit, but not unduly formal, developments of the techniques required to make sense of them. The text transforms what may be a daunting cascade of definitions and theorems into a logical and interesting flow of ideas 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 student is much better prepared to grasp what constitutes a proper mathematical proof and how to construct one now that he or she is acutely aware of the necessity for rigor.

The central narrative of the second edition has been developed and refined through fifteen years of classroom experience with the first version of Understanding Analysis. Approximately 150 new exercises have been added to a selection of the top exercises from the first edition, and three more project-style parts have been included. Investigations of Euler's computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book's seminal results, acting as motivation and payoff for the starting student to learn the analytical methods.

Author: Stephen Abbott

Link to buy: https://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/1493927116/

Ratings: 4.6 out of 5 stars (from 404 reviews)

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#10 in Mathematical Analysis (Books)

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