Understanding analysis
 Responsibility
 Stephen Abbott.
 Edition
 Second edition.
 Publication
 New York ; Heidelberg : Springer, [2015]
 Copyright notice
 ©2001
 Physical description
 xii, 312 pages : illustrations ; 25 cm.
 Series
 Undergraduate texts in mathematics.
Course reserve
 Course
 MATH83N01  Proofs and Modern Mathematics
 Instructor(s)
 Sauermann, Lisa
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA300 .A18 2015  On reserve at Li and Ma Science Library 4hour loan 
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Description
Creators/Contributors
 Author/Creator
 Abbott, Stephen, 1964 author.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 305306) and index.
 Contents

 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.
 (source: Nielsen Book Data)
 Summary

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 from the first edition, and three more projectstyle 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. Review of the first edition: "This is a dangerous book. Understanding Analysis is so wellwritten and the development of the theory so wellmotivated 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 singlevariable introductory analysis course ..."  Steve Kennedy, MAA Reviews.
(source: Nielsen Book Data)
Subjects
 Subject
 Mathematical analysis.
Bibliographic information
 Publication date
 2015
 Copyright date
 2015
 Series
 Undergraduate texts in mathematics, 01726056
 ISBN
 9781493927111 (hd. bd.)
 1493927116 (hd. bd.)
 9781493927128 (eBook)