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Understanding analysis / Stephen Abbott.

By: Material type: TextTextSeries: Undergraduate texts in mathematicsPublication details: New York : Springer Science+Business Media, 2015.Edition: 2nd edDescription: xii, 312 p. : illustrations ; 25 cmISBN:
  • 9781493927111
Subject(s): DDC classification:
  • 515 23 Ab134
Contents:
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.
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.
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Includes bibliographical references and index.

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.

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.

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