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Numbers and Functions
Steps into Analysis

3rd Edition

$63.00 ( ) USD

  • Date Published: February 2015
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781316028971

$ 63.00 USD ( )
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About the Authors
  • The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this third edition of Numbers and Functions, Professor Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of more than 800 problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, of which most are supplied with brief answers, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. Carefully corrected and updated throughout, this new edition also includes extra questions on integration and an introduction to convergence. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.

    • The third edition has been revised and updated
    • Helps students transition from school-level calculus to undergraduate mathematical analysis
    • Contains more than 800 exercises with brief answers and hints
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    Reviews & endorsements

    "This third edition of Numbers and Functions continues the author's long-term commitment to support every reader in making sense of mathematics by responding to a succession of well-chosen questions that encourage personal reflection and discussion with others. Groups of questions are followed by a summary to build the bigger picture. Every chapter includes details of the historical development and ends with a full list of solutions. The author is aware of the difficulties that students encounter with the complexity of the limit concept and begins with a pragmatic approach to null sequences. This broadens into a full study of limits of sequences, completeness, and a full range of tests for convergence of infinite series … This latest edition maintains the original chapters of the original, while benefiting from detailed improvements that have arisen from the experience of many readers. Thoroughly recommended."
    David Tall, University of Warwick

    Review of previous edition: "… written in a very comprehensible but exact way … an excellent guide through the basic course of mathematical analysis at university."
    European Mathematical Society Newsletter

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    Product details

    • Edition: 3rd Edition
    • Date Published: February 2015
    • format: Adobe eBook Reader
    • isbn: 9781316028971
    • contains: 65 b/w illus. 800 exercises
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    Preface to first edition
    Preface to second edition
    Preface to third edition
    Glossary
    Part I. Numbers:
    1 Mathematical induction
    2. Inequalities
    3. Sequences: a first bite at infinity
    4. Completeness: what the rational numbers lack
    5. Series: infinite sums
    Part II. Functions:
    6. Functions and continuity: neighbourhoods, limits of functions
    7. Continuity and completeness: functions on intervals
    8. Derivatives: tangents
    9. Differentiation and completeness: mean value theorems, Taylor's Theorem
    10. Integration: the fundamental theorem of calculus
    11. Indices and circle functions
    12. Sequences of functions
    Appendix 1. Properties of the real numbers
    Appendix 2. Geometry and intuition
    Appendix 3. Questions for student investigation and discussion
    Bibliography
    Index.

  • Author

    R. P. Burn, University of Exeter
    R. P. Burn is an Honorary University Fellow at the University of Exeter. His other titles include Groups: A Path to Geometry (1985) and A Pathway into Number Theory (1982).

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