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Alice in Numberland

A Students’ Guide to the Enjoyment of Higher Mathematics

  • Textbook
  • © 1988
  • Latest edition

Overview

Authors:
  1. John Baylis
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  2. Rod Haggarty
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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
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  2. Alice in Logiland — in which we meet Alice, Tweedledee and Tweedledum, and Logic …

    • John Baylis, Rod Haggarty
    Pages 1-13

  3. Unique Factorisation — in which trivial arithmetic reveals a glimpse of hidden depths

    • John Baylis, Rod Haggarty
    Pages 14-20

  4. Numbers—in which we abandon logic to achieve understanding, then use logic to deepen understanding

    • John Baylis, Rod Haggarty
    Pages 21-35

  5. The Real Numbers—in which we find holes in the number line and pay the price for repairs

    • John Baylis, Rod Haggarty
    Pages 36-51

  6. A Variety of Versions and Uses of Induction—in which another triviality plays the lead

    • John Baylis, Rod Haggarty
    Pages 52-71

  7. Permutations—in which ALICE is transformed

    • John Baylis, Rod Haggarty
    Pages 72-88

  8. Nests—in which the rationals give birth to the reals and the scene is set for arithmetic in ℝ

    • John Baylis, Rod Haggarty
    Pages 89-97

  9. Axioms for ℝ—in which we invent Arithmetic, Order our numbers and Complete our description of the reals

    • John Baylis, Rod Haggarty
    Pages 98-110

  10. Some Infinite Surprises—in which some wild sets are tamed, and some nearly escape

    • John Baylis, Rod Haggarty
    Pages 111-140

  11. Sequences and Series— in which we discover very odd behaviour in even the smallest infinite set

    • John Baylis, Rod Haggarty
    Pages 141-160

  12. Graphs and Continuity—in which we arrange a marriage between Intuition and Rigour

    • John Baylis, Rod Haggarty
    Pages 161-176

  13. Back Matter

    Pages 177-205
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Keywords

About this book

...quite the best one I have had the fortune to read... admirable alternative reading for a foundation course introducing university mathematics.' David Tall, The Times Higher Educational Supplement

Bibliographic Information

  • Book Title: Alice in Numberland

  • Book Subtitle: A Students’ Guide to the Enjoyment of Higher Mathematics

  • Authors: John Baylis, Rod Haggarty

  • DOI: https://doi.org/10.1007/978-1-349-09532-2

  • Publisher: Red Globe Press London

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: John Baylis and Rod Haggarty 1988

  • Edition Number: 1

  • Number of Pages: IX, 205

  • Additional Information: Previously published under the imprint Palgrave

  • Topics: Number Theory

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