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Elements of Logic via Numbers and Sets

  • Textbook
  • © 1998

Overview

Authors:
  1. D. L. Johnson

    1. Department of Mathematics, University of Nottingham, Nottingham, UK

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  • AN ELEMENTARY TEXT THAT WILL INTRODUCE SCHOOL-LEAVERS TO THE CHANGE IN ATTITUDE AND APPROACH NECESSARY TO BECOME UNIVERSITY STUDENTS INTRODUCES THE ROLE AND NATURE OF PROOFS, AND SET THEORIES
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Undergraduate Mathematics Series (SUMS)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Numbers

    • D. L. Johnson
    Pages 1-33

  3. Logic

    • D. L. Johnson
    Pages 35-51

  4. Sets

    • D. L. Johnson
    Pages 53-70

  5. Relations

    • D. L. Johnson
    Pages 71-88

  6. Maps

    • D. L. Johnson
    Pages 89-111

  7. Cardinal Numbers

    • D. L. Johnson
    Pages 113-130

  8. Back Matter

    Pages 131-174
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Keywords

About this book

In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.

Reviews

From the reviews: “It took me a while to appreciate the need for a course intended to introduce mathematics undergraduates to advanced mathematics after they finish the calculus sequence. … This was the first book I found that seems really close to the core. It is well-written and very well suited to such a course.” (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)

Authors and Affiliations

  • Department of Mathematics, University of Nottingham, Nottingham, UK

    D. L. Johnson

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