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  • Cited by 27
    • The digital format of this book is no longer available to purchase from Cambridge Core. Other formats may be available.
    • This edition is no longer available and has been replaced by: 9781108539890
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    • Publisher:
      Cambridge University Press
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      January 2006
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      DOI:
      https://doi.org/10.1017/CBO9780511808234
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      • Subjects:
      Mathematics, Logic, Categories and Sets
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    Subjects:
    Mathematics, Logic, Categories and Sets
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    Book description

    Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

    Reviews

    'The book begins with the basic concepts of logic and theory … These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. No background standard in high scholl mathematics is assumed.'

    Source: L'Enseignement Mathématique

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    Contents

    Contents
    • 1 - Sentential Logic
      pp 8-54
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