9781575863245

Mathematical Reasoning with Diagrams : From Intuition to Automation

by
  • ISBN13:

    9781575863245

  • ISBN10:

    1575863243

  • Format: Paperback
  • Copyright: 2001-11-01
  • Publisher: Univ of Chicago Pr
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Supplemental Materials

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  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

Summary

Mathematicians at every level use diagrams to prove theorems.Mathematical Reasoning with Diagramsinvestigates the possibilities of mechanizing this sort of diagrammatic reasoning in a formal computer proof system, even offering a semi-automatic formal proof system--called Diamond--which allows users to prove arithmetical theorems using diagrams.

Author Biography

Elizabeth A. Kaye specializes in communications as part of her coaching and consulting practice. She has edited Requirements for Certification since the 2000-01 edition.


Table of Contents

Foreword vii
Preface xi
Introduction
1(10)
The History of Diagrammatic Systems
11(16)
Diagrammatic Theorems and the Problem Domain
27(22)
The Constructive w-Rule and Schematic Proofs
49(22)
Designing a Diagrammatic Reasoning System
71(18)
Diagrammatic Operations
89(14)
The Construction of Schematic Proofs
103(20)
The Verification of Schematic Proofs
123(26)
Diamond in Action
149(14)
Complete Automation
163(12)
Appendix A: More Examples of Diagrammatic Theorems 175(6)
Appendix B: The w-Rule 181(4)
Glossary 185(5)
References 190(9)
Index 199

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