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Relational Mathematics

$125.00 (C)

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: December 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521762687

$ 125.00 (C)

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About the Authors
  • Relational mathematics is to operations research and informatics what numerical mathematics is to engineering: it is intended to help modelling, reasoning, and computing. Its applications are therefore diverse, ranging from psychology, linguistics, decision aid, and ranking to machine learning and spatial reasoning. Although many developments have been made in recent years, they have rarely been shared amongst this broad community of researchers. This first comprehensive overview begins with an easy introduction to the topic, assuming a minimum of prerequisites; but it is nevertheless theoretically sound and up to date. It is suitable for applied scientists, explaining all the necessary mathematics from scratch using a multitude of visualised examples, via matrices and graphs. It ends with tangible results on the research level. The author illustrates the theory and demonstrates practical tasks in operations research, social sciences and the humanities.

    • A thorough reference for researchers working in a wide variety of fields
    • The theory is illustrated by a wealth of exercises and practical examples
    • Assumes only basic prerequisites with mathematics explained from scratch
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    Reviews & endorsements

    "This book is an important contribution to the literature on relational algebra, especially for English speakers. Much of the work in the field has been done in German, or else maybe in English but scattered among individual papers or in volumes of proceedings. It is good to have a comprehensive, albeit very theoretical, book in English."
    Anthony J. Duben, Computing Reviews

    "This text is deliberately encyclopedic, extremely precise and detailed, and the results aimed toward applications in areas such as psychology, linguistics, decision analysis and machine learning."
    S.I. Gendler, Mathematical Reviews

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    Product details

    • Date Published: December 2010
    • format: Hardback
    • isbn: 9780521762687
    • length: 582 pages
    • dimensions: 234 x 156 x 32 mm
    • weight: 0.99kg
    • contains: 420 b/w illus. 70 exercises
    • availability: Available
  • Table of Contents

    1. Introduction
    Part I. Representations of Relations:
    2. Sets, subsets and elements
    3. Relations
    Part II. Operations and Constructions:
    4. Algebraic operations on relations
    5. Order and function: the standard view
    6. Relations and vectors
    7. Domain construction
    Part III. Algebra:
    8. Relation algebra
    9. Orders and lattices
    10. Rectangles, fringes, inverses
    11. Concept analysis
    Part IV. Applications:
    12. Orderings: an advanced view
    13. Preference and indifference
    14. Aggregating preferences
    15. Relational graph theory
    16. Standard Galois mechanisms
    Part V. Advanced Topics:
    17. Mathematical applications
    18. Implication structures
    19. Power operations
    Appendix A. Notations
    Appendix B. Postponed proofs of Part II
    Appendix C. Algebraic visualization
    Appendix D. Historical annotations
    Table of symbols

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    Relational Mathematics

    Gunther Schmidt

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  • Author

    Gunther Schmidt, Universität der Bundeswehr München
    Gunther Schmidt was a Professor in the Faculty for Informatics of the Universität der Bundeswehr München before his retirement in 2004.

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