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  • Book
  • © 1999

Knowledge Spaces

Authors:

  1. Jean-Paul Doignon

    1. Département de Mathématiques, Université Libre de Bruxelles, Bruxelles, Belgium

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    You can also search for this author in PubMed   Google Scholar

  2. Jean-Claude Falmagne

    1. Department of Cognitive Science, University of California, Irvine, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Interdisciplinary representation of the theory of Knowledge Spaces.

  • Application oriented introduction based on real and simulated data.

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xv
    PDF

  2. Overview and Mathematical Glossary

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 1-17

  3. Knowledge Structures and Spaces

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 18-43

  4. Well-Graded Knowledge Structures

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 44-61

  5. Surmise Systems

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 62-85

  6. Skill Maps, Labels and Filters

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 86-103

  7. Entailments and the Maximal Mesh

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 104-119

  8. Galois Connections

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 120-141

  9. Probabilistic Knowledge Structures

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 142-174

  10. Stochastic Learning Paths

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 175-205

  11. Descriptive and Assessment Languages

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 206-218

  12. Uncovering the State of an Individual: A Continuous Markov Procedure

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 219-246

  13. Uncovering the State of an Individual: A Markov Chain Procedure

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 247-273

  14. Building the Knowledge Structure in Practice

    • Jean-Paul Doignon, Jean-Claude Falmagne
    Pages 274-309

  15. Back Matter

    Pages 310-333
    PDF
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About this book

Knowledge spaces offer a rigorous mathematical foundation for various practical systems of knowledge assessment. An example is offered by the ALEKS system (Assessment and LEarning in Knowledge Spaces), a software for the assessment of mathematical knowledge. From a mathematical standpoint, knowledge spaces generalize partially ordered sets. They are investigated both from a combinatorial and a stochastic viewpoint. The results are applied to real and simulated data. The book gives a systematic presentation of research and extends the results to new situations. It is of interest to mathematically oriented readers in education, computer science and combinatorics at research and graduate levels. The text contains numerous examples and exercises and an extensive bibliography.
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Keywords

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Authors and Affiliations

  • Département de Mathématiques, Université Libre de Bruxelles, Bruxelles, Belgium

    Jean-Paul Doignon

  • Department of Cognitive Science, University of California, Irvine, USA

    Jean-Claude Falmagne

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Bibliographic Information

  • Book Title: Knowledge Spaces

  • Authors: Jean-Paul Doignon, Jean-Claude Falmagne

  • DOI: https://doi.org/10.1007/978-3-642-58625-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1999

  • Softcover ISBN: 978-3-540-64501-6Published: 20 October 1998

  • eBook ISBN: 978-3-642-58625-5Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XVI, 334

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Discrete Mathematics, Artificial Intelligence, Combinatorics

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Buy it now

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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