Knowledge Spaces

By: Jean-Paul Doignon, Jean-Claude Falmagne

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Paperback | 20 October 1998

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356 Pages

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23.39 x 15.6 x 1.88

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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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Overview and Mathematical Glossary	p. 1
Knowledge Structures and Spaces	p. 18
Well-Graded Knowledge Structures	p. 44
Surmise Systems	p. 62
Skill Maps, Labels and Filters	p. 86
Entailments and the Maximal Mesh	p. 104
Galois Connections	p. 120
Probabilistic Knowledge Structures	p. 142
Stochastic Learning Paths	p. 175
Descriptive and Assessment Languages	p. 206
Uncovering the State of an Individual: A Continuous Markov Procedure	p. 219
Uncovering the State of an Individual: A Markov Chain Procedure	p. 247
Building the Knowledge Structure in Practice	p. 274
References	p. 310
Index of Names	p. 321
Index of Terms	p. 325
Table of Contents provided by Blackwell. All Rights Reserved.

Knowledge Spaces

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Paperback

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