Knowledge Spaces
Knowledge Spaces offers a rigorous mathematical foundation for various practical systems of knowledge assessment, applied to real and simulated data. The systematic presentation extends research results to new situations, as well as describing how to build the knowledge structure in practice. The book also contains numerous examples and exercises and an extensive bibliography. This interdisciplinary representation of the theory of knowledge spaces will be of interest to mathematically...
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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.
0Overview and Mathematical Glossary11Knowledge Structures and Spaces182Well-Graded Knowledge Structures443Surmise Systems624Skill Maps, Labels and Filters865Entailments and the Maximal Mesh1046Galois Connections1207Probabilistic Knowledge Structures1428Stochastic Learning Paths1759Descriptive and Assessment Languages20610Uncovering the State of an Individual: A Continuous Markov Procedure21911Uncovering the State of an Individual: A Markov Chain Procedure24712Building the Knowledge Structure in Practice274References310Index of Names321Index of Terms325
