Authors: Jean-Paul Doignon, Jean-Claude Falmagne
ISBN-13: 9783540645016, ISBN-10: 3540645012
Format: Paperback
Publisher: Springer-Verlag New York, LLC
Date Published: January 2008
Edition: 1st Edition
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.
0 | Overview and Mathematical Glossary | 1 |
1 | Knowledge Structures and Spaces | 18 |
2 | Well-Graded Knowledge Structures | 44 |
3 | Surmise Systems | 62 |
4 | Skill Maps, Labels and Filters | 86 |
5 | Entailments and the Maximal Mesh | 104 |
6 | Galois Connections | 120 |
7 | Probabilistic Knowledge Structures | 142 |
8 | Stochastic Learning Paths | 175 |
9 | Descriptive and Assessment Languages | 206 |
10 | Uncovering the State of an Individual: A Continuous Markov Procedure | 219 |
11 | Uncovering the State of an Individual: A Markov Chain Procedure | 247 |
12 | Building the Knowledge Structure in Practice | 274 |
References | 310 | |
Index of Names | 321 | |
Index of Terms | 325 |