Learning spaces : interdisciplinary applied mathematics

Auteur :
Falmagne Jean-Claude
Doignon Jean-Paul, auteur
Publication :
Berlin, Heidelberg : Springer Berlin Heidelberg : Springer e-books, 2011
Collection :
Mathematics and Statistics
Note :
Numerisation de l'édition de : New York : Springer Science+Business Media, LLC et Springer e-books, 2011
Bibliogr. Index
Résumé :
Learning 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, learning spaces as well as knowledge spaces (which made the title of the first edition) 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
Contenu :
Overview and Mathematical Glossary Knowledge Structures and Learning Spaces Knowledge Spaces Well-Graded Families Surmise Systems Skill Maps, Labels and Filters Entailments and the Maximal Mesh Galois Connections Descriptive and Assessment Languages Greedoids, Learning Spaces, and Antimatroids Learning Spaces and Media Probabilistic Knowledge Structures Stochastic Learning Paths A Continuous Markov Procedure A Markov Chain Procedure Building a Knowledge Structure Building a Learning Space Applications Open Problems
Disponible en ligne
Langue :
Type de document :
Ressource électronique
Thèmes :
Computer science
Multimedia systems
Artificial intelligence
Applications of Mathematics
Artificial Intelligence (incl. Robotics)
Multimedia Information Systems
Math Applications in Computer Science
Mathematics Education
Computers and Education