Learning Spaces Interdisciplinary Applied Mathematics / by Jean-Claude Falmagne, Jean-Paul Doignon.

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 s...

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Bibliographic Details
Main Authors: Falmagne, Jean-Claude. (Author, http://id.loc.gov/vocabulary/relators/aut), Doignon, Jean-Paul. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Format: eBook
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Edition:1st ed. 2011.
Series:Springer eBook Collection.
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.