Learning spaces

Learning spaces: interdisciplinary applied mathematics

by Falmagne, Jean-Claude

Type Book
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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 result…

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Title Statements

  • Full title :Learning spaces : interdisciplinary applied mathematics / Jean-Claude Falmagne and Jean-Paul Doignon.

Summary

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.

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Edition Statements

  • Publication Date:2010.

Publication Statements

  • Publisher(s):Springer
  • Place of Publication:Berlin
  • Language:eng
  • Publication Date:2010.

The Physical Object

  • Description:1 online resource

Edition Identifiers

  • ISBN:9783642010392, 3642010393
  • oclc:on1100881125
  • LC Classification:LB1028.73
  • Dewey Decimal:371.33463

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.

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Subjects

Artificial intelligence -- Educational … Classement et notation (Élèves et étudi… Grading and marking (Students) Intelligence artificielle -- Applicatio… Intelligent tutoring systems Tutoriels

Writers

Falmagne, Jean-Claude Doignon, Jean-Paul

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