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Learning Spaces

Interdisciplinary Applied Mathematics

  • Jean-Claude Falmagne
  • Jean-Paul Doignon

Table of contents

  1. Front Matter
    Pages i-xv
  2. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 1-21
  3. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 23-41
  4. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 43-60
  5. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 61-79
  6. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 81-101
  7. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 103-117
  8. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 119-131
  9. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 133-150
  10. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 151-162
  11. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 163-185
  12. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 187-214
  13. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 215-240
  14. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 241-272
  15. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 273-296
  16. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 297-333
  17. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 335-357
  18. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 359-374
  19. Jean-Claude Falmagne, Jean-Paul Doignon
    Pages 375-377
  20. Back Matter
    Pages 379-417

About this book

Introduction

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.

Keywords

ALEKS Markov processes antimatroid knowledge knowledge assessment knowledge space learning space mathematical psychology online learning psychometric methods skill map

Authors and affiliations

  • Jean-Claude Falmagne
    • 1
  • Jean-Paul Doignon
    • 2
  1. 1.School of Social Sciences, Dept. Cognitive SciencesUniversity of California, IrvineIrvineUSA
  2. 2.Dépt. MathematiqueUniversité Libre de BruxellesBruxellesBelgium

Bibliographic information