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© 2011

Learning Spaces

Interdisciplinary Applied Mathematics

Book

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

  1. 1.School of Social Sciences, Dept. Cognitive SciencesUniversity of California, IrvineIrvineUSA
  2. 2.Dépt. MathematiqueUniversité Libre de BruxellesBruxellesBelgium

About the authors

Jean-Paul Doignon is a professor at the mathematics department of the Université Libre de Bruxelles, Belgium. His research covers various aspects of discrete mathematics (graphs, ordered sets, convex polytopes, etc.) and applications to behavioral sciences (preference modeling, choice representation, knowledge assessment, etc.). Jean-Claude Falmagne is emeritus professor of cognitive sciences at the University of California, Irvine. His research interests span various areas, focusing on the application of mathematics to educational technology, psychophysics, choice theory, and the philosophy of science, in particular measurement theory.

Bibliographic information

Reviews

From the reviews:

“The book deals with the construction of knowledge spaces and learning spaces … . Thus, the creative mathematician will find material capable of entertaining him or her for some time. The practitioner may be interested in applications. … there is no doubt that reading and working with this book will be rewarding for the mathematician and useful for scientists from very different areas. In many aspects it has the potential to serve as a guideline to a new and theoretically better founded form of psychometry.” (Reinhard Suck, SIAM Review, Vol. 54 (2), 2012)

“This book is an enlarged second edition of the 1999 ‘Knowledge Spaces’ by the same authors. … The authors cover both deterministic and probabilistic models, justify their findings and give good examples and applications, such as pattern recognition and medical diagnosis. … We recommend it to doctoral and postdoctoral studies.” (George Stoica, Zentralblatt MATH, Vol. 1205, 2011)