Learning Spaces

Interdisciplinary Applied Mathematics

Authors: Falmagne, Jean-Claude, Doignon, Jean-Paul

  • Introduces learning space as a special case of knowledge space.
  • Exposes theory and several applications of learning spaces and ancillary assessment procedures.
  • Presents ALEKS as a practical application of learning spaces for an efficient web based learning environment.
see more benefits

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-3-642-01039-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-642-01038-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-3-642-42277-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

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.

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.

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)


Table of contents (18 chapters)

  • Overview and Basic Mathematical Concepts

    Falmagne, Jean-Claude (et al.)

    Pages 1-21

  • Knowledge Structures and Learning Spaces

    Falmagne, Jean-Claude (et al.)

    Pages 23-41

  • Knowledge Spaces

    Falmagne, Jean-Claude (et al.)

    Pages 43-60

  • Well-Graded Knowledge Structures

    Falmagne, Jean-Claude (et al.)

    Pages 61-79

  • Surmise Systems

    Falmagne, Jean-Claude (et al.)

    Pages 81-101

Buy this book

eBook $139.00
price for USA (gross)
  • ISBN 978-3-642-01039-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.00
price for USA
  • ISBN 978-3-642-01038-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $179.00
price for USA
  • ISBN 978-3-642-42277-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Learning Spaces
Book Subtitle
Interdisciplinary Applied Mathematics
Authors
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-01039-2
DOI
10.1007/978-3-642-01039-2
Hardcover ISBN
978-3-642-01038-5
Softcover ISBN
978-3-642-42277-5
Edition Number
1
Number of Pages
XV, 417
Topics