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Learning Spaces - Jean-Claude Falmagne, Jean-Paul Doignon

Learning Spaces

Interdisciplinary Applied Mathematics
Buch | Softcover
XV, 417 Seiten
2014 | 2011
Springer Berlin (Verlag)
978-3-642-42277-5 (ISBN)
CHF 249,95 inkl. MwSt
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Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Describing the underlying theory and applications involved with ancillary assessment procedures, Learning Spaces provides an overview for mathematically oriented readers in education, computer science, and additional disciplines.

Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes.

Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At the heart of ALEKS is an artificial intelligence engine that assesses each student individually and continously.

The book is of interest to mathematically oriented readers in education, computer science, engineering, and combinatorics at research and graduate levels. Numerous examples and exercises are included, together with an extensive bibliography.

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.

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

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)

Erscheint lt. Verlag 28.11.2014
Zusatzinfo XV, 417 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 664 g
Themenwelt Schulbuch / Wörterbuch
Mathematik / Informatik Informatik Grafik / Design
Informatik Office Programme Outlook
Informatik Theorie / Studium Künstliche Intelligenz / Robotik
Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Angewandte Mathematik
Sozialwissenschaften Pädagogik
Schlagworte ALEKS • antimatroid • Knowledge • knowledge assessment • knowledge space • learning space • Markov Processes • Mathematical Psychology • Online Learning • psychometric methods • skill map
ISBN-10 3-642-42277-2 / 3642422772
ISBN-13 978-3-642-42277-5 / 9783642422775
Zustand Neuware
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