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Catalogue Information
Field name	Details
Dewey Class	519
Title	Learning Spaces ([Ebook]) : Interdisciplinary Applied Mathematics / by Jean-Claude Falmagne, Jean-Paul Doignon.
Author	Falmagne, Jean-Claude
Added Personal Name	Doignon, Jean-Paul
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 2011.
Physical Details	XV, 417 pages: 60 illus., 30 illus. in color. : online resource.
ISBN	9783642010392
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-642-01039-2
Links to Related Works	Subject References: Applications of Mathematics . Artificial intelligence . Artificial Intelligence (incl. Robotics) . Computers and Education . Math Applications in Computer Science . Mathematics Education . Multimedia systems . Authors: author . Doignon, Jean-Paul . Falmagne, Jean-Claude . Corporate Authors: SpringerLink (Online service) . Classification: 519 . 519 (DDC 23) .

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Learning Spaces: Interdisciplinary Applied Mathematics

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