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＜電子ブック＞
Learning Spaces : Interdisciplinary Applied Mathematics / by Jean-Claude Falmagne, Jean-Paul Doignon

版	1st ed. 2011.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2011
本文言語	英語
大きさ	XV, 417 p : online resource
著者標目	*Falmagne, Jean-Claude author Doignon, Jean-Paul author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Artificial intelligence LCSH:Multimedia systems LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Education -- Data processing  全ての件名で検索 LCSH:Mathematics -- Study and teaching   全ての件名で検索 FREE:Applications of Mathematics FREE:Artificial Intelligence FREE:Multimedia Information Systems FREE:Mathematical Applications in Computer Science FREE:Computers and Education FREE:Mathematics Education
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-01039-2

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