Learning spaces: interdisciplinary applied mathematics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XV, 417 S. Ill., graph. Darst. |
| ISBN: | 9783642010385 |
Internformat
MARC
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
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Datensatz im Suchindex
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| adam_text |
CONTENTS OVERVIEW AND BASIC MATHEMATICAL CONCEPTS 1 1.1 MAIN CONSTRUCTS
2 1.2 POSSIBLE LIMITATIONS 9 1.3 A PRACTICAL APPLICATION: THE ALEKS
SYSTEM 10 1.4 POTENTIAL APPLICATIONS TO OTHER FIELDS 11 1.5 ON THE
CONTENT AND ORGANIZATION OF THIS BOOK 12 1.6 BASIC MATHEMATICAL CONCEPTS
AND NOTATION 13 1.7 ORIGINAL SOURCES AND MAIN REFERENCES 17 PROBLEMS 19
KNOWLEDGE STRUCTURES AND LEARNING SPACES 23 2.1 FUNDAMENTAL CONCEPTS 23
2.2 AXIOMS FOR LEARNING SPACES 26 2.3 THE NONDISCRIMINATIVE CASE* 30 2.4
PROJECTIONS 31 2.5 ORIGINAL SOURCES AND RELATED WORKS 38 PROBLEMS 39
KNOWLEDGE SPACES 43 3.1 OUTLINE 43 3.2 GENERATING KNOWLEDGE SPACES BY
QUERYING EXPERTS 44 3.3 CLOSURE SPACES 45 3.4 BASES AND ATOMS 47 3.5 AN
ALGORITHM FOR CONSTRUCTING THE BASE 49 3.6 BASES AND ATOMS: THE INFINITE
CASE* 52 3.7 THE SURMISE RELATION 54 3.8 QUASI ORDINAL SPACES 56 3.9
ORIGINAL SOURCES AND RELATED WORKS 58 PROBLEMS 59 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/1000033740 DIGITALISIERT DURCH XII
CONTENTS 4 WELL-GRADED KNOWLEDGE STRUCTURES 61 4.1 LEARNING PATHS,
GRADATIONS, AND FRINGES 61 4.2 A WELL-GRADED FAMILY OF RELATIONS: THE
BIORDERS* 66 4.3 INFINITE WELLGRADEDNESS* 69 4.4 FINITE LEARNABILITY 72
4.5 VERIFYING WELLGRADEDNESS FOR A U-CLOSED FAMILY 73 4.6 ORIGINAL
SOURCES AND RELATED WORKS 77 PROBLEMS 78 5 SURMISE SYSTEMS 81 5.1 BASIC
CONCEPTS 81 5.2 KNOWLEDGE SPACES AND SURMISE SYSTEMS 85 5.3 AND/OR
GRAPHS 87 5.4 SURMISE FUNCTIONS AND WELLGRADEDNESS 90 5.5 HASSE SYSTEMS
92 5.6 RESOLUBILITY AND ACYCLICITY 96 5.7 ORIGINAL SOURCES AND RELATED
WORKS 99 PROBLEMS 100 6 SKILL MAPS, LABELS AND FILTERS 103 6.1 SKILLS
103 6.2 SKILL MAPS: THE DISJUNCTIVE MODEL 106 6.3 MINIMAL SKILL MAPS 107
6.4 SKILL MAPS: THE CONJUNCTIVE MODEL 110 6.5 SKILL MULTIMAPS: THE
COMPETENCY MODEL 112 6.6 LABELS AND FILTERS 113 6.7 ORIGINAL SOURCES AND
RELATED WORKS 116 PROBLEMS 117 7 ENTAILMENTS AND THE MAXIMAL MESH 119
7.1 ENTAILMENTS 120 7.2 ENTAIL RELATIONS 124 7.3 MESHABILITY OF
KNOWLEDGE STRUCTURES 125 7.4 THE MAXIMAL MESH 127 7.5 ORIGINAL SOURCES
AND RELATED WORKS 130 PROBLEMS 131 8 GALOIS CONNECTIONS* 133 8.1 THREE
EXEMPLARY CORRESPONDENCES 133 8. CONTENTS XIII 9 DESCRIPTIVE AND
ASSESSMENT LANGUAGES* 151 9.1 LANGUAGES AND DECISION TREES 151 9.2
TERMINOLOGY 155 9.3 RECOVERING ORDINAL KNOWLEDGE STRUCTURES 157 9.4
RECOVERING KNOWLEDGE STRUCTURES 160 9.5 ORIGINAL SOURCES AND RELATED
WORKS 161 PROBLEMS 162 10 LEARNING SPACES AND MEDIA 163 10.1 MAIN
CONCEPTS OF MEDIA THEORY 164 10.2 SOME BASIC LEMMAS 168 10.3 THE CONTENT
OF A STATE 169 10.4 ORIENTED MEDIA 174 10.5 LEARNING SPACES AND CLOSED,
ROOTED MEDIA 179 10.6 ORIGINAL SOURCES AND RELATED WORKS 183 PROBLEMS
183 11 PROBABILISTIC KNOWLEDGE STRUCTURES 187 11.1 BASIC CONCEPTS AND
EXAMPLES 187 11.2 AN EMPIRICAL APPLICATION 191 11.3 THE LIKELIHOOD RATIO
PROCEDURE 195 11.4 LEARNING MODELS 198 11.5 A COMBINATORIAL RESULT 200
11.6 MARKOV CHAIN MODELS 203 11.7 PROBABILISTIC PROJECTIONS 206 11.8
NOMENCLATURES AND CLASSIFICATIONS 209 11.9 INDEPENDENT PROJECTIONS 209
11.10 ORIGINAL SOURCES AND RELATED WORKS 213 PROBLEMS 213 12 STOCHASTIC
LEARNING PATHS* 215 12.1 A KNOWLEDGE STRUCTURE IN EUCLIDEAN GEOMETRY 215
12.2 BASIC CONCEPTS 216 12.3 GENERAL RESULTS 221 12.4 ASSUMPTIONS ON
DISTRIBUTIONS 224 12.5 THE LEARNING LATENCIES 225 12.6 EMPIRICAL
PREDICTIONS 228 12.7 LIMITATIONS OF THIS THEORY 231 12. XIV CONTENTS 13
UNCOVERING THE LATENT STATE: A CONTINUOUS MARKOV PROCEDURE 241 13.1 A
DETERMINISTIC ALGORITHM 241 13.2 OUTLINE OF A MARKOVIAN STOCHASTIC
PROCESS 243 13.3 BASIC CONCEPTS 246 13.4 SPECIAL CASES 249 13.5 GENERAL
RESULTS 253 13.6 UNCOVERING THE LATENT STATE 255 13.7 A TWO-STEP
ASSESSMENT ALGORITHM 259 13.8 REFINING THE ASSESSMENT 265 13.9 PROOFS*
267 13.10 ORIGINAL SOURCES AND RELATED WORKS 271 PROBLEMS 271 14 A
MARKOV CHAIN PROCEDURE 273 14.1 OUTLINE 273 14.2 THE STOCHASTIC
ASSESSMENT PROCESS 277 14.3 COMBINATORIAL ASSUMPTIONS ON THE STRUCTURE
279 14.4 MARKOV CHAINS TERMINOLOGY 283 14.5 RESULTS FOR THE FAIR CASE
284 14.6 UNCOVERING A STOCHASTIC STATE: EXAMPLES 287 14.7 INTRACTABLE
CASES 292 14.8 ORIGINAL SOURCES AND RELATED WORKS 295 PROBLEMS 295 15
BUILDING A KNOWLEDGE SPACE 297 15.1 BACKGROUND TO THE QUERY ROUTINE 298
15.2 KOPPEN'S ALGORITHM 302 15.3 KAMBOURI'S EXPERIMENT 310 15.4 RESULTS
315 15.5 COSYN AND THIERY'S WORK 324 15.6 REFINING A KNOWLEDGE STRUCTURE
328 15.7 SIMULATIONS OF VARIOUS REFINEMENTS 330 15.8 ORIGINAL SOURCES
AND RELATED WORKS 332 PROBLEMS 332 16 BUILDING A LEARNING SPACE 335 16.1
PREPARATORY CONCEPTS AND AN EXAMPLE 336 16. CONTENTS XV 17 ANALYZING THE
VALIDITY OF AN ASSESSMENT 359 17.1 THE CONCEPT OF VALIDITY FOR AN
ASSESSMENT 359 17.2 THE ALEKS ASSESSMENT ALGORITHM 361 17.3 THE METHODS
362 17.4 DATA ANALYSIS 367 17.5 SUMMARY 373 PROBLEMS 374 18 OPEN
PROBLEMS 375 18.1 KNOWLEDGE SPACES AND U-CLOSED FAMILIES 375 18.2
WELLGRADEDNESS AND THE FRINGES 376 18.3 ABOUT GRANULARITY 377 18.4
MISCELLANEOUS 377 GLOSSARY 379 BIBLIOGRAPHY 397 INDEX 409 |
| any_adam_object | 1 |
| author | Falmagne, Jean-Claude 1934- Doignon, Jean-Paul |
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| dewey-full | 006.336 150.151 |
| dewey-hundreds | 000 - Computer science, information, general works 100 - Philosophy & psychology |
| dewey-ones | 006 - Special computer methods 150 - Psychology |
| dewey-raw | 006.336 150.151 |
| dewey-search | 006.336 150.151 |
| dewey-sort | 16.336 |
| dewey-tens | 000 - Computer science, information, general works 150 - Psychology |
| discipline | Informatik Psychologie Mathematik |
| format | Book |
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| spelling | Falmagne, Jean-Claude 1934- Verfasser (DE-588)120260980 aut Learning spaces interdisciplinary applied mathematics Jean-Claude Falmagne ; Jean-Paul Doignon Berlin [u.a.] Springer 2011 XV, 417 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wissensraumtheorie (DE-588)7696652-5 gnd rswk-swf Algorithmische Lerntheorie (DE-588)4701014-9 gnd rswk-swf Wissensraumtheorie (DE-588)7696652-5 s Algorithmische Lerntheorie (DE-588)4701014-9 s DE-604 Doignon, Jean-Paul Verfasser aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423777&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020199061&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Falmagne, Jean-Claude 1934- Doignon, Jean-Paul Learning spaces interdisciplinary applied mathematics Wissensraumtheorie (DE-588)7696652-5 gnd Algorithmische Lerntheorie (DE-588)4701014-9 gnd |
| subject_GND | (DE-588)7696652-5 (DE-588)4701014-9 |
| title | Learning spaces interdisciplinary applied mathematics |
| title_auth | Learning spaces interdisciplinary applied mathematics |
| title_exact_search | Learning spaces interdisciplinary applied mathematics |
| title_full | Learning spaces interdisciplinary applied mathematics Jean-Claude Falmagne ; Jean-Paul Doignon |
| title_fullStr | Learning spaces interdisciplinary applied mathematics Jean-Claude Falmagne ; Jean-Paul Doignon |
| title_full_unstemmed | Learning spaces interdisciplinary applied mathematics Jean-Claude Falmagne ; Jean-Paul Doignon |
| title_short | Learning spaces |
| title_sort | learning spaces interdisciplinary applied mathematics |
| title_sub | interdisciplinary applied mathematics |
| topic | Wissensraumtheorie (DE-588)7696652-5 gnd Algorithmische Lerntheorie (DE-588)4701014-9 gnd |
| topic_facet | Wissensraumtheorie Algorithmische Lerntheorie |
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