Mathematical model techniques for learning theories:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Acad. Press
1972
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 288 S. graph. Darst. |
| ISBN: | 0124452507 |
Staff View
MARC
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| 100 | 1 | |a Levine, Gustav |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical model techniques for learning theories |c Gustav Levine ; C. J. Burke |
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1972 | |
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| 650 | 4 | |a Psicología del aprendizaje - Modelos matemáticos | |
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Record in the Search Index
| _version_ | 1804116422061719552 |
|---|---|
| adam_text | Titel: Mathematical model techniques for learning theories
Autor: Levine, Gustav
Jahr: 1972
Contents
Preface
Chapter One INTRODUCTION
Mathematical Analogies for Learning
The Theory Generates the Equation
The Theories Are Restricted in Scope
Data Collection Is Essential to Mathematical Model Development
The Basic Terms of a Mathematical Model
A Theory s Theorems and a Model s Equations
The Use of the Term Model
Three Submodels
The Purpose of This Book
Chapter Two PROBABILITY THEORY AND THE
DIRECT METHOD
Random Variables
Expected Values
Probability
The Three Basic Axioms of Probability
Conditional Probability
Joint Events
vii
Viii CONTENTS
Probability Distributions 23
Unique Shapes of Probability Distributions 23
Recurrent Probability Distributions 23
The Direct Method 31
The Theory Underlying Bowels One-Element Model 32
Application of the Direct Method to Bower s Theory 34
Sums of Geometric Series 40
Finite Series 41
Infinite Series 44
Applications of Summation of Geometric Series in Bower s Model 48
Problems 54
Chapter Three DIFFERENCE EQUATIONS
Mathematical Induction 57
The Summation Technique for Solving Difference Equations 65
Application of the Summation Technique for Solving Difference
Equations 69
The Multiple Operator Technique for Solving Difference Equations 81
The Meaning of Higher-Order Difference Equations 81
Solving Difference Equations in LaBerge s Model 92
Problems 97
Chapter Four LINEAR OPERATOR MODELS
Mathematical Implications of a Single-Operator Model 102
A Multiple-Operator Model 104
Control of Experimental Outcome 105
Problems 132
Chapter Five MATRIX ALGEBRA
Transition Matrices 134
Matrix Addition 136
Matrix Multiplication 136
The Inverse of a Matrix 140
Obtaining the nth Power of a Matrix 150
Problems 159
Chapter Six MARKOV CHAINS
Independence of Previous Sequence of States in Markov Processes
A Single Matrix Represents All Information in a Markov Chain
162
165
CONTENTS ix
The Canonical Matrix 168
Summary 194
Problems 195
Chapter Seven A MARKOV CHAIN ANALYSIS OF
AVOIDANCE CONDITIONING
Some Theories for an Avoidance Conditioning Paradigm 198
General Solutions for a General Transition Matrix 205
Parameter Estimation 224
Chapter Eight OBSERVABLE STATES AND
IDENTIFIABLE PARAMETERS
A Theory with Nonobservable States 236
An Example of Conversion to an Observable States Theory 238
Obtaining Identifiable Parameters 243
Working with Four Unknowns and Three Independent Equations 246
Comparing Two Models of the Same Theory 249
Problems 255
REFERENCES 257
SOLUTIONS TO PROBLEMS 259
Index
285
|
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| dewey-full | 370.15/2/0151 511/.8 |
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| dewey-ones | 370 - Education 511 - General principles of mathematics |
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| dewey-search | 370.15/2/0151 511/.8 |
| dewey-sort | 3370.15 12 3151 |
| dewey-tens | 370 - Education 510 - Mathematics |
| discipline | Pädagogik Psychologie Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV001977190 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:15Z |
| institution | BVB |
| isbn | 0124452507 |
| language | English |
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| physical | XII, 288 S. graph. Darst. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Acad. Press |
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| spelling | Levine, Gustav Verfasser aut Mathematical model techniques for learning theories Gustav Levine ; C. J. Burke New York [u.a.] Acad. Press 1972 XII, 288 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Apprentissage, Psychologie de l' - Modèles mathématiques Leertheorieën gtt Matemáticas para psicólogos Psicología del aprendizaje - Modelos matemáticos Wiskundige modellen gtt Mathematisches Modell Learning, Psychology of Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Lerntheorie (DE-588)4114402-8 gnd rswk-swf Psychologie (DE-588)4047704-6 gnd rswk-swf Lerntheorie (DE-588)4114402-8 s Psychologie (DE-588)4047704-6 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Burke, C. J. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001289626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Levine, Gustav Burke, C. J. Mathematical model techniques for learning theories Apprentissage, Psychologie de l' - Modèles mathématiques Leertheorieën gtt Matemáticas para psicólogos Psicología del aprendizaje - Modelos matemáticos Wiskundige modellen gtt Mathematisches Modell Learning, Psychology of Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Lerntheorie (DE-588)4114402-8 gnd Psychologie (DE-588)4047704-6 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4114402-8 (DE-588)4047704-6 |
| title | Mathematical model techniques for learning theories |
| title_auth | Mathematical model techniques for learning theories |
| title_exact_search | Mathematical model techniques for learning theories |
| title_full | Mathematical model techniques for learning theories Gustav Levine ; C. J. Burke |
| title_fullStr | Mathematical model techniques for learning theories Gustav Levine ; C. J. Burke |
| title_full_unstemmed | Mathematical model techniques for learning theories Gustav Levine ; C. J. Burke |
| title_short | Mathematical model techniques for learning theories |
| title_sort | mathematical model techniques for learning theories |
| topic | Apprentissage, Psychologie de l' - Modèles mathématiques Leertheorieën gtt Matemáticas para psicólogos Psicología del aprendizaje - Modelos matemáticos Wiskundige modellen gtt Mathematisches Modell Learning, Psychology of Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Lerntheorie (DE-588)4114402-8 gnd Psychologie (DE-588)4047704-6 gnd |
| topic_facet | Apprentissage, Psychologie de l' - Modèles mathématiques Leertheorieën Matemáticas para psicólogos Psicología del aprendizaje - Modelos matemáticos Wiskundige modellen Mathematisches Modell Learning, Psychology of Mathematical models Lerntheorie Psychologie |
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