Mathematics behavior

Earl Hunt0521850126, 9780521850124, 9780511250408

Mathematical thinking provides a clear, crisp way of defining problems. Our whole technology is based on it. What is less appreciated is that mathematical thinking can also be applied to problems in the social and behavioral sciences. This book illustrates how mathematics can be used to understand human and animal behavior, using examples in psychology, sociology, economics, ecology, and even marriage counseling.

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Table of contents :
Cover……Page 1
Half-title……Page 3
Title……Page 5
Copyright……Page 6
Contents……Page 7
Preface……Page 11
1.1. WHAT’S IN THE BOOK?……Page 13
1.2. SOME EXAMPLES OF FORMAL AND INFORMAL THINKING……Page 14
1.3. A BIT OF HISTORY……Page 16
1.4. HOW BIG IS THE EARTH? ERATOSTHENES’ SOLUTION……Page 17
1.5. A CRITIQUE OF ERATOSTHENES……Page 24
1.6. APPLICATIONS OF MATHEMATICS TO SOCIAL AND BEHAVIORAL ISSUES……Page 26
1.7. STATISTICS……Page 28
2.1. INTRODUCTION……Page 30
2.2. DEFINING PROBABILITY AND PROBABILITY MEASURES……Page 31
2.3. HOW CLOSELY CONNECTED ARE WE?……Page 35
2.4. CONSCIOUS AND UNCONSCIOUS MEMORIES……Page 39
APPENDIX 2A. THE BASIS FOR KOLMOGOROV’S AXIOMS……Page 44
Joint, Conditional, and Complementary Probability……Page 45
Probability Distributions……Page 48
Standard Scores……Page 50
The Normal (Gaussian) Distribution……Page 51
3.1. THE PSYCHOPHYSICAL PROBLEM……Page 54
3.2. WEBER’S LAW……Page 56
3.3. FECHNER’S LAW……Page 59
3.4. STEVENS’S SCALING TECHNIQUE: DERIVING THE PSYCHOPHYSICAL FUNCTION FROM MAGNITUDE ESTIMATION……Page 65
3.5. JUDGING COMPLEX OBJECTS……Page 73
3.6. A COMMENT ON MEASUREMENT……Page 77
4.1. SYSTEMS OF VARIABLES……Page 79
4.2. DIFFERENCES AND DIFFERENTIATION……Page 80
Derivatives and Difference Equations……Page 81
4.3. EXPONENTIAL GROWTH AND DECAY……Page 82
4.4. NUMERICAL ANALYSIS: THE TRANSMISSION OF JOKES AND COLDS……Page 88
Exploring the Model……Page 90
4.5. QUESTIONS ABOUT MODELING……Page 93
Challenge Problem: How Should an Influenza Vaccine Be Distributed?……Page 97
Historical Note……Page 98
Richardson’s Hostility Model (Expanded)……Page 99
The Burden of Arms……Page 102
Challenge Problem: The General Conditions for System Stability……Page 106
4.7. MAKING LOVE, NOT WAR: THE GOTTMAN-MURRAY MODEL OF MARITAL INTERACTIONS……Page 108
4.8. CONCLUDING COMMENTS ON MODELING SIMPLE SYSTEMS……Page 113
APPENDIX 4A. A PROOF OF THE EXPONENTIAL GROWTH EQUATION……Page 115
5.1. CONTINUOUS CHANGE AND SUDDEN JUMPS……Page 116
5.2. THE LOTKA-VOLTERRA MODEL OF PREDATOR AND PREY INTERACTIONS……Page 118
5.3. THE LOGISTIC EQUATION: INTRODUCTION AND BEHAVIOR WHEN K