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# Introduction to Mathematical SociologyPhillip Bonacich & Philip Lu

 TABLE OF CONTENTS:List of Figures ixList of Tables xiiiPreface xvChapter 1. Introduction 1Epidemics 2Residential Segregation 6Exercises 11Chapter 2. Set Theory and Mathematical Truth 12Boolean Algebra and Overlapping Groups 19Truth and Falsity in Mathematics 21Exercises 23Chapter 3. Probability: Pure and Applied 25Example: Gambling 28Two or More Events: Conditional Probabilities 29Two or More Events: Independence 30A Counting Rule: Permutations and Combinations 31The Binomial Distribution 32Exercises 36Chapter 4. Relations and Functions 38Symmetry 41Reflexivity 43Transitivity 44Weak Orders-Power and Hierarchy 45Equivalence Relations 46Structural Equivalence 47Transitive Closure: The Spread of Rumors and Diseases 49Exercises 51Chapter 5. Networks and Graphs 53Exercises 59Chapter 6. Weak Ties 61Bridges 61The Strength of Weak Ties 62Exercises 66Chapter 7. Vectors and Matrices 67Sociometric Matrices 69Probability Matrices 71The Matrix, Transposed 72Exercises 72Chapter 8. Adding and Multiplying Matrices 74Multiplication of Matrices 75Multiplication of Adjacency Matrices 77Locating Cliques 79Exercises 82Chapter 9. Cliques and Other Groups 84Blocks 86Exercises 87Chapter 10. Centrality 89Degree Centrality 93Graph Center 93Closeness Centrality 94Eigenvector Centrality 95Betweenness Centrality 96Centralization 99Exercises 101Chapter 11. Small-World Networks 102Short Network Distances 103Social Clustering 105The Small-World Network Model 111Exercises 116Chapter 12. Scale-Free Networks 117Power-Law Distribution 118Preferential Attachment 121Network Damage and Scale-Free Networks 129Disease Spread in Scale-Free Networks 134Exercises 136Chapter 13. Balance Theory 137Classic Balance Theory 137Structural Balance 145Exercises 148The Markov Assumption: History Does Not Matter 156Transition Matrices and Equilibrium 157Exercises 158Chapter 15. Demography 161Mortality 162Life Expectancy 167Fertility 171Population Projection 173Exercises 179Chapter 16. Evolutionary Game Theory 180Iterated Prisoner's Dilemma 184Evolutionary Stability 185Exercises 188Chapter 17. Power and Cooperative Games 190The Kernel 195The Core 199Exercises 200Chapter 18. Complexity and Chaos 202Chaos 202Complexity 206Exercises 212Afterword: "Resistance Is Futile" 213Bibliography 217Index 219Return to Book DescriptionFile created: 4/21/2017 Questions and comments to: webmaster@press.princeton.eduPrinceton University Press