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Introduction to Mathematical Sociologyby Phillip Bonacich
Synopses & ReviewsPublisher Comments:Mathematical models and computer simulations of complex social systems have become everyday tools in sociology. Yet until now, students had no uptodate textbook from which to learn these techniques. Introduction to Mathematical Sociology fills this gap, providing undergraduates with a comprehensive, selfcontained primer on the mathematical tools and applications that sociologists use to understand social behavior.
Phillip Bonacich and Philip Lu cover all the essential mathematics, including linear algebra, graph theory, set theory, game theory, and probability. They show how to apply these mathematical tools to demography; patterns of power, influence, and friendship in social networks; Markov chains; the evolution and stability of cooperation in human groups; chaotic and complex systems; and more.
Introduction to Mathematical Sociology also features numerous exercises throughout, and is accompanied by easytouse Mathematicabased computer simulations that students can use to examine the effects of changing parameters on model behavior.
Synopsis:"A firstrate introduction. The coverage is exemplary, starting with basic math techniques and progressing to models that incorporate a number of these techniques. Chapters on evolutionary game theory, cooperative games, and chaos are significantly innovative, as is the incorporation of simulations. This book brings mathematics to life for students who may entertain doubts about the role of math in sociology."Peter Abell, professor emeritus, London School of Economics and Political Science
"This book provides a concise and uptodate introduction to mathematical sociology and social network analysis. It presents a solid platform for engaging undergraduates in mathematical approaches to sociological inquiry, and includes Mathematica modules with which students can explore the properties and implications of a variety of formal models. I plan on using it in my courses on social networks."Noah E. Friedkin, coauthor of Social Influence Network Theory: A Sociological Examination of Small Group Dynamics Synopsis:Mathematical models and computer simulations of complex social systems have become everyday tools in sociology. Yet until now, students had no uptodate textbook from which to learn these techniques. Introduction to Mathematical Sociology fills this gap, providing undergraduates with a comprehensive, selfcontained primer on the mathematical tools and applications that sociologists use to understand social behavior.
Phillip Bonacich and Philip Lu cover all the essential mathematics, including linear algebra, graph theory, set theory, game theory, and probability. They show how to apply these mathematical tools to demography; patterns of power, influence, and friendship in social networks; Markov chains; the evolution and stability of cooperation in human groups; chaotic and complex systems; and more. Introduction to Mathematical Sociology also features numerous exercises throughout, and is accompanied by easytouse Mathematicabased computer simulations that students can use to examine the effects of changing parameters on model behavior.
About the AuthorPhillip Bonacich is professor emeritus of sociology at the University of California, Los Angeles. Philip Lu is a PhD candidate in sociology at UCLA.
Table of ContentsList of Figures ix
List of Tables xiii Preface xv
Chapter 1. Introduction 1 Epidemics 2 Residential Segregation 6 Exercises 11
Chapter 2. Set Theory and Mathematical Truth 12 Boolean Algebra and Overlapping Groups 19 Truth and Falsity in Mathematics 21 Exercises 23
Chapter 3. Probability: Pure and Applied 25 Example: Gambling 28 Two or More Events: Conditional Probabilities 29 Two or More Events: Independence 30 A Counting Rule: Permutations and Combinations 31 The Binomial Distribution 32 Exercises 36
Chapter 4. Relations and Functions 38 Symmetry 41 Reflexivity 43 Transitivity 44 Weak OrdersPower and Hierarchy 45 Equivalence Relations 46 Structural Equivalence 47 Transitive Closure: The Spread of Rumors and Diseases 49 Exercises 51
Chapter 5. Networks and Graphs 53 Exercises 59
Chapter 6. Weak Ties 61 Bridges 61 The Strength of Weak Ties 62 Exercises 66
Chapter 7. Vectors and Matrices 67 Sociometric Matrices 69 Probability Matrices 71 The Matrix, Transposed 72 Exercises 72
Chapter 8. Adding and Multiplying Matrices 74 Multiplication of Matrices 75 Multiplication of Adjacency Matrices 77 Locating Cliques 79 Exercises 82
Chapter 9. Cliques and Other Groups 84 Blocks 86 Exercises 87
Chapter 10. Centrality 89 Degree Centrality 93 Graph Center 93 Closeness Centrality 94 Eigenvector Centrality 95 Betweenness Centrality 96 Centralization 99 Exercises 101
Chapter 11. SmallWorld Networks 102 Short Network Distances 103 Social Clustering 105 The SmallWorld Network Model 111 Exercises 116
Chapter 12. ScaleFree Networks 117 PowerLaw Distribution 118 Preferential Attachment 121 Network Damage and ScaleFree Networks 129 Disease Spread in ScaleFree Networks 134 Exercises 136
Chapter 13. Balance Theory 137 Classic Balance Theory 137 Structural Balance 145 Exercises 148 The Markov Assumption: History Does Not Matter 156 Transition Matrices and Equilibrium 157 Exercises 158
Chapter 15. Demography 161 Mortality 162 Life Expectancy 167 Fertility 171 Population Projection 173 Exercises 179
Chapter 16. Evolutionary Game Theory 180 Iterated Prisoner’s Dilemma 184 Evolutionary Stability 185 Exercises 188
Chapter 17. Power and Cooperative Games 190 The Kernel 195 The Core 199 Exercises 200
Chapter 18. Complexity and Chaos 202 Chaos 202 Complexity 206 Exercises 212
Afterword: "Resistance Is Futile" 213 Bibliography 217 Index 219
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