A comprehensive textbook on the tools of mathematical sociology and their applicationsMathematical models and computer simulations of complex social systems have become everyday tools in sociology. Yet until now, students had no up-to-date textbook from which to learn these techniques. Introduction to Mathematical Sociology fills this gap, providing undergraduates with a comprehensive, self-contained 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 easy-to-use Mathematica-based computer simulations that students can use to examine the effects of changing parameters on model behavior.

List of Figures ixList of Tables xiiiPreface xvChapter 1. Introduction 1Epidemics 2Residential Segregation 6Exercises 11
Chapter 2. Set Theory and Mathematical Truth 12Boolean Algebra and Overlapping Groups 19Truth and Falsity in Mathematics 21Exercises 23
Chapter 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 36
Chapter 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 51
Chapter 5. Networks and Graphs 53Exercises 59
Chapter 6. Weak Ties 61Bridges 61The Strength of Weak Ties 62Exercises 66
Chapter 7. Vectors and Matrices 67Sociometric Matrices 69Probability Matrices 71The Matrix, Transposed 72Exercises 72
Chapter 8. Adding and Multiplying Matrices 74Multiplication of Matrices 75Multiplication of Adjacency Matrices 77Locating Cliques 79Exercises 82
Chapter 9. Cliques and Other Groups 84Blocks 86Exercises 87
Chapter 10. Centrality 89Degree Centrality 93Graph Center 93Closeness Centrality 94Eigenvector Centrality 95Betweenness Centrality 96Centralization 99Exercises 101
Chapter 11. Small-World Networks 102Short Network Distances 103Social Clustering 105The Small-World Network Model 111Exercises 116
Chapter 12. Scale-Free Networks 117Power-Law Distribution 118Preferential Attachment 121Network Damage and Scale-Free Networks 129Disease Spread in Scale-Free Networks 134Exercises 136
Chapter 13. Balance Theory 137Classic Balance Theory 137Structural Balance 145Exercises 148The Markov Assumption: History Does Not Matter 156Transition Matrices and Equilibrium 157Exercises 158
Chapter 15. Demography 161Mortality 162Life Expectancy 167Fertility 171Population Projection 173Exercises 179
Chapter 16. Evolutionary Game Theory 180Iterated Prisoner's Dilemma 184Evolutionary Stability 185Exercises 188
Chapter 17. Power and Cooperative Games 190The Kernel 195The Core 199Exercises 200
Chapter 18. Complexity and Chaos 202Chaos 202Complexity 206Exercises 212
Afterword: "Resistance Is Futile" 213Bibliography 217Index 219