Introduction to Mathematical Sociology

by Phillip Bonacich, Philip Lu

Overview

A comprehensive textbook on the tools of mathematical sociology and their applications

Mathematical 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.

• Provides an up-to-date and self-contained introduction to mathematical sociology


• Explains essential mathematical tools and their applications


• Includes numerous exercises throughout


• Features easy-to-use computer simulations to help students master concepts

Product Details

ISBN-13:	9781400842452
Publisher:	Princeton University Press
Publication date:	04/01/2012
Sold by:	Barnes & Noble
Format:	eBook
Pages:	240
File size:	7 MB

About the Author

Phillip 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 Contents

List 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 Orders-Power 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. Small-World Networks 102
Short Network Distances 103
Social Clustering 105
The Small-World Network Model 111
Exercises 116
Chapter 12. Scale-Free Networks 117
Power-Law Distribution 118
Preferential Attachment 121
Network Damage and Scale-Free Networks 129
Disease Spread in Scale-Free 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

What People are Saying About This

From the Publisher

"A first-rate 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 up-to-date 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

Editorial Reviews

"[T]he volume offers certain important building blocks that can represent a bonus for students willing to learn simulation in the future. . . . Bonacich and Lu's work brillantly introduces much of what ABM students will be requested to know in their subsequent studies."—-Giangiacomo Bravo, JASSS

"If you are interested in sociology specifically, or in some of the others social sciences (especially political science), then this book is a very good introduction for you. . . . I would certainly recommend it to students and others who have some mathematical maturity and are interested in mathematical sociology, mathematical political science, or mathematical psychology."—-JamesM. Cargal, UMAP Journal

From the Publisher

If you are interested in sociology specifically, or in some of the others social sciences (especially political science), then this book is a very good introduction for you. . . . I would certainly recommend it to students and others who have some mathematical maturity and are interested in mathematical sociology, mathematical political science, or mathematical psychology.

UMAP Journal - JamesM. Cargal

[T]he volume offers certain important building blocks that can represent a bonus for students willing to learn simulation in the future. . . . Bonacich and Lu's work brillantly introduces much of what ABM students will be requested to know in their subsequent studies.

JASSS - Giangiacomo Bravo

[T]he volume offers certain important building blocks that can represent a bonus for students willing to learn simulation in the future. . . . Bonacich and Lu's work brillantly introduces much of what ABM students will be requested to know in their subsequent studies.
— Giangiacomo Bravo

JASSS