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Introduction to Mathematical Sociology

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Introduction to Mathematical Sociology Cover

 

Synopses & Reviews

Publisher Comments:

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

Synopsis:

"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

Synopsis:

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

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

Product Details

ISBN:
9780691145495
Author:
Bonacich, Phillip
Publisher:
Princeton University Press
Author:
Lu, Philip
Subject:
Methodology
Subject:
Sociology
Subject:
Mathematics | Probability and Statistics
Publication Date:
20120431
Binding:
HARDCOVER
Language:
English
Illustrations:
25 halftones. 58 line illus. 30 tables.
Pages:
240
Dimensions:
10 x 7 in

Related Subjects

Health and Self-Help » Self-Help » General
History and Social Science » Politics » General
History and Social Science » Politics » United States » Foreign Policy
History and Social Science » Sociology » General
History and Social Science » Sociology » Reference and Methodology
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Modeling
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Introduction to Mathematical Sociology New Hardcover
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$45.00 In Stock
Product details 240 pages Princeton University Press - English 9780691145495 Reviews:
"Synopsis" by , "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

"Synopsis" by , 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

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