Introduction to Mathematical Sociology

 
 
Princeton University Press
  • 1. Auflage
  • |
  • erschienen am 1. April 2012
  • |
  • 240 Seiten
 
E-Book | PDF mit Adobe DRM | Systemvoraussetzungen
978-1-4008-4245-2 (ISBN)
 

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

    • Englisch
    • New Jersey
    • |
    • USA
    • Windows
    • 7,28 MB
    978-1-4008-4245-2 (9781400842452)
    140084245X (140084245X)
    weitere Ausgaben werden ermittelt
    Phillip Bonacich & Philip Lu
    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

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