Graph Algebra

Courtney Brown is an Associate Professor in the Department of Political Science at Emory University.  Dr. Brown has taught differential equation modeling to graduate and undergraduate students for over 20 years.  His teaching and research interests also include other quantitative methods, political musicology, science fiction and politics, electoral behavior, political parties, democratic development, and politics and the environment.  He has authored five books that deal with differential equation models in the social sciences, including three titles for the Quantitative Applications in the Social Sciences series.

• Series Editor′s IntroductionAcknowledgments1. Systems AnalysisStructure and FunctionAn Overview of the Substantive Examples Found in Subsequent Chapters2. Graph Algebra BasicsInputs, Outputs, and the Forward PathFeedback Loops and Mason′s RuleAn Example From Economics: The Keynesian Multiplier3. Graph Algebra and Discrete-Time Linear OperatorsDelay and Advance Operators for Discrete TimeIncluding an Additive Constant With Graph AlgebraDifference and Summation Operators for Discrete TimeAn Estimated Example: Labor Union Membership4. Working With Systems of EquationsRichardson′s Arms Race Model Using Graph AlgebraVariations of Richardson′s Arms Race ModelAn Estimated Example of a Multiple-Equation System With Nonlinear or Embedded Parameters: Richardson′s Arms Race5. Applying Graph Algebra to Continuous TimeUsing Graph Algebra With Continuous-Time Operators6. Graph Algebra and NonlinearityNonlinear FiltersThe Logistic FunctionPlacement Rules for Operators in Nonlinear ModelsGraph Algebra and ChaosForced Oscillators7. Working With Conditional PathsLogical and Decision SystemsAn Example of Democratic Transition8. Systems, Shocks, and Stochasticity9. Graph Algebra and Social TheorySystems and EquilibriaReferencesIndexAbout the Author

"Brown is well known for research on mathematical modeling in the social sciences.  His book introduces the graph algebra approach to modeling systems in the social sciences."—CHOICE