"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."
Graph Algebra: Mathematical Modeling with a Systems Approach introduces a new modeling tool to students and researchers in the social sciences. Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modeling that offers social scientists a variety of tools that are both sophisticated and easily applied.
- Designed for readers in the social sciences with minimal mathematical training: In this volume, the author assists readers in developing their own difference and differential equation model specifications
- Incorporates Social Theory: This book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated algebraic statements of social and political phenomena. Graph algebra can be used to algebraically "flesh-out" even the most complicated and sophisticated of theories.
- Contains social science examples of graph algebra models: Social science readers can see many examples of how graph algebra can be used to model theories from a wide variety of substantive areas and disciplines. The book also describes how to estimate such models, and two examples are fully worked out.
- Explains linear and nonlinear model specifications using graph algebra from a social science perspective: Readers can move beyond simple linear regression models by using graph algebra.
This text is ideal for use in graduate courses such as Statistical Modeling, Quantitative Methods, and Applied Mathematics.
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|Structure and Function|
|An Overview of the Substantive Examples Found in Subsequent Chapters|
|Inputs, Outputs, and the Forward Path|
|Feedback Loops and Mason's Rule|
|An Example From Economics: The Keynesian Multiplier|
|Delay and Advance Operators for Discrete Time|
|Including an Additive Constant With Graph Algebra|
|Difference and Summation Operators for Discrete Time|
|An Estimated Example: Labor Union Membership|
|Richardson's Arms Race Model Using Graph Algebra|
|Variations of Richardson's Arms Race Model|
|An Estimated Example of a Multiple-Equation System With Nonlinear or Embedded Parameters: Richardson's Arms Race|
|Using Graph Algebra With Continuous-Time Operators|
|The Logistic Function|
|Placement Rules for Operators in Nonlinear Models|
|Graph Algebra and Chaos|
|Logical and Decision Systems|
|An Example of Democratic Transition|
|Systems and Equilibria|