Graph Algebra

Mathematical Modeling With a Systems Approach
1. Auflage 2007
ISBN: 978-1-4129-4109-9
Verlag: Sage Publications, Inc

Buch, Englisch, Band 151, 104 Seiten, Format (B × H): 140 mm x 216 mm, Gewicht: 143 g

Reihe: Quantitative Applications in the Social Sciences

"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

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.

Key Features:

- 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.

Autoren/Hrsg.

Brown, Courtney

Brown, Courtney M.

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Forschungsmethodik, Wissenschaftliche Ausstattung
• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Demographie, Demoskopie

Inhaltsverzeichnis

Series Editor's Introduction
Acknowledgments
1. Systems Analysis
Structure and Function
An Overview of the Substantive Examples Found in Subsequent Chapters
2. Graph Algebra Basics
Inputs, Outputs, and the Forward Path
Feedback Loops and Mason's Rule
An Example From Economics: The Keynesian Multiplier
3. Graph Algebra and Discrete-Time Linear Operators
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
4. Working With Systems of Equations
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
5. Applying Graph Algebra to Continuous Time
Using Graph Algebra With Continuous-Time Operators
6. Graph Algebra and Nonlinearity
Nonlinear Filters
The Logistic Function
Placement Rules for Operators in Nonlinear Models
Graph Algebra and Chaos
Forced Oscillators
7. Working With Conditional Paths
Logical and Decision Systems
An Example of Democratic Transition
8. Systems, Shocks, and Stochasticity
9. Graph Algebra and Social Theory
Systems and Equilibria
References
Index
About the Author

Über Autor(innen)

Brown, Courtney M.
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.