Modeling Social Phenomena

Course Content and Objectives:
SNAPSHOT: This advanced seminar is designed for juniors and seniors who want to have an exciting and fun introduction to nonlinear and dynamic modeling of social and political phenomena. The course content covers a range of very practical and easy-to-use tools that are used to construct and evaluate mathematical models that are relevant to a wide range of important applications in fields such as political science, international studies and development, public health, public policy, economics, business, the environment, and even law. The course is taught with an extremely user-friendly approach, and students should have little or no trouble mastering the course content. High school algebra is all that is required to begin. (Honest!) This course is also useful for honors students who desire to develop a theory about society for their final thesis paper. Other students may simply want to know how to develop and investigate their own theories for other reasons or purposes, perhaps to prepare for graduate school in political science, or perhaps just out of curiosity. Thus, this course may be both interesting and useful to a wide range of students.

EXTENDED VIEW: The core of this course involves the study of graph algebra. Graph algebra is a tremendous breakthrough in model construction. Graph algebra is a paper-and-pencil language and process that allows you to create sophisticated mathematical models of social and political processes by simply sketching and connecting boxes and arrows that describe the phenomenon being investigtated. Graph algebra helps translate social theory into mathematical form. Mathematical model building can now be a relatively straightforward process, and undergraduate and graduate students can develop their own unique models with a combination of ease and sophistication that would have been impossible before the development of graph algebra. Don't settle for simple linear models! Create your own models that have your "stamp" on them. You can even impress your friends and relatives by showing them your mathematical models without also showing them the graph algebra that made it so easy to make these models. Computer aided graphics are also taught in this course that bridge the model building and analysis components of social research. Computer assignments involving parameter estimation as well as graphical analysis are given. Throughout the course, all of the mathematical techniques introduced are integrated with strategies for using these things to describe how societies change.

Class Requirements:

This course is a seminar. Weekly reading and bi-weekly short writing assignments are matched with class discussions, all focusing on the interpretation of various approaches to mathematical modeling with respect to society and politics. There is also a final writing project that is longer and is submitted in three drafts. This final project allows all students the opportunity to develop a fully-fleshed out theory of some social or political phenomenon. The course grade depends on the evaluation of all writing assignments, as well as class participation and attendance. The work load for graduate students will be more than that for undergraduates, of course.

There are no exams. The grades are determined as follows:

10% Attendance (Two absences are permitted without penalty.)
40% Bi-weekly writing assignments (Undergraduates need complete only seven of these assignments.)
25% Final Project writing assignment (All three drafts are required.)
25% Class participation (students will make presentations to the class)

The Department of Political Science has a grading standard that applies to all courses. You can read about it here.

The Honor Code is strictly enforced in this course. Plagiarism is an honor code violation. Signature forgeries on attendance are an honor code violation.

Podcast Policy:

Podcasting courses can assist students tremendously. Students can listen to lectures more than once, and they can catch up on classes that were missed for, say, reasons of illness or religious obligation. I record and podcast many of the classes in this course. By taking this course, all students are automatically giving their permission to be recorded during class participation. No further written permission is required.

Disabilities Statement:

It is the policy of Emory University to make reasonable accommodations for qualified students with disabilities. All students with special requests or need for accommodations should make this request in person as soon as possible after first visiting the Office of Disabilities.

Required Texts:

Brown, Courtney. 2008 (Published July 2007). Graph Algebra: Mathematical Modeling with a Systems Approach. Thousand Oaks, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 151.

Brown, Courtney. 2007. Differential Equations: A Modeling Approach. 2007. Thousand Oaks, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 150.

Brown, Courtney. 1995. Chaos and Catastrophe Theories. Thousand Oaks, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 107.

Huckfeldt, R. Robert, C. W. Kohfeld, and Thomas W. Likens. 1982. Dynamic Modeling: An Introduction. Newbury Park, California: Sage Publications. Series: Quantitative Applications in the Social Sciences, Number 27.

Reserve Readings:

Brown, Courtney. 1995. Serpents in the Sand: Essays on the Nonlinear Nature of Politics and Human Destiny. Ann Arbor, Michigan: University of Michigan Press.

Brown, Courtney. 1991. Ballots of Tumult: A Portrait of Volatility in American Voting. Ann Arbor, Michigan: University of Michigan Press.

Cortés, Fernando, Adam Przeworski, and John Sprague. 1974. Systems Analysis for Social Scientists. New York: John Wiley & Sons.

Goldstein, Larry J., David I. Schneider, and Martha J. Siegel. 1988. Finite Mathematics and Its Applications, 3rd Ed., Englewood Cliffs: Prentice-Hall.

Lave, Charles A., and James G. March. 1993(1975). An Introduction to Models in the Social Sciences. New York: University Press of America.

Przeworski, Adam. 1975. Institutionalization of Voting Patterns, or is Mobilization the Source of Decay, American Political Science Review, 69:49-67.

Przeworski, Adam and Glaucio A. D. Soares. 1971. Theories in Search of a Curve: A Contextual Interpretation of Left Vote. American Political Science Review 65:51-65.

Simon, Herbert A. 1957. Models of Man: Social and Rational. New York: John Wiley & Sons.

Sprague, John. 1984(1981). "One-Party Dominance in Legislatures." In The Research Process in Political Science, W. Phillips Shively (Editor), pp. 225-67. Itasca, Illinois: F. E. Peacock Publishers, Inc. Also reprinted from Legislative Studies Quarterly, Vol. VI, No. 2, May 1981.

Internet Resources:

General Math -
A great web site on fractal geometry and chaos
Professor Strang's Linear Algebra Class Lecture Videos (MIT)
Professor Strang's Web Programs for Linear Algebra (MIT)

Data and Statistical -
Emory University Library's Political Methodology Research Guide
Emory University's Electronic Data Center
Gary King's excellent advice on writing your first publishable paper
How to Use a Codebook, from Princeton University
Inter-University Consortium for Political and Social Research (ICPSR)
National Election Studies, The University of Michigan
Rice Virtual Lab in Statistics
SAS Documentation for version 8.2
SAS Documentation for version 9.1 (This is the one we use in class.)
Statistical Abstract of the United States
Statistics Calculators from UCLA
SticiGui Online Statistics Text, by Philip B. Stark, University of California, Berkeley
Surf Stat, an online statistics text

Simulations
Robert Hanneman's list of useful links

WEEKLY OUTLINE

Week 1
Presentation and Discussion: Difference Equations
Readings: Goldstein, Schneider, and Siegel (chapter 11)
Lave and March (chapter 1)
Huckfeldt, Kohfeld, and Likens (chapter 1)
Graph Algebra (chapters 1 & 2)

Week 2
Presentation and Discussion: Graph Algebra I - An Introduction
Readings: Lave and March (chapter 2)
Cortés, Przeworski, and Sprague (chapters 1 & 2)
Graph Algebra (chapters 3 & 4)

Week 3
Presentation and Discussion: Graph Algebra II - Discrete Time Operators
Readings: Lave and March (chapter 3)
Cortés, Przeworski, and Sprague (chapters 3 & 4)
Graph Algebra (chapters 5 & 6)
Written Assignment Due: Assignment #1

Week 4
Presentation and Discussion: Graph Algebra II - Operators for Discrete Time (Continued)
Readings: Cortés, Przeworski, and Sprague (chapter 5)
Graph Algebra (chapters 7 & 8)
Written Assignment Due: Assignment #2

Week 5
Presentation and Discussion: Dynamic Modeling I
Readings: Huckfeldt, Kohfeld, and Likens, chapters 1 & 2
Rudas (chapter 3), Sprague
Graph Algebra (chapter 9)
Written Assignments Due: Assignment #3, First draft of final writing project

Week 6
Presentation and Discussion: Dynamic Modeling II
Readings: Lave and March, chapter 7
Huckfeldt, Kohfeld, and Likens, chapter 3
Differential Equations (chapters 1 & 2)
Written Assignment Due: Assignment #4

Week 7
Presentation and Discussion: Dynamic Modeling III
Readings: Huckfeldt, Kohfeld, and Likens, begin chapter 4
Ballots of Tumult, chapters 1 & 7
Differential Equations (chapter 3)
Written Assignment Due: Assignment #5

Week 8
Presentation and Discussion: Graph Algebra III - Graph Algebra II - Working with Systems
Readings: Huckfeldt, Kohfeld, and Likens, continue with chapter 4
Differential Equations (chapter 4)
Written Assignments Due: Assignment #6, Second draft of final writing project

Week 9
Presentation and Discussion: Graph Algebra IV - Operators for Continuous Time
Readings: Huckfeldt, Kohfeld, and Likens, finish chapter 4
Differential Equations (chapter 5)
Written Assignment Due: Assignment #7

Week 10
Presentation and Discussion: Richardson's Arms Race Model
Readings: Huckfeldt, Kohfeld, and Likens, begin chapter 5
Ballots of Tumult, chapter 2
Differential Equations (chapter 6)
Written Assignment Due: Assignment #8

Week 11
Presentation and Discussion: Working with Systems using Phaser I
Readings: Huckfeldt, Kohfeld, and Likens, continue with chapter 5
Differential Equations (chapter 7)
Written Assignment Due: Assignment #9, Third draft of final writing project

Week 12
Presentation and Discussion: Working with Systems using Phaser II
Readings: Huckfeldt, Kohfeld, and Likens, finish chapter 5
Brown (Chaos and Catastrophe) chapters 1-3
Differential Equations (chapter 8)
Written Assignment Due: Assignment #10

Week 13
Presentation and Discussion: Working with Systems using Phaser III
Readings: Huckfeldt, Kohfeld, and Likens, chapter 6
Serpents in the Sand, chapter 1
Brown (Chaos and Catastrophe) chapters 4 & 5
Written Assignment Due: Assignment #11

Week 14
Presentation and Discussion: Graph Algebra and Nonlinear Systems Topic
Readings: Ballots of Tumult, chapter 8
Serpents in the Sand, chapter 2
Brown (Chaos and Catastrophe) chapters 6 & 7
Written Assignments Due: Assignments #12 and #13, Final writing project due on the last day of normally scheduled class.

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